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ORiON Abstracts

This page contains a full bibliography of all papers that have appeared in ORiON since its inception. Full abstracts are also included in virtually all cases. From Volume 6 (1990) onwards links to pdf electronic copies of full papers are also provided. Electronic copies of new papers are only made available (free of charge) one year after they have appeared in print.

First Author A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


The bibliography is arranged alphabetically according to first author.


A

Akume D, Luderer B & Wunderlich R, 2009, Optimal portfolio strategies under a shortfall constraint, ORiON, 25(1), pp. 31-44.
Abstract. We impose dynamically, a shortfall constraint in terms of Tail Conditional Expectation on the portfolio selection problem in continuous time, in order to obtain optimal strategies. The financial market is assumed to comprise n risky assets driven by geometric Brownian motion and one risk-free asset. The method of Lagrange multipliers is combined with the Hamilton-Jacobi-Bellman equation to insert the constraint into the resolution framework. The constraint is re-calculated at short intervals of time throughout the investment horizon. A numerical method is applied to obtain an approximate solution to the problem. It is found that the imposition of the constraint curbs investment in the risky assets.
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Anrig B & Beichelt F, 2000, Disjoint sum forms in reliability theory, ORiON, 16(1), pp. 75-86.
Abstract. The structure function f of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of f, an improved Abraham algorithm is proposed for generating the disjoint sum form of f. This form is the base for subsequent numerical reliability calculations. The approach is generalized to multivalued systems. Examples are discussed.
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B

Baitshenyetsi LT, Hattingh JM & Kruger HA, 2011, Tiragatso Ya Itlhagiso Ya Setlhare Se Se Okeditsweng Ka Kgetsi Mo Bothateng Jwa Popo Ya Metato Ya Dipeipi Tsa Oli, ORiON, 27(2), pp. 101-117.
Abstract. Go na le mathata a mantsi a ditshwetso tsa tiriso tse di welang mo mathateng a a mo setlhopheng sa kelelo ya kgokagano le palo e kgolo ya dikai tsa tiragatso tse di ka bonwang mo dikgaolong jaaka tsa neeletsanyokgakala, thwalo, boenjineri, saense ya dikhomphutara jalo le jalo. Mo pampiring e, kgonagalo ya go tlhagisa mmotlele wa kelelo ya kgokagano o o leng mmotlele wa kgokagano ya setlhare mme morago re e rarabolole ka go dirisa itlhagiso ya setlhare se se okeditsweng ka kgetsi ka go e batlisisa. Go bapisa le go tlhwatlhwafatsa thekeniki e e tlhagisiwang, thuto ya nnete e e totobetseng e e dirilweng (bothata jwa popo ya motato wa dipeipi tsa oli) e tlhophilwe go tswa mo dikwalong gore e dirisiwe go nna motheo wa porojeke e ya patlisiso. Ka go latela pono ya bothata jwa popo ya metato ya dipeipi, tlhabololo ya sekao sa setlhare se se okeditsweng ka kgetsi se tlaa tlhagisiwa. Tiragatso ya mokgwa o mo bothateng jwa popo ya metato ya dipeipi tsa oli e tlaa tlhagisiwa morago. Maduo a a bonwang a tlaa tlhagisiwa mme a bontsha gore go na le boleng jwa go ka dirisa itlhagiso ya setlhare se se okeditsweng ka kgetsi go ka rarabolola tse dingwe tsa mathata a kelelo ya dikgokagano.
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Beichelt F, 1997, Some current problems in reliability theory, ORiON, 13(1/2), pp. 19-36.
Abstract. Reliability work occupies an increasingly important place in engineering practice. Although the details differ depending on whether mechanical, electrical, chemical, or other systems are under analysis, the reliability concepts and the mathematical foundations cut across the specific fields of application. Over the past 50 years thousands of papers and dozens of books on mathematical models of reliability have been published. A comprehensive survey alone on the current developments in the mathematical theory of reliability would fill a voluminous book. Based on importance both for theory and application and taking into account the interests of the author, current investigations in four important branches of reliability theory are considered: coherent systems, stochastic networks, software reliability, and maintenance theory.
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Beichelt F, 1997, Total repair cost limit replacement policies, ORiON, 13(1/2), pp. 37-44.
Abstract. Practical applications of stochastic maintenance models frequently fail due to insufficient information on the lifetime distribution of the systems. Moreover, the structure of numerous maintenance policies which have been proposed up till now is so complicated that they have purely academic significance. This paper presents a policy for optimal scheduling of replacement intervals where decisions are based only on the maintenance cost parameters. The simple structure of this policy and the circumstance that the cost parameters are usually known facilitates its practical application.
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Beichelt F, 1999, A general approach to total repair cost limit replacement policies, ORiON, 15(1/2), pp. 67-75.
Abstract. A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment when its long-run maintenance cost rate is minimal. However, the strict application of the economic lifetime does not take into account the individual deviations of maintenance cost rates of single systems from the average cost development. Hence, Beichet proposed the total repair cost limit replacement policy: the system is replaced by a new one as soon as its total repair cost reaches or exceeds a given level. He modelled the repair cost development by functions of the Wiener process with drift. Here the same policy is considered under the assumption that the one-dimensional probability distribution of the process describing the repair cost development is given. In the examples analysed, applying the total repair cost limit replacement policy instead of the economic life-time leads to cost savings of between 4% and 30%. Finally, it is illustrated how to include the reliability aspect into the policy.
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Beichelt F, 2000, Combinatorial methods in network reliability analysis, ORiON, 16(1), pp. 63-73.
Abstract. In this paper, a stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes. Its connectedness probability is determined by reliability preserving network reduction. The principle of this method consists in splitting the underlying deterministic graph of the stochastic network into two edge-disjoint subgraphs via a separating node set. One of the subgraphs is replaced with a simpler structured graph (replacement graph) in such a way that the interesting reliability criterion of the original stochastic network is retained. Special attention is given to the construction of suitable replacement graphs. The case of a 3-point separating node set is considered in more detail.
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Bekker JF, Mostert M & Van Dyk FE, 2005, Simulation of fruit pallet movement in the port of Durban: A case study, ORiON, 21(1), pp. 63-75.
Abstract. This paper gives an overview of a discrete-event simulation study that was performed on pallet movement at Fresh Produce Terminals in the port of Durban, South Africa. The study formed part of an extended study of the logistics infrastructure of the South African fresh fruit industry and its export supply chain. The focus in this paper is on pallet movement in the terminal and its requirement on the storage capacity of the cold store facility. Specifics pertaining to input data analysis are provided, as well as a discussion of simulation model validation and output data analysis.
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Bekker JF & Schmid JP, 2006, Planning the safe transit of a ship through a mapped minefield, ORiON, 22(1), pp. 1-18.
Abstract. Sea minefields obstructing naval missions have to be breached with minimum effort and acceptable risk. With the advent of autonomous mapping, it is feasible to have high quality information of obstructing sea minefields and their environment before moving into them. The challenge remains to use this knowledge optimally to minimise risk, time and effort in crossing the sea minefield. To achieve this, two interlinked processes are required, consisting of finding the shortest route with acceptable risk or route with minimum risk through the sea minefield, and if no route of acceptable risk exists, removing the optimum combination of sea mines to create a route of acceptable risk. This paper describes the use of Dijkstra�s Algorithm and a genetic algorithm to achieve practical strategies and a method in which two optimisation techniques interact to provide a safe route considering the risk of both the sea mine and the environment and making it applicable to sea mine avoidance. This methodology may readily be applied to general ship routing in risk areas and may be expanded to routing through any area where no known routes exist.
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Berjak SG & Hearne JW, 2002, Spatial fire modeling in Mkuze Game Reserve: A case study, ORiON, 18(1/2), pp. 37-57.
Abstract. Controlled burning is a necessary and regular activity in Mkuze Game Reserve, South Africa. Predicting the rate and extent of fire spread in controlled burning operations is, therefore, an important management objective. In this paper we evaluate a cellular automaton model for fire spread in terms of this objective using empirical data for two case studies in Mkuze Game Reserve. Incorporating data relating to factors such as temperature reduction in the early evening, subsequent dew formation and increased fuel moisture content, the model was found to closely resemble the observed fire behaviour.
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Bhyat MF, 1996, Implementing an integrated information system to support development planning, ORiON, 12(1/2), pp. 37-42.
Abstract. Not available.
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Bothma A, Botha HL & Le Roux NJ, 2004, School results and access test results as indicators of first-year performance at university, ORiON, 20(1), pp. 73-88.
Abstract. The goals set by the National Plan for Higher Education, the fact that many schools are still severely disadvantaged as well as far-reaching changes in the school system demand that South African universities urgently reconsider their admission procedures. Redesigning admission procedures calls for a thorough understanding of the interrelationships between school marks, results in existing access tests and first-year university performance. These interrelationships were statistically investigated in the case of the 1999, 2000 and 2001 intake groups, who were compelled to write access tests before being admitted to Stellenbosch University. The results of this investigation confirm an alarming degree of unpreparedness among many prospective students regarding what is expected of them at university. This is aggravated by school marks creating a totally unrealistic expectation of performance in the first year at university. It is emphasised that schools and authorities dealing with admission of prospective students at universities should be cognisant of the findings reported here. Furthermore, the statistical analyses demonstrate several novel techniques for investigating the interrelationship between school marks, access test results and university performance.
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Broomhead MA, 1986, A computer simulation model of a private railway system, ORiON, 2(2), pp. 52-71.
Abstract. The paper describes an operational study of a private railway system in the Transvaal. The main objective of the study was to recommend the minimum requirements for railway lines, locomotives and wagons and an economic, safe and reliable operating method for the proposed traffic levels, controlled by a remote signalling system. A survey of locomotive and train activities was undertaken to measure actual system activity times. The railway system was successfully modelled using the Firm's simulated train haul programme and HOCUS language. The resulting proposals showed a large capital saving, in the order of 100 times the study cost, below previously estimated capital costs.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 2(2).

Bruwer PJS & Hattingh JH, 1985, Constrained regression models for optimization and forecasting, ORiON, 1(1), pp. 2-15.
Abstract. Linear regression models and the interpretation of such models are investigated. In practice problems often arise with the interpretation and use of a given regression model in spite of the fact that researchers may be quite "satisfied" with the model. In this article methods are proposed which overcome these problems. This is achieved by constructing a model where the "area of experience" of the researcher is taken into account. This area of experience is represented as a convex hull of available data points. With the aid of a linear programming model it is shown how conclusions can be formed in a practical way regarding aspects such as optimal levels of decision variables and forecasting.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 1(1).

Burger AP, Nieuwoudt I & Van Vuuren JH, 2007, On the Delta(d) chromatic number of a complete, balanced multipartite graph, ORiON, 23(1), pp. 29-49.
Abstract. In this paper we solve (approximately) the problem of finding the minimum number of colours with which the vertices of a complete, balanced, multipartite graph G may be coloured such that the maximum degrees of all colour class induced subgraphs are at most some specified integer d. The minimum number of colours in such a colouring is referred to as the Delta(d)�chromatic number of G. The problem of finding the Delta(d)�chromatic number of a complete, balanced, multipartite graph has its roots in an open graph theoretic characterisation problem and has applications conforming to the generic scenario where users of a system are in conflict if they require access to some shared resource. These conflicts are represented by edges in a so�called resource access graph, where vertices represent the users. An efficient resource access schedule is an assignment of the users to a minimum number of groups (modelled by means of colour classes) where some threshold d of conflict may be tolerated in each group. If different colours are associated with different time periods in the schedule, then the minimum number of groupings in an optimal resource access schedule for the above set of users is given by the Delta(d)�chromatic number of the resource access graph. A complete balanced multipartite resource access graph represents a situation of maximum conflict between members of different user groups of the system, but where no conflict occurs between members of the same user group (perhaps due to an allocation of diverse duties to the group members).
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Burger AP, Van der Merwe M & Van Vuuren JH, 2013, The evolutionary spatial prisoner's dilemma on a cycle, ORiON, 29(1), pp. 1-16.
Abstract. In this paper we consider the Evolutionary Spatial Prisoner's Dilemma (ESPD) in which players are modelled by the vertices of a cycle representing a spatial or organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in the cycle play a classical prisoner's dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way players are able to adapt and learn from each other's strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the game as well as the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game's states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameter values for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the cycle increases..
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C

Chalmers AG, Hearne JW & Scogings CJ, 1989, Evaluating parallel optimization on transputers, ORiON, 5(2), pp. 75-83.
Abstract. The faster processing power of modern computers and the development of efficient algorithms have made it possible for operations researchers to tackle a much wider range of problems than ever before. Further improvements in processing speed can be achieved utilising relatively inexpensive transputers to process components of an algorithm in parallel. The Davidon-Fletcher-Powell method is one of the most successful and widely used optimisation algorithms for unconstrained problems. This paper examines the algorithm and identifies the components that can be processed in parallel. The results of some experiments with these components are presented which indicates under what conditions parallel processing with an inexpensive configuration is likely to be faster than the traditional sequential implementations. The performance of the whole algorithm with its parallel components is then compared with the original sequential algorithm. The implementation serves to illustrate the practicalities of speeding up typical OR algorithms in terms of difficulty, effort and cost. The results give an indication of the savings in time a given parallel implementation can be expected to yield.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 5(2).

Cochran JJ, 2009, Pedagogy in Operations Research: Where has the discipline been, where is it now, and where should it go?, ORiON, 25(2), pp. 161-184.
Abstract. This paper provides a review of the history of operations research pedagogy and the progress the discipline has made in improving the quality of education it provides college students since its recognized inception during World War II. Recent and current trends are examined and ongoing activities and initiatives in operations research pedagogy are discussed. Finally, implications for the future of operations research are considered.
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Cockayne EJ, 2007, An algorithm for the <r,s>-domination number of a tree, ORiON, 23(1), pp. 51-58.
Abstract. Suppose that at most r units of some commodity may be positioned at any vertex of a graph G = (V,E) while at least s (>= r) units must be present in the vicinity (i.e. closed neighbourhood) of each vertex. Suppose that the function f : V -> {0,...,r}, whose values are the numbers of units stationed at vertices, satisfies the above requirement. Then f is called an s-dominating r-function. We present an algorithm which finds the minimum number of units required in such a function and a function which attains this minimum, for any tree.
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Coetzer RLJ & Keyser MJ, 2004, Robustness studies on coal gasification process variables, ORiON, 20(2), pp. 89-108.
Abstract. Optimisation of the Sasol-Lurgi gasification process was carried out by utilising the method of Factorial Experimental Design on the process variables of interest from a specifically equipped full-scale test gasifier. The process variables that govern gasification are not always fully controllable during normal operation. This paper discusses the application of statistical robustness studies as a method for determining the most efficient combination of process variables that might be hard-to-control during normal operation. Response surface models were developed in the process variables for each of the performance variables. It will be shown how statistical robustness studies provided the optimal conditions for sustainable gasifier operability and throughput. In particular, the optimum operability region is significantly expanded towards higher oxygen loads by changing and controlling the particle size distribution of the coal.
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Conradie W, 1996, The RDP - A challenge and opportunity, ORiON, 12(1/2), pp. 11-13.
Abstract. Not available.
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Currin DC & Ittmann HW, 1985, Multi-product allocation and distribution, ORiON, 1(2), pp. 70-82.
Abstract. This paper describes techniques used by a beer company to optimise the allocation and distribution of their beer. These techniques are also applicable to other manufacturing and distribution environments. Of particular interest is a two-phase model that allows a "look-ahead" to future sales, the decomposition of the problem into a large number of sub-problems (to reduce solution time), and the equitable distribution of material when stocks are over- or undersupplied. The optimisation is part of an interactive planning system, and the relationship between the optimisation module and the rest of the system is briefly described.
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D

Davis S & Durbach I, 2010, Modelling household responses to energy efficiency interventions via system dynamics and survey data, ORiON, 26(2), pp. 79-96.
Abstract. An application of building a system dynamics model of the way households might respond to interventions aimed at reducing energy consumption (specifically the use of electricity) is described in this paper. A literature review of past research is used to build an initial integrated model of household consumption, and this model is used to generate a small number of research hypotheses about how households possessing different characteristics might react to various types of interventions. These hypotheses are tested using data gathered from an efficiency intervention conducted in a town in the South African Western Cape in which households were able to exchange regular light bulbs for more efficient compact fluorescent lamp light bulbs. Our experiences are (a) that a system dynamics approach proved useful in advancing a non-traditional point of view for which, for historical and economic reasons, data were not abundantly available; (b) that, in areas where traditional models are heavily quantitative, some scepticism to a system dynamics model may be expected; and (c) that a statistical comparison of model results by means of empirical data may be an effective tool in reducing such scepticism.
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De Jongh PJ, De Jongh E, Pienaar M, Gordon-Grant H, Oberholzer M & Santana L, 2015, The impact of pre-selected variance inflation factor thresholds on the stability and predictive power of logistic regression models in credit scoring ORiON, 31(1), pp. 17-37.
Abstract. Standard Bank, South Africa, currently employs a methodology when developing application or behavioural scorecards that involves logistic regression. A key aspect of building logistic regression models entails variable selection which involves dealing with multicollinearity. The objective of this study was to investigate the impact of using different variance inflation factor (VIF) thresholds on the performance of these models in a predictive and discriminatory context and to study the stability of the estimated coefficients in order to advise the bank. The impact of the choice of VIF thresholds was researched by means of an empirical and simulation study. The empirical study involved analysing two large data sets that represent the typical size encountered in a retail credit scoring context. The first analysis concentrated on fitting the various VIF models and comparing the fitted models in terms of the stability of coefficient estimates and goodness-of-fit statistics while the second analysis focused on evaluating the fitted models' predictive ability over time. The simulation study was used to study the effect of multicollinearity in a controlled setting. All the above-mentioned studies indicate that the presence of multicollinearity in large data sets is of much less concern than in small data sets and that the VIF criterion could be relaxed considerably when models are fitted to large data sets. The recommendations in this regard have been accepted and implemented by Standard Bank.
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De Kock HC & Sinclair M, 1987, Micro-based decision support systems for stock farmers, ORiON, 3(1), pp. 1-22.
Abstract. Decision support systems were developed for use on stock farms. The systems were designed to run on Commodore 8032 microcomputers. They give the user quantitative results on which decisions such as feed mixes, sale of livestock, work programmes, etc can be based. In this paper these systems are described and illustrated with printouts from sample runs.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 3(1).

De Kock HC & Visagie SE, 1998, Wisselboustelsels in die Swartland, ORiON, 14(1/2), pp. 37-56.
Abstract. In the Swartland region farmers do not plant wheat exclusively. There are a lot of reasons for this. The main reason is that farmers who plant only one crop will end up with a situation where they will have to buy so much fertiliser that they would not be able to make any money. Every crop influences the crops on the same land later on. It is up to the farmer to decide what the influence will be. That means it is up to the farmer to decide what crop to plant on what land. The farmer ends up rotating a certain number of crops on his land. This rotation of crops is called a rotary crop system. In this situation arises the problem of what sequence of crops should be planted to ensure an optimal income to the farmer without exhausting the land. The problem could be solved by means of linear programming (LP). This problem, however, seem to get very large as the number of crops as well as the number of years over which the problem is solved is increased. By assuming that the influence of crops are only for three years and by restricting the number of years over which the problem is solved the problem is greatly reduced. If we look at the dual of the problem we find a further reduction. The solution of the dual problem also leads to the formulation of strategies. If we formulate the problem by means of the above

mentioned strategies the problem reduces to a linear programming problem with only on constraint (which is the knapsack problem). The solution of this knapsack problem with help of a little game theory is then used in a computer program to assist farmers in deciding which crops to plant.

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De Villiers AP, Matthews J & Visagie SE, 2013, Metaheuristic approaches to order sequencing on a unidirectional picking line, ORiON, 29(1), pp. 55-73.
Abstract. In this paper the sequencing of orders on a unidirectional picking line is considered. The aim of the order sequencing is to minimise the number of cycles travelled by a picker within the picking line to complete all orders. A tabu search, simulated annealing, genetic algorithm, generalised extremal optimisation and a random local search are presented as possible solution approaches. Computational results based on real life data instances are presented for these metaheuristics and compared to the performance of a lower bound and the solutions used in practise. The random local search exhibits the best overall solution quality, however, the generalised extremal optimisation approach delivers comparable results in considerably shorter computational times.
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De Wet PO, 2005, The rectilinear Steiner ratio, ORiON, 21(1), pp. 53-61.
Abstract. The rectilinear Steiner ratio was shown to be 3/2 by Hwang [Hwang FK, 1976, On Steiner minimal trees with rectilinear distance, SIAM Journal on Applied Mathematics, 30, pp. 104� 114.]. We use continuity and introduce restricted point sets to obtain an alternative, short and self-contained proof of this result.
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De Wet PO, 2008, The Steiner ratio for points on a triangular lattice, ORiON, 24(2), pp. 185-193.
Abstract. The study of spanning trees and Steiner trees arises naturally in applications, such as in the design of integrated circuit boards, communication networks, power networks and pipelines of minimum cost. In such applications the Steiner ratio is an indication of how badly a minimum spanning tree performs compared to a Steiner minimal tree. In this paper a short proof is presented for the Steiner ratio for points on a triangular lattice in the Euclidean plane. A Steiner tree in two dimensions is "lifted" to become a rectilinear tree in three dimensions, where it is altered. The rectilinear tree is then projected back into the plane and the result readily follows. A short note at the end of the paper compares our three-dimensional rectilinear trees to "impossible objects" such as Escher's "Waterfall."
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De Waal A & Ritchie T, 2007, Combining morphological analysis and Bayesian networks for strategic decision support, ORiON, 23(2), pp. 105-121.
Abstract. Morphological analysis (MA) and Bayesian networks (BN) are two closely related modelling methods, each of which has its advantages and disadvantages for strategic decision support modelling. MA is a method for defining, linking and evaluating problem spaces. BNs are graphical models which consist of a qualitative and quantitative part. The qualitative part is a cause-and-effect, or causal graph. The quantitative part depicts the strength of the causal relationships between variables. Combining MA and BN, as two phases in a modelling process, allows us to gain the benefits of both of these methods. The strength of MA lies in defining, linking and internally evaluating the parameters of problem spaces and BN modelling allows for the definition and quantification of causal relationships between variables. Short summaries of MA and BN are provided in this paper, followed by discussions how these two computer aided methods may be combined to better facilitate modelling procedures. A simple example is presented, concerning a recent application in the field of environmental decision support.
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Diegel A, 1987, Cutting paper in Richards Bay: Dynamic local or global optimization in the trim problem, ORiON, 3(1), pp. 42-55.
Abstract. The cutting stock or trim problem arises when jumbo rolls of paper are slit into reels of various width ("deckled"). The problem was examined as early as 1954; it is now seen as a classical Linear Programming formulation. The problem may be easy to formulate, but it is difficult to solve for genuine data. This is so not only because of the computations required to find good cutting plans. The major problem is this: such plans are based on certain data, but the data change as the plan is being executed and the plan no longer applies. So here it may not be optimal to optimise globally, but to work on a local heuristic basis. We can propose a heuristic procedure that compares well with an absolute solution and that can be used on a local basis. This heuristic is in use at Mondi Paper in Richards Bay.
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Douglas RBM, 1986, Microcomputer simulation of a cloathing distribution centre, ORiON, 2(1), pp. 15-25.
Abstract. A computerised simulation model of the Distribution Centre of a sizeable clothing company is developed. This article reviews the model constructed, and the estimation of its parameters, introducing the simulation language SLAM II as a modelling framework. The flexibility of the computer model and its usefulness as a decision support tool, are highlighted.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 2(1).

Du Preez ND, 1986, Die gebruik van simulasie by die operasionele ontwerp van die innamestelsel van 'n graansilo, ORiON, 2(2), pp. 72-84.
Abstract. Unique arrival patterns as well as low service rates are the main causes for long queues at processing plants for agricultural products. Simulation is used to determine operational design standards for both the layout as well as service capacities of such plants.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 2(2).

Du Preez ND & Sinclair M, 1991, Network models for the expansion of grain storage facilities, ORiON, 7(2), pp. 57-70.
Abstract. This study was undertaken for a number of grain co-operatives from a certain region in South Africa. A previous study done for these co-operatives indicated that existing storage facilities should be extended to accommodate increased production in the region. The proposed extension plan recommended the phased construction of extensions to silos in the region. These extensions should have a predetermined total storage capacity. The questions that remained were: How many silos should be extended, which silos should be extended and what should the capacity of each extension be? The objective is to minimise the sum of construction costs and the total cost of transportation between farmers and silos. A linear mixed integer programming model can be used to solve this problem. However, given the computational facilities at the disposal of the researchers, it was decided to rather use a heuristic procedure based on a transshipment model. These network models, their solution and the recommendations made on the strength of those solutions will be discussed.
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Du Toit C & Conradie WJ, 2006, A realised volatility measurement using quadratic variation and dealing with microstructure effects, ORiON, 22(2), pp. 117-129.
Abstract. A volatility measurement that overcomes the respective problems encountered when implementing the realised and Discrete Sine Transform volatility measurements is defined and discussed in this paper. First the shortcomings of these measurements are briefly discussed. Then a modified realised volatility measurement is defined and relevant theoretical results are derived. Finally simulation results are used to evaluate these three volatility measurements.
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Durbach I & Davis S, 2012, Decision support for selecting a shortlist of electricity-saving options: A modified SMAA approach, ORiON, 28(2), pp. 99-116.
Abstract. This paper describes an application providing decision support for generating a shortlist of promising electricity-saving options for households in South Africa. The decision problem is characterised by constraints on time and other resources, and by substantial uncertainty around the preferences for energy-related attributes and the performance of alternatives on those attributes. We use a stochastic multi-criteria acceptability analysis model to incorporate preferential uncertainties, and adapt this for use with quantiles and other "simplified" formats for representing uncertain attribute evaluations.
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Durbach I, Scott L, Nyirenda J & Silal S, 2013, Operational Research(ers) in development: Growing a new generation of operational researchers, ORiON, 29(1), pp. 87-102.
Abstract. This paper explores the theme of training operational research (OR) practitioners in South Africa by critically evaluating a Masters program in Operational Research in Development (ORD), launched in 2005 at the University of Cape Town. This program was specifically focused on applying OR to the problems of the developing world in general and Africa in particular. We describe the program and review the practical work undertaken by students participating in the program. Topics range widely across domains including health (antimalarial drug resistance); poverty (food banking); governance (NGO management structures and monitoring of local government performance) and sustainable livelihoods (spaza shop operations). We use the review to highlight strengths and weaknesses of the program, as well as challenges faced in the OR education in South Africa at a postgraduate level.
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Ekhosuehi VU, 2016, On the dynamics of workforce-mix in a manpower system ORiON, 32(2), pp. 105-122.
Abstract. This paper focuses on a manpower system with a fixed number of jobs that uses both permanent and temporary staff. The dynamics of workforce-mix in such a system is modelled as an optimal control problem. The objective is to find the most economical workforce-mix for the manpower system, subject to the fluctuations in workforce caused by wastage and the hiring of temporary staff. The fluctuations in the workforce-mix are modelled using a model similar to the Vidale-Wolfe advertising model. The solution is found by applying Pontryagin's principle, and a number of resulting propositions are presented along with their proofs. A real-life manpower setting is used to illustrate the utility of the model.
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Erasmus CM, 1994, A choice reduction model for the concept phase of a weapon system, ORiON, 10(1/2), pp. 1-32.
Abstract. During the concept phase of a weapon system it is often necessary to decide between a number of different development or purchasing options. This typically involves using a multidimensional value system that incorporates aspects such as performance, cost, risk, logistics and time-scales. This paper describes a model which assists in the choice in the performance dimension by including application battlefield scenarios in the analysis, and calculating the relative worth of competing systems based on the expected utility of the component weapon system attributes. The author would like to acknowledge the contributions of Mr B L Logan and Mr A E Heijdenrijch in the development of the model. This project would not have been possible without their suggestions and support, especially on the detail procedures for implementing the model.
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Erens G, Salamink P & Van der Merwe CA, 1992, Regional manpower planning, ORiON, 8(1), pp. 33-53.
Abstract. Particular problems come to the fore when planning development at the regional level. These range from the complexities of the multifarious interactions between the sect oral and local components of the region to the necessity of achieving extensive participation of regional stakeholders in the planning process. In this paper a methodology for regional manpower planning is proposed. The methodology is designed to accommodate the full range of problems by applying a systems approach which is based on the disciplines of operations research and strategic planning.
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Ericsson D, 2011, Demand chain management --- The evolution, ORiON, 27(1), pp. 45-81.
Abstract. The concepts of Supply Chain Management (SCM) and Demand Chain Management (DCM) are among the new and debated topics concerning logistics in the literature. The question considered in this paper is: ``Are these concepts needed or will they just add to the confusion?''

Lasting business concepts have always evolved in close interaction between business and academia. Different approaches start out in business and they are then, more or less simultaneously, aligned, integrated, systemised and structured in academia. In this way a terminology (or language) is provided that helps in further diffusion of the concepts. There is a lack of consensus on the definition of the concept of SCM. This may be one of the major reasons for the difficulty in advancing the science and measuring the results of implementation in business. Relationships in SCM span from rather loose coalitions to highly structured virtual network integrations. DCM is a highly organised chain in which the key is mutual interdependence and partnership. The purpose is to create a distinctive competence for the chain as a whole that helps to identify and satisfy customer needs and wishes. The classical research concerning vertical marketing systems is very helpful in systemising the rather unstructured discussions in current SCM research. The trend lies in increasing competition between channels rather than between companies, which in turn leads to the creation of channels with a high degree of partnership and mutual interdependence between members. These types of channels are known as organised vertical marketing systems in the classic marketing channel research. The behaviour in these types of channels, as well as the formal and informal structures, roles in the network, power and dependence relations, etc. are well covered topics in the literature. The concept of vertical marketing systems lies behind the definition of demand chains and demand chain management proposed in this paper. A demand chain may be defined as an integrated and aligned chain built on partnership and mutual interdependence aiming at the creation of a unique competence to identify and satisfy customer perceived value, while demand chain management may be defined as the effort to create, retain and continuously develop a dynamically aligned demand chain.

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Ericsson D, 2011, Demand chain management - The implementation, ORiON, 27(2), pp. 119-145.
Abstract. Most current supply chain models were developed during a period of relative stability. Today, the environment is discontinuous, volatile and unpredictable. This requires a major rethinking and revitalisation of existing supply chain models. Supply chains are much more than warehouses, transportation and technology, they are people powered and have to be treated as social and political as well as economic and technical systems.

The most difficult yet challenging and rewarding factor is the change of mindset from approaches based on the old industrial paradigm to the new knowledge oriented paradigm. From "one size fits all" to customisation and buyer behaviour oriented segmentation based on structural flexibility. The new approach requires a change of processes and management systems, but most of all, a change of mindset, organisation structure and behaviour. This may create internal resistance that has to be overcome to reach the desired future state. This future state is highly dependent on cooperation and consensus with external companies, and the next step is therefore to extend the alignment approach to the chosen partners in the demand chain. The development towards channel rather than company competition requires an interorganisational approach to channel design. Internal alignment and cooperation is necessary but not sufficient, which means that an agile and dynamically aligned demand chain has to be created. All this is well known and documented in both research and theory. However, the challenge is to implement these theories, models and behaviour in practice. This paper presents one practical approach to implementation of the theories put forth by Ericsson [Ericsson D, 2011, Demand chain management - The evolution, ORiON, 27(1), pp. 45-81.].

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Fatti LP, 1992, Wildlife management using the AHP, ORiON, 8(2), pp. 54-68.
Abstract. Two applications of Saaty's Analytic Hierarchy Process towards solving decision problems in Wildlife Management are discussed. The first involves structuring the management objectives of a National Park and establishing priorities for the implementation of various possible strategic management plans in the Park. The second deals with the problem faced by the various non-governmental organisations concerned with the conservation of the Rhino and Elephant populations in Southern Africa, of deciding how best to allocate their funds towards this purpose. General conclusions are drawn concerning the use of analytical techniques, particularly the AHP, in planning and decision making in Wildlife Management.
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Fatti LP, 1996, The RDP - A challenge and opportunity, ORiON, 12(1/2), pp. 1-5.
Abstract. Not available.
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Fatti LP, 1998, Use of data envelopment analysis and regression for establishing manpower requirements in a bank, ORiON, 14(1/2), pp. 57-66.
Abstract. We describe an approach towards forecasting the manpower requirements in each of the branches of a bank, based on regression models fitted to the sets of efficient branches. DEA is employed to identify the efficient branches within a category, using the numbers of employees in the different grades at each branch as input variables, and the average volumes of different types of work performed by them during a month as output variables. Forecasts of future volumes of work are obtained by fitting a model which takes into account branch and seasonal effects, as well as separate trend effects for each of the branches. The models have been tested on data from a large bank, with very encouraging results. The approach holds great promise for use towards a decision support system for managing the bank's total branch manpower requirements.
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Fatti LP, 2009, The role of Statistics in Operations Research: Some personal reflections, ORiON, 25(2), pp. 107-123.
Abstract. Statistics has a very important role to play in Operations Research (OR), yet many standard texts relegate it to a subordinate position behind, for example, deterministic optimisation techniques. I argue in this paper that statistics, and statistical thinking, are essential for the OR practitioner operating in the real, uncertain world. Using many examples from my own experience, I demonstrate that statistics is very useful, and indeed essential, when tackling real-world OR problems. Many of these examples have not been published before and will therefore hopefully be of interest in themselves, as well as illustrations of the points I wish to make.
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Fatti LP, 2013, How healthy are the rhinoceros populations in the Hluhluwe-iMfolosi Park?, ORiON, 29(1), pp. 17-29.
Abstract. Arising from a study conducted in the Hluhluwe-iMfolosi Park by the author in the late nineties, a method is proposed for improving the estimate of the size of a wildlife population by combining data from current and past surveys. The method is based on a simple state space model which takes into account the (unknown) birth rate in the population and all known losses (mortalities and relocations) and gains (introductions) in the population between successive surveys, as well as the errors in the survey estimates. The method is applied to the White- and Black Rhinoceros populations in the Hluhluwe-iMfolosi Park and tentative conclusions are drawn on the health of these two populations.
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Fatti LP & Stadler A, 1988, Evaluating South Africa's various alternative futures via the AHP, ORiON, 4(1), pp. 26-46.
Abstract. This paper describes a pilot study in which Saaty's Analytic Hierarchy Process (AHP) is used to try and gain some insight into what form of society will prevail in South Africa in the foreseeable future. The problem is structured in a hierarchy in which the actors, or power-groups, are at the top and the alternative future scenarios are at the bottom. Panellists are used to establish the relative influences of the different actors as well as the preferences which each of the actors have for the different scenarios, by means of two-way matrices of paired comparisons. The results of the exercise are discussed, as is the use of this approach in a more serious attempt to forecast South Africa's future political, social and economic system.
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Ferreira E, 1996, The RDP - A challenge and opportunity, ORiON, 12(1/2), pp. 7-10.
Abstract. Not available.
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Finkelstein MS, 2000, A note on parametric availability, ORiON, 16(2), pp. 129-138.
Abstract. Availability of a binary repairable system is generalised on the case when the quality of the system�s operation is characterised by some decreasing in time (since the latest renewal) function of performance. The corresponding equation for the time-dependent availability is derived and the stationary characteristic is considered as well. The probability of exceeding the fixed level of performance for an arbitrary instant of time is also obtained. A further generalisation is performed by assuming the possibility of a gradual repair. This means that the system can be partly available (with the decreased level of performance) during the process of repair. Finally, the specific case of imperfect repair is treated. Possible generalisations of the last approach are discussed.
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Finkelstein MS, 2001, On some optimal switching strategies, ORiON, 17(1/2), pp. 1-11.
Abstract. Systems of components with increasing failure rates are considered. Switching from an operating component on standby can be performed at each instant of time. Optimal switching strategies, maximizing the time to the first failure of a component and to the total failure of a system are investigated. A new type of a strategy: the limit strategy is introduced. It is proved that this strategy is optimal, when there is no additional information on the state of the system. Some simple examples are considered.
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Fossati RJ & Wolvaardt JS, 2001, The construction of drape surfaces with constrained first derivatives, ORiON, 17(1/2), pp. 65-80.
Abstract. The need to construct optimal drape surfaces arises in airborne geophysical surveys where it is necessary to fly a safe distance above the ground and within the performance of the aircraft used, but as close as possible to the surface. The problem is formulated as an LP with constraints at every point of a grid covering the area concerned, yielding a huge problem. The lifting algorithm is suggested. This is a surprisingly simple algorithm which starts with the drape surface at ground level and lifts it one point at a time. Only points which are too low relative to one or more of their neighbours are considered and they are lifted just enough to bring them into kilter with their neighbours. It is shown that the lifting algorithm is both exact and has great speed advantages. Some numerical results confirming exactness and speed are presented. An enhanced method with better complexity is proposed and tested numerically.
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Fourie PduT, 1999, Community OR and OR for development, ORiON, 15(1/2), pp. 53-66.
Abstract. An overview is given of Community Operations Research and of the connection between OR and development. The RDP is the main framework for development in South Africa, and its present state is described. Some suggestions are made as to ways in which ORSSA could support the RDP and development in South Africa.
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Fourie PduT, Nieuwoudt I & Van Vuuren JH, 2003, Methods of OR: A new graduate course, ORiON, 19(1/2), pp. 1-31.
Abstract. A new course entitled "Methods of Operations Research (OR)" was introduced at the Department of Applied Mathematics of Stellenbosch University during the second half of 2001. The aim of this course was to introduce students of OR to the trauma of mathematical modelling in real-world scenarios, instead of merely teaching them a number of theoretical OR-related topics in the form of a lecture-driven course with an examination at the end. Therefore this project-driven course, which is offered in collaboration with a number of partners in industry, is assessed on a continued evaluation basis, by means of written reports and oral presentations by students, after having physically, or at least virtually, visited real-world OR application sites. The objectives of the course, its structure and contents, as well as lessons learnt and some student feedback are described in this paper. A selection of projects used in the course are described in some detail in an appendix.
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Fourie PduT, 2007, Operations research and development, ORiON, 23(1), pp. 59-72.
Abstract. The paper begins with a discussion of the concepts operations research and development. An overview is next given of the RDP (Reconstruction and Development Programme), which still embodies the vision of development in South Africa associated with the political transition in 1994. The efforts of ORSSA (the Operations Research Society of South Africa) to help with the implementation of the RDP are described. The international OR (Operations Research) community has been involved in various ways with the promotion of development, especially through IFORS (the International Federation of Operational Research Societies), and these are reviewed. Sustainable development, which deals specifically with a long-term view of development, is mentioned briefly. Lastly some suggestions are made as to how ORSSA and its members could help to promote development in South Africa. In the Appendix a summary is given of a paper by Gerhard Geldenhuys in which he analyzes the needs identified by the RDP as well as relevant OR methods.
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Gal T, 1990, Degeneracy problems in mathematical programming and degeneracy graphs, ORiON, 6(1), pp. 3-36.
Abstract. Degeneracy may cause various computing and other complications in any mathematical programming problem of the kind where the constraint set defines a convex polyhedral set (particularly, a polytope). In order to be able to study various seemingly independent degeneracy phenomena from a unifying viewpoint a so-called degeneracy graph (DG for short) is defined, and its properties analysed. Cycling of the simplex method for LP is analysed and a method to construct cycling examples of arbitrary size is proposed. The neighbourhood problem is solved by a new approach to determine a minimal N-tree (N for neighbour), and an efficient method to determine all vertices of a convex polytope is described. A new version of the simplex method is indicated that does not need Phase 1, should be faster than commercial codes and automatically contains an anticycling device. For a degenerate optimal solution of an LP-problem, sensitivity analysis as well as shadow price determination and interpretation are tackled by using a special class of DG's, the so-called optimum DG's. The connection between weakly redundant constraints, a degenerate optimal solution of the associated LP and sensitivity analysis as well as shadow price determination is analysed.
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Gardner S, Le Roux NJ, Rypstra T & Swart JPJ, 2005, Extending a scatterplot for displaying group structure in multivariate data: A case study, ORiON, 21(2), pp. 111-124.
Abstract. The power of canonical variate analysis (CVA) biplots, when regarded as extensions of ordinary scatterplots to describe variation and group structure in multivariate observations, is demonstrated by presenting a case study from the South African wood pulp industry. It is shown how multidimensional standards specified by users of a product may be added to the biplot in the form of acceptance regions such that the roles of the respective variables that influence the product can be ascertained. The case study considers an alternative to CVA and multivariate analysis of variance (MANOVA) when the application of these procedures becomes questionable as a result of dealing with small sample sizes and heterogeneity of covariance matrices. It is explained how analysis of distance (AOD) analogous to analysis of variance may be performed in such cases. Biplots to accompany AOD are provided. The biplots and AOD illustrated in the case study from the wood pulp industry have the potential to be used widely where a primary product, influenced by several variables, is produced and where this product is of importance to various secondary manufacturers depending on which set of multidimensional specifications are met.
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Geldenhuys G, 1991, A hypergame analysis of the battle of Magersfontein, ORiON, 7(1), pp. 1-6.
Abstract. The battle of Magersfontein, 11 December 1899, can be modelled as a hypergame. The analysis shows how British misconceptions of the Boer strategies and strength led to an ill-advised British attack with disastrous results for them. Several points in connection with hypergames are illustrated in this case study.
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Geldenhuys G & Botha EM, 1994, A note on Dupuy's QJM and new square law, ORiON, 10(1/2), pp. 45-55.
Abstract. T N Duputy has developed various operations research models in an attempt to quantify lessons that can be learned from military history. We discuss two of his models, the Quantified Judgment Model (QJM), and the "new square law". The QJM was developed by Duputy for the analysis of military operations. We point out mathematical discrepancies in a part of the model and make suggestions to remove these discrepancies. Duputy's new square law is an attempt to modify the well-known Lanchester equations for aimed fire, taking into account some results that were obtained in the QJM. We show that the new square law cannot be accepted as a valid mathematical model of combat attrition.
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Geldenhuys G, De Kock HC, Botha E & Hattingh L, 1992, A two-phase method for university library acquisitions allocation, ORiON, 8(1), pp. 1-11.
Abstract. A two-phase method for the allocation of funds for library materials to the various faculties and departments of a university is proposed. It consists of a first phase in which goal programming is used to allocate funds to the faculties, followed by a second phase in which a proportional formula is used for the allocation of funds to departments in the faculties. Sensitivity analyses of both phases are also discussed.
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Geldenhuys G, Fourie PduT & Le Roux J, 1988, The eastern province blood transfusion service: A case study, ORiON, 4(2), pp. 81-91.
Abstract. An analysis was made of the location of the nine blood banks in the Eastern Province Blood Transfusion Service. The banks were considered as the vertices of an undirected graph. The cost of collecting and distributing blood was assumed to be proportional to the distances between vertices, and to the population of each district. The 9-median of the graph was calculated and the corresponding cost compared with the cost of the actual configuration, which turned out to be about 3% higher.
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Geldenhuys G, Sciocatti MJ & Fourie PduT, 1993, A simulation of a proposed three-phase method for proportional representation in South Africa, ORiON, 9(1), pp. 1-12.
Abstract. In October 1922 the President's Council of the Republic of South Africa approved a report on a proportional polling system for the country in a new constitutional dispensation. A three-phase method is proposed to ensure that there is not only proportionality with respect to the electoral regions of the country, but also on a party basis with respect to the votes cast in the election. A lower house of parliament with 400 seats is proposed. In the first phase 300 of the seats are made available to the various regions in proportion to the number of eligible voters in the respective regions. In the election the various parties compete for these 300 seats in the different regions. The second phase consists of allocating the seats to the parties on the basis of the actual votes cast for them in the regions. Because of factors such as variable percentage polls and support for the parties in the separate regions, it could happen that a particular party's portion of the 300 seats is not in accordance with the votes that it receives nationally. In the third phase the remaining 100 seats are used to rectify such situations. On the basis of the votes cast, these 100 seats are used for compensatory purposes, so that the final allocation of the 400 seats to the parties should be proportional to the support for the parties in the election. Fixed regional party lists of candidates for the election and the Jefferson allocation method are used in the applicable phases. We translate the pose of the President's Council report into formal mathematical descriptions of the proposed methods. Several hypothetical examples are used to illustrate the methods and to point out possible problems. A computer program which implements the methods is described briefly and is used to simulate various elections. These simulations show that 100 compensatory seats should be sufficient for the purpose for which they were introduced. We hope that our descriptions and analyses will contribute to the debate on an acceptable and practical electoral system in a new South Africa.
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Gevers WR, 1989, Dynamic repayment of mortgage loans: A solution for the low-income sector?, ORiON, 5(2), pp. 84-101.
Abstract. By using a dynamic instalment repayment plan to finance a mortgage loan rather than the usual fixed instalment financing, the threshold at which a prospective homeowner may enter the housing market may be lowered substantially. In this paper this method of financing will be evaluated to determine under which circumstances it could be used to help the low-income group to obtain housing, and also to highlight some of its deficiencies. Historic trends of income are also analysed to determine the income growth potential of the low-income sector. The income growth potential does not seem to distract from the potential of the dynamic repayment of mortgage loans.
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Govender U & Kruger J, 2009, A resource allocation model to support efficient air quality management in South Africa, ORiON, 25(1), pp. 53-68.
Abstract. Research into management interventions that create the required enabling environment for growth and development in South Africa are both timely and appropriate. In the research reported in this paper, the authors investigated the level of efficiency of the Air Quality Units within the three spheres of government viz. National, Provincial, and Local Departments of Environmental Management in South Africa, with the view to develop a resource allocation model. The inputs to the model were calculated from the actual man-hours spent on twelve selected activities relating to project management, knowledge management and change management. The outputs assessed were aligned to the requirements of the mandates of these departments. Several models were explored using multiple regressions and stepwise techniques. The model that best explained the efficiency of the organisations from the input data was selected. Logistic regression analysis was identified as the most appropriate tool. This model is used to predict the required resources per Air Quality Unit in the different spheres of government in an attempt at supporting and empowering the air quality regime to achieve improved output efficiency.
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Greben JM, Elphinstone C, & Holloway J, 2006, A model for election night forecasting applied to the 2004 South African elections, ORiON, 22(1), pp. 89-103.
Abstract. A novel model has been developed to predict elections on the basis of early results. The electorate is clustered according to their behaviour in previous elections. Early results in the new elections can then be translated into voter behaviour per cluster and extrapolated over the whole electorate. This procedure is of particular value in the South African elections which tend to be highly biased, as early results do not give a proper representation of the overall electorate. In this paper we explain the methodology used to obtain the predictions. In particular, we look at the different clustering techniques that can be used, such as kmeans, fuzzy clustering and k-means in combination with discriminant analysis. We assess the performances of the different approaches by comparing their convergence towards the final results.
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Greef AR & Reinecke R, 1988, Problem solving using artificial intelligence techniques, ORiON, 4(1), pp. 47-64.
Abstract. Real-world problems often do not lend themselves to an algorithmic solution. Humans, however, cope with these problems despite their fallible problem solving techniques. Instead of trying to construct algorithms to solve problems AI researchers have concentrated on using the more successful methods used by humans. This paper reviews the area of problem solving in the field of Artificial Intelligence. This includes problem representation for computation, "weak" methods of searching for a problems solution, knowledge representations that facilitate more efficient search strategies and planning - an advanced problem solving technique.
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Greef AR & Reinecke R, 1990, Knowledge based systems: A powerful yet deceptive engineering tool, ORiON, 6(2), pp. 79-92.
Abstract. Knowledge Based System (KBS) technology emanating from a sub-field of Artificial Intelligence can be a powerful and yet deceptive engineering tool. It's power is evident from the magnitude of published KBS applications. It's deceit lies in the illusion that the technology is universally powerful and relatively simple to implement. This paper attempts to aid the engineer with the handling and application of this new tool : by firstly presenting an overview of the historical evolution of KBS's and describing their organisation, and secondly, by describing a number of successful engineering applications of KBS's. Common deceptive pitfalls and simplifications are exposed at each step.
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Groves GW & Van Vuuren JH, 2005, Efficient heuristics for the rural postman problem, ORiON, 21(1), pp. 33-51.
Abstract. A local search framework for the (undirected) Rural Postman Problem (RPP) is presented in this paper. The framework allows local search approaches that have been applied successfully to the well�known Travelling Salesman Problem also to be applied to the RPP. New heuristics for the RPP, based on this framework, are introduced and these are capable of solving significantly larger instances of the RPP than have been reported in the literature. Test results are presented for a number of benchmark RPP instances in a bid to compare efficiency and solution quality against known methods.
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Guo R, Asher H & Love E, 2000, Generalized models of repairable systems: A survey via stochastic processes formalism, ORiON, 16(2), pp. 87-128.
Abstract. In this article, we survey the developments in the generalised models of repairable systems reliability during 1990s, particularly the last five years. In this field, we notice the sharp fundamental problem that voluminous complex models were developed but there is an absence of sufficient data of interest for justifying the success in tackling the real engineering problems. Instead of following the myth of using simple models to face the complex reality, we select and review some practical models, particularly the stochastic processes behind them. The Models in three quick growth areas: age models, condition monitoring technique related models, say, proportional intensity and their extensions, and shock and wearing models, including the delay-time models are reviewed. With the belief that only those stochastic processes reflecting the instinct nature of the actual physical processes of repairable systems, without excessive assumptions, may have a better chance to meet the demands of engineers and managers.
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Gweshe T & Durbach I, 2013, An analysis of the efficiency of player performance at the 2011 Cricket World Cup, ORiON, 29(2), pp. 137-153.
Abstract. In limited overs cricket, efficiency plays a significant role in team success. Batsmen especially are under pressure to score quickly rather than in large quantities because only 50 overs are available per innings. This paper uses data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA) to assess the efficiency with which players at the 2011 Cricket World Cup converted inputs (balls faced or bowled) into performance outputs. The effect that non-discretionary variables like the cricketing resources available to a player have on his efficiency is controlled for, allowing for a fairer assessment across players from different countries.
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Hasan MB, 2012, Managing uncertainty in fishing and processing of an integrated fishery, ORiON, 28(1), pp. 37-58.
Abstract. This paper considers uncertainties in fishing trawler scheduling and production planning in a quota-based integrated commercial fishery. A commercial fishery faces uncertainty mainly from variation in catch rate, which may be due to weather, and other environmental factors. The firm attempts to manage this uncertainty through planning co-ordination of fishing trawler scheduling, catch quota, processing and labour allocation, and inventory control. Schedules must necessarily be determined over some finite planning time horizon, and the trawler schedule itself introduces man-made variability, which in turn induces inventory in the processing plant. This induced inventory must be managed, and is complicated by the inability to plan beyond the current planning time horizon. A simple constraint is introduced requiring beginning inventory to equal ending inventory of the planning period. This enables management to calculate a profit-maximizing safety stock that counter-acts the man-made variability due to the trawler scheduling. It is found that the variability of catch rate had virtually no effects on the profitability. Numerical results for several planning time horizon models are presented, based on data for a major New Zealand fishery.
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Hasan MB & Raffensperger JF, 2006, A mixed integer linear program for an integrated fishery, ORiON, 22(1), pp. 19-34.
Abstract. In this paper fishing trawler scheduling and production planning for a quota-based integrated commercial fishery is modelled mathematically. The catch capacity of fishing trawlers and the capacity of processing firms are two major factors which influence the scheduling of fishing trawlers. Production planning in fish processing firms depends on steady supply of fresh fish from the fishing trawlers to the processing firms. We develop a mixed integer linear programming (MILP) model to co-ordinate trawler scheduling, fishing, processing, and labour allocation of quota based integrated fisheries. We demonstrate the workability of our model with a numerical example and sensitivity analysis based on data obtained from one of the major fisheries in New Zealand.
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Hasan MB & Raffensperger JF, 2008, Two pricing methods for solving an integrated fishery planning model, ORiON, 24(2), pp. 115-130.
Abstract. In this paper, we develop two novel pricing methods for solving an integer program. We demonstrate the methods by solving an integrated commercial fishery planning model (IFPM). In this problem, a fishery manager must schedule fishing trawlers (determine when and where the trawlers should go fishing, and when the trawlers should return the caught fish to the factory). The manager must then decide how to process the fish into products at the factory. The objective is to maximise profit. The problem may be modelled as a single integer program, with both the trawler scheduling and production planning parts integrated. Inventory constraints connect the two parts of the problem. Production planning alone would result

in an easy linear program, but due to the trawler scheduling aspect, the IFPM is a hard integer program in the sense that traditional solution methods result in computation times that are far too long to be practical. The two pricing methods developed in this paper are a decomposition{based O'Neill pricing method and a reduced cost{based pricing method. We demonstrate the methods by means of numerical examples for different planning horizons, corresponding to differently sized problems.

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Hattingh M & Uys DW, 2014, In-season retail sales forecasting using survival models ORiON, 30(2), pp. 59-71.
Abstract. A large South African retailer (hereafter referred to as the Retailer) faces the problem of selling out inventory within a specified finite time horizon by dynamically adjusting product prices, and simultaneously maximising revenue. Consumer demand for the Retailer's fashion merchandise is uncertain and the identification of products eligible for markdown is therefore problematic. In order to identify products that should be marked down, the Retailer forecasts future sales of new products. With the aim of improving on the Retailer's current sales forecasting method, this study investigates statistical techniques, viz. classical time series analysis (Holt's smoothing method) and survival analysis. Forecasts are made early in the product life cycle and results are compared to the Retailer's existing forecasting method. Based on the mean squared errors of predictions resulting from each method, the most accurate of the methods investigated is survival analysis.
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Hauman C & Bekker JF, 2014, Application of the multi-objective cross-entropy method to the vehicle routing problem with soft time windows ORiON, 30(1), pp. 19-40.
Abstract. The vehicle routing problem with time windows is a widely studied problem with many real-world applications. The problem considered here entails the construction of routes that a number of identical vehicles travel to service different nodes within a certain time window. New benchmark problems with multi-objective features were recently suggested in the literature and the multi-objective optimisation cross-entropy method is applied to these problems to investigate the feasibility of the method and to determine and propose reference solutions for the benchmark problems. The application of the cross-entropy method to the multi-objective vehicle routing problem with soft time windows is investigated. The objectives that are evaluated include the minimisation of the total distance travelled, the number of vehicles and/or routes, the total waiting time and delay time of the vehicles and the makespan of a route.
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Hawkins DM & Bartlett HE, 1987, The mysterious case of the missing half-ton of gold, ORiON, 3(2), pp. 85-100.
Abstract. A milling circuit in the concentrator processing ore at one of the gold mines managed by Johannesburg Consolidated Investments had apparently been losing a substantial part of the gold input to it for several months. At the time of investigation, the gold unaccounted for totalled nearly half a ton, worth some $5 million. A specially adapted distributed lag model was fitted to measurements made of the input and output, and far from confirming the apparent loss of gold, indicated that the plant's output balanced its input. The apparent contradiction between the total input and output and the more detailed accounting of the distributed lag model (which included variable time lags explicitly) gave rise to a closer investigation of the circuit which led to an explanation of the apparent discrepancies, and the actual location of a large amount of gold.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 3(2).

Hearne JW, Santika T & Goodman P, 2008, Portfolio selection theory and wildlife management, ORiON, 24(2), pp. 103-113.
Abstract. With a strong commercial incentive driving the increase in game ranching in Southern Africa the need has come for more advanced management tools. In this paper the potential of Port-folio Selection Theory to determine the optimal mix of species on game ranches is explored. Land, or the food it produces, is a resource available to invest. We consider species as investment choices. Each species has its own return and risk profile. The question arises as to what proportion of the resource available should be invested in each species. We show that if the objective is to minimise risk for a given return, then the problem is analogous to the Portfolio Selection Problem. The method is then implemented for a typical game ranch. We show that besides risk and return objectives, it is necessary to include an additional objective so as to ensure sufficient species to maintain the character of a game ranch. Some other points of difference from the classical Portfolio Selection problem are also highlighted and discussed.
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Hearne JW, Swart J & Goodman P, 1991, A conservation model for black rhino, ORiON, 7(1), pp. 25-37.
Abstract. Over the past thirty years the black rhinoceros (Diceros bicornis) population in Africa has declined from about 65 000 to 3 500. In contrast the South African and Namibian population has increased four-fold to 1 000 over the same period. The recently developed national conservation strategy for black rhino has as its main goal a further four-fold increase in the current population in as short a period as possible. To achieve this, the growth rate of the population as a whole will have to be maximised. This involves removing animals from areas where the population is approaching the ecological carrying capacity and establishing new viable populations in other suitable reserves. A model incorporating what is known about the population biology of black rhino, was developed to give guidance to managers on the most appropirate harvesting strategy to adopt for their populations; in particular, to determine the rate of removals and the age and sex of individuals to be removed to attain the conservation goal as soon as possible.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 7(1).

Hearne JW & Uys PW, 1991, Conservation versus traditional cattle farming - the economic implications, ORiON, 7(1), pp. 7-24.
Abstract. In many areas of South Africa traditional subsistence farming practices entail overstocking of cattle. The resulting damage to the veld can be arrested only by providing the farmers with economic incentives to reduce stocking densities. In this paper cattle offtake strategies are investigated with a view to maximising revenue at lower stocking densities. This is achieved by developing a mathematical model which predicts the revenue generated by a given strategy. It is shown that although the model is nonlinear, a transformation can be made to enable optimisation by linear programming.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 7(1).

Horsley DA & Splaine M, 1986, An easy to use simulation program for gold mine transport problems, ORiON, 2(2), pp. 85-99.
Abstract. Efficient transportation of ore bearing rock is an important aspect of the gold mining industry. Simulations of these networks provide management with one of the cheapest ways of dealing with transportation problems. One such simulation model, namely GOLDTRAM, is used extensively by Anglo American Corporation. The scope of problem that can be tackled by the non-specialist user is indicated by the input required and output available.
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Ittmann HW, 1987, Operations research - future perspectives, ORiON, 3(2), pp. 56-75.
Abstract. Many of the current exciting developments in operations Research (OR) will have a major impact on its future. Advances in computer technology and the resulting creation of opportunities for making these technologies available to decision-makers are playing a major role in current OR practice and will continue to do so in the future. Some of these new developments and their potential for operations researchers are discussed in this paper. Emphasis is placed on both mathematical and non-mathematical issues, and future challenges are highlighted.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 3(2).

Ittmann HW, 1988, Retrospective value analysis of decision support benefits from a production planning system for a brewery, ORiON, 4(1), pp. 65-79.
Abstract. A decision support system for production planning in a brewing company was developed to assist with the planning of brewing, packaging and distribution of beer and to minimise production costs. Having been in operation for some time, the system has changed and adapted in a very dynamic environment. The system's present form and current use are discussed. Initial management approval for system development was based on faith rather than proper cost-benefit and value analyses. This paper aims at retrospectively highlighting these values and benefits with regard to supporting decision-making in the company.
No electronic copy of this paper is available. Obtain a hard copy of this paper by subscribing to Issue 4(1).

Ittmann HW, 1996, The RDP - What can OR offer?, ORiON, 12(1/2), pp. 21-35.
Abstract. South Africa has made historical changes during the past six years. With the change of Government in May 1994, the majority party of the Government of National Unity, the ANC, announced its master plan for the new South Africa. That was the birth of the Reconstruction and Development Programme (the RDP). Within the RDP document the five major aspects or problem areas in South Africa that need attention are quoted, namely: meeting basic needs; developing our human resources; building the economy; democratising the state and society; and implementing this programme.
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Ittmann HW, 2001, Tips, tricks and techniques in practicing OR - a different twist!, ORiON, 17(1/2), pp. 55-64.
Abstract. This paper is a personal account of marketing and selling Operations Research (OR) in South Africa. The author reflects on this activity that has occupied him over the past ten to fifteen years. The traditional marketing mix is possibly not ideal for selling a consulting service such as OR. The author shows how he used ingredients such as able people, physical evidence and process in selling the services of the group he represented. The main elements of being successful are: one or more success stories, credibility, a network of people (potential clients), quality staff, a sense of urgency within the group and a recognition that the client is always king.
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Ittmann HW, 2007, Operations research at CSIR: A brief history through cases, ORiON, 23(1), pp. 73-88.
Abstract. Apart from work in the mining industry during the 1950s, the first real Operations Research (OR) group in South Africa was established at CSIR in the early 1960s. Those initially involved in this group played a significant role in establishing OR at various universities in South Africa. The OR group at CSIR did, however, continue and today the group still exists. This paper presents a brief history of this group and endeavours to provide a glimpse of some of the projects conducted over the many years since its establishment.
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Ittmann HW, 2009, Recent developments in Operations Research: A personal perspective, ORiON, 25(2), pp. 87-105.
Abstract. At the 25th anniversary of ORiON it is appropriate to look at the advances in OR during the last 25 years. This paper focuses on what has happened on the international front --- there is not a focus on OR developments in South Africa as such. By doing this two observations immediatly follow. Firstly, there have been very few new techniques or tools developed over this period. The classic tools and main techniques of OR are still what they were 25 years ago although vast developments and extensions of these have occurred. Secondly, OR practice has extended into almost all industries as well as all areas of human activity. It is almost impossible to highlight all these advances and give a comprehensive overview --- an endeavour has rather been made to give a personal perspective on some of these advances.
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Ittmann HW, 2013, A review of the Tom Rozwadowski medal, ORiON, 29(1), pp. 103-124.
Abstract. The Tom Rozwadowski (TR) medal is the most prestigious award of the Operations Research Society of South Africa (ORSSA). The award, first presented in 1971, was established in honour of one of ORSSA's founding members. Initially the medal was to be presented to a member of the society for a paper of most outstanding merit, but the rules were subsequently adapted and currently the medal is awarded to the best paper published during the previous calendar year. This review endeavours to present an analysis of all the award winning papers since its inception. The aim is three-fold, namely: to present a historical review, to detect any trends within Operations Research (OR) in South Africa and to present a view of OR in the country. The analysis indicates that these award-winning papers are very diverse in nature, which certainly epitomises OR in South Africa, but the sample is small and thus not representative enough to be used to draw strict conclusions about the evolution of OR in South Africa. The papers, in general, exhibit originality, quality and clarity of exposition while there is clear interaction between theory and practice.
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Ittmann HW, Holloway JP & Dudeni-Tlhone N, 2017, 2014 Election forecast - a post-election analysis ORiON, 33(1), pp. 35-55.
Abstract. General elections are held every five years in South Africa. During the 12 to 24 hour period after the close of the voting booths, the expected final results are of huge interest to the electorate and politicians. In the past, the Council for Scientific and Industrial Research (CSIR) has developed an election forecasting model in order to provide the media and political analysts with forecasts of the final results during this period of peak interest. In formulating this model, which forecasts the election results as the results from voting districts (VDs) become available, some assumptions had to be made. In particular, assumptions were made about the clustering of previous voting patterns as well as the order in which VD results are released.

This election forecasting model had been used successfully for a number of elections in the past and in these previous elections, with around 5%-10% of the results available, the predictions produced by the model were very close to the final outcome, particularly for the ANC, being the largest party. For the 2014 national election, however, the predictions, with close to 50% of the voting district results known (equivalent to an estimated 40% of the total votes), were still not accurate and varied by more than 1% for both the ANC and the EFF. This paper outlines a post-election analysis to determine the reasons for these discrepancies and how they relate directly to the model assumptions. The aim is to highlight how practical realities can affect the assumptions and consequently their impact on the forecasted results. Reference is made to previous election forecasts and the 2014 post-election analysis is presented.

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Jenkins L, 2003, An experiment on selecting most informative variables in socio-economic data, ORiON, 19(1/2), pp. 75-85.
Abstract. In many studies where data are collected on several variables, there is a motivation to find if fewer variables would provide almost as much information. Variance of a variable about its mean is the common statistical measure of information content, and that is used here. We are interested whether the variability in one variable is sufficiently correlated with that in one or more of the other variables that the first variable is redundant. We wish to find one or more �principal variables� that sufficiently reflect the information content in all the original variables. The paper explains the method of principal variables and reports experiments using the technique to see if just a few variables are sufficient to reflect the information in 11 socioeconomic variables on 130 countries from a World Bank (WB) database. While the method of principal variables is highly successful in a statistical sense, the WB data varies greatly from year to year, demonstrating that fewer variables would be inadequate for this data.
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Jenkins L & Anderson M, 2002, Omitting correlated variables, ORiON, 18(1/2), pp. 21-36.
Abstract. Data collected on the physical, biological or man-made world are often highly correlated, posing the question of whether fewer variables would contain almost as much information. A crude solution is simply to look at the Pearson correlation matrix and omit one of a pair of highly correlated variables. A more systematic method is to condition on one or more variables, and observe the resulting partial covariance matrix. If the variables have little variance after the conditioning, then the conditioning variables contain most of the information of all the original variables. Paralleling the usual tests applied in judging how many principal components are sufficient to represent all the data, we can use the amount of variance explained by the conditioning variable (s), as a measure of information content. The paper references earlier work in this area, explains the computation and includes examples using published data sets. The approach is found to be highly competitive with using principal components, and has the obvious advantage over principal components of simply omitting some of the original variables from further consideration. The method

has been coded in Visual-Basic add-ins to an Excel spreadsheet.

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Jolayemi JK, 2001, A model for scheduling projects under the condition of inflation and under penalty and reward arrangements, ORiON, 17(1/2), pp. 81-99.
Abstract. A zero-one mixed integer linear programming model is developed for the scheduling of projects under the condition of inflation and under penalty and reward arrangements. The effects of inflation on time-cost trade-off curves are illustrated and a modified approach to time-cost trade-off analysis presented. Numerical examples are given to illustrate the model and its properties. The examples show that misleading schedules and inaccurate project-cost estimates will be produced if the inflation factor is neglected in an environment of high inflation. They also show that award of penalty or bonus is a catalyst for early completion of a project, just as it can be expected.
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Joubert JW & Claasen SJ, 2006, A sequential insertion heuristic for the initial solution to a constrained vehicle routing problem, ORiON, 22(1), p. 105-116.
Abstract. The Vehicle Routing Problem (VRP) is a well-researched problem in the Operations Research literature. It is the view of the authors of this paper that the various VRP variants have been researched in isolation. This paper embodies an attempt to integrate three specific variants of the VRP, namely the VRP with multiple time windows, the VRP with a heterogeneous fleet, and the VRP with double scheduling, into an initial solution algorithm. The proposed initial solution algorithm proves feasible for the integration, while the newly introduced concept of time window compatibility decreases the computational burden when using benchmark data sets from literature as a basis for efficiency testing. The algorithm also improves the quality of the initial solution for a number of problem classes.
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Joubert JW & Conradie DG, 2005, A fixed recourse integer programming approach towards a scheduling problem with random data: A case study, ORiON, 21(1), pp. 1-11.
Abstract. Regardless of the success that linear programming and integer linear programming has had in applications in engineering, business and economics, one has to challenge the assumed reality that these optimization models represent. In this paper the certainty assumptions of an integer linear program application is challenged in an attempt to improve the solution robustness in an uncertain environment. The authors resort to a two-stage, fixed recourse program to introduce random variables with a uniform distribution instead of deterministic expected values in a workforce sizing and scheduling problem. Although the solution to the problem comprises a significantly larger fulltime staff complement than that determined via the problem without the introduction of random variables, the expected workforce requirements preempt and consider the costly expense of casual workers.
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Joubert MJ, 1985, A mathematical model for residential planning in Richards Bay, ORiON, 1(1), pp. 28-42.
Abstract. The formulation of a systems dynamics model which was applied to obtain forecasts of important urban variables such as population and housing, is discussed. It is shown that the model simulated the growth trends in the town, at least for the period for which data was available, satisfactorily. A sensitivity analysis of the model was carried out and no sensitive parameters were identified during the 6 year simulation interval. An optimisation strategy by which the occupation rate of housing was restricted to certain limits, is also discussed.
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Kabera MG & Haines LM, 2013, A note on the statistical analysis of point judgment matrices, ORiON, 29(1), pp. 75-86.
Abstract. The Analytic Hierarchy Process is a multicriteria decision making technique developed by Saaty in the 1970s. The core of the approach is the pairwise comparison of objects according to a single criterion using a 9-point ratio scale and the estimation of weights associated with these objects based on the resultant judgment matrix. In the present paper some statistical approaches to extracting the weights of objects from a judgment matrix are reviewed and new ideas which are rooted in the traditional method of paired comparisons are introduced.
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Kahimbaara JA, 1996, Spatial foundations for addressing the statistical needs of the reconstruction and development programme, ORiON, 12(1/2), pp. 55-68.
Abstract. Not available.
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Kanniappan P & Thangavel K, 1993, An optimization model for selection of IRDP schemes, ORiON, 9(1), pp. 13-20.
Abstract. The problem considered in this paper is to select various schemes under the integrated Rural Development Program (IRDP) and to maximise the number of beneficiaries so as to optimise the annual income generated from each scheme. There are typical constraints prescribed by the government in the allocation of funds to several schemes from the budget outlay for IRDP each year. In this paper, with the help of the data drawn from the District Rural Development Agency of Dindigul Anna District, Tamil Nadu, India, we develop a linear programming model for maximising the annual income generated from the schemes.
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Kent G, Kruger HA & du Toit JV, 2016, Class ranking of secondary schools in the North West province of South Africa ORiON, 32(2), pp. 123-146.
Abstract. The education system in South Africa finds itself in a dismal position. Existing research reports and general news bulletins suggest that schools in South Africa suffer from a general lack of efficiency measures and therefore underperform in comparison with those in other countries. This paper proposes a class-ranking technique as a means to evaluate schools. The technique implements Pareto optimality principles and utilises a mathematical model that is based on output variables (e.g. pass rates) only. The model also provides for the construction of a step-by-step improvement plan for underperforming schools. The suggested framework was applied to 54 secondary schools in one of the four major municipal districts in the North West province of South Africa. Results are contrasted with the application of an ordinary DEA model that is based on input and output variables and showed that the suggested approach offers a more reliable alternative to evaluate, monitor and improve the performance of schools ranked as inefficient.
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Kheirfam B, 2014, An interior-point method for the Cartesian P*(k)-linear complementarity problem over symmetric cones ORiON, 30(1), pp. 41-58.
Abstract. A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
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Kidd MP, 2010, A tabu-search for minimising the carry-over effects value of a round-robin tournament, ORiON, 26(2), pp. 125-141.
Abstract. A player b in a round-robin sports tournament receives a carry-over effect from another player a if some third player opposes a in round i and b in round i+1. Let gamma_ab denote the number of times player b receives a carry-over effect from player a during a tournament. Then the carry-over effects value of the entire tournament T on n players is given by Gamma(T) = sum_{i=1}^{n} sum_{j=1}^{n} gamma_{ij}^{2}. Furthermore, let Gamma(n) denote the minimum carry-over effects value over all round-robin tournaments on n players. A strict lower bound on Gamma(n) is n(n-1) (in which case there exists a round-robin tournament of order n such that each player receives a carry-over effect from each other player exactly once), and it is known that this bound is attained for n = 2^r, n = 20 and n = 22. It is also known that round-robin tournaments can be constructed from so-called starters; round-robin tournaments constructed in this way are called cyclic. It has previously been shown that cyclic round-robin tournaments have the potential of admitting small values for Gamma(T), and in this paper a tabu-search is used to find starters which produce cyclic tournaments with small carry-over effects values. The best solutions in the literature are matched for n <= 22, and new upper bounds are established on Gamma(n) for 24 <= n <= 40.
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Kohlas J, Anrig B & Bissig R, 2000, Reliability and diagnostic of modular systems, ORiON, 16(1), pp. 47-62.
Abstract. Reliability and diagnostic are in general two problems discussed separately. Yet the two problems are in fact closely related to each other. Here, this relation is considered in the simple case of modular systems. We show, how the computation of reliability and diagnostic can efficiently be done within the same Bayesian network induced by the modularity of the structure function of the system.
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Koen R, Holloway JP, Elphinstone CD & Stylianides T, 2012, Developing a planning tool for South African prosecution resources: Challenges and approach, ORiON, 28(2), pp. 85-98.
Abstract. In every country the prosecution of criminal cases is governed by different laws, policies and processes. In South Africa, the National Prosecuting Authority (NPA) has the responsibility of planning and managing all prosecution functions. The NPA has certain unique characteristics that make it different from other similar organisations internationally. The development of a planning tool that the NPA could use to plan their future resource requirements over the short to medium term required extensive modelling, and its final form included features which, to the best knowledge of the development team, make it unique both locally and internationally. Model design was largely influenced by the challenges emanating from the special requirements and context of the problem. Resources were not forecasted directly, but were derived with the help of simulation models that traced docket flows through various resource-driven processes. Docket flows were derived as a proportion of reported crimes, and these were forecasted using a multivariate statistical model which could take into account explanatory variables as well as the correlations between the patterns observed within different crime categories. The simulation consisted of a number of smaller models which could be run independently, and not of one overarching model. This approach was found to make the best use of available data, and compensated for the fact that certain parameters, linking different courts and court types, were not available. In addition, it simplified scenario testing and sensitivity analysis. The various components of the planning tool, including inputs and outputs of the simulation models and the linkages between the forecasts and the simulation models, were implemented in a set of spreadsheets. By using spreadsheets as a common user interface, the planning tool could be used by prosecutors and managers who may not have extensive mathematical or modelling experience.
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Kok BJ & Bekker JF, 2007, A procurement decision model for a video rental store - A case study, ORiON, 23(2), pp. 89-103.
Abstract. A procurement decision model for a video rental store is presented in this paper. The model is based on inventory management, but many classical inventory management principles are inappropriate since the commodities (movie titles) are removed from, and after a certain time period, returned to inventory. The commodities also have a decaying demand in general; hence the video rental store owner (the decision maker) is required to procure new titles periodically. The question addressed in this paper is how to determine which movie titles to acquire, and how many copies of each in order to best maximise profit. An approximated demand function is presented, and attributes of movie titles in inventory are used to classify candidate movie titles and predict their future demand. This allows the decision maker to select the most profitable candidate items from a list, whilst remaining within a predetermined budget. The procurement decision model is evaluated by means of predicting the expected turnover using the procurement decision model solution, and then comparing it to the turnover achieved using the procurement strategy followed by the store owner. The model is not prescriptive � the decision maker may still utilise his/her experience to acquire new movie titles. The procurement decision model, however, does assist the decision making process by presenting a point of departure from which procurement decisions may be made.
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Kourie DG, 2012, Modelling soft error probability in firmware: A case study, ORiON, 28(1), pp. 19-35.
Abstract. This case study involves an analysis of firmware that controls explosions in mining operations. The purpose is to estimate the probability that external disruptive events (such as electromagnetic interference) could drive the firmware into a state which results in an unintended explosion. Two probabilistic models are built, based on two possible types of disruptive events: a single spike of interference, and a burst of multiple spikes of interference. The models suggest that the system conforms to the IEC 61508 Safety Integrity Levels, even under very conservative assumptions of operation. The case study serves as a platform for future researchers to build on when modelling probabilistic soft errors in other contexts.
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Kruger HA & Hattingh JM, 2006, A combined AHP-GP model to allocate internal auditing time to projects, ORiON, 22(1), p. 59-76.
Abstract. The optimal allocation of internal auditing time among competing projects is a multi-criteria problem that includes both qualitative and quantitative factors. This paper discusses an integrated approach where the analytic hierarchy process (AHP) is used to deal with qualitative risk assessments and a goal programming (GP) model to distribute available hours in such a way that risk is minimised. Additional considerations, such as maximum and minimum allowable project hours, risk reducing factors and risk levels, are also taken into account. Following a description of the models and framework, a brief case study is presented in which the framework was empirically evaluated.
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Kruger MF & Hattingh JM, 2003, A partitioning scheme for solving the 0-1 knapsack problem, ORiON, 19(1/2), pp. 33-52.
Abstract. The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth included cardinality constraints to derive tight upper bounds for the 0-1 Knapsack Problem. Encouraged by their results, we partition the search space by using equality cardinality constraints. Instead of solving the original problem, an equivalent problem, which consists of one or more 0-1 Knapsack Problem with an exact cardinality bound, is solved. By explicitly including a bound on the cardinality, one is able to reduce the size of each subproblem and compute tight upper bounds. Good feasible solutions found along the way are employed to reduce the computational effort by reducing the number of trees searched and the size of the subsequent search trees. We give a brief description of two Lagrangian-based Branch-and-Bound algorithms proposed in Kruger for solving the exact cardinality bounded subproblems and report on results of numerical experiments with a sequential implementation. Implications for and strategies

towards parallel implementation are also given.

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Kruger PS, 1986, Micro-computer simulation software: A review, ORiON, 2(1), pp. 1-14.
Abstract. Simulation modelling has proved to be one of the most powerful tools available to the Operations Research Analyst. The development of micro-computer technology has reached a state of maturity where the micro-computer can provide the necessary computing power and consequently various powerful and inexpensive simulation languages for micro-computers have became available. This paper will attempt to provide an introduction to the general philosophy and characteristics of some of the available micro-computer simulation languages. The emphasis will be on the characteristics of the specific micro-computer implementation rather than on a comparison of the modelling features of the various languages. Such comparisons may be found elsewhere.
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Kruger PS, 1987, Recent advances in the development of simulation software, ORiON, 3(2), pp. 76-84.
Abstract. Since the first microcomputer simulation languages became available significant developments have taken place such as major enhancements of existing languages, the availability of animation capabilities, the development of simulation systems specifically designed for microcomputers, domain dependent simulators and powerful user interfaces. This paper will attempt to identify, analyse and discuss these trends in the development of microcomputer simulation software, the associated changes that are taking place in the application of the simulation modelling approach and the relevant implications for the simulation user.
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Kruger PS, 1990, Animated simulation models: Miracle or menace, ORiON, 6(2), pp. 53-63.
Abstract. There has been a dramatic increase in the use of computer based simulation modelling over the last decade. A development that has made a significant contribution to the popularity of the simulation approach is the availability of animation facilities. These facilities are usually part of simulation model development software and often do not require very expensive microcomputer equipment. Animation provides some significant advantages during most phases of a simulation modelling effort but also has some inherent dangers and pitfalls. The purpose of this paper is: to identify and discuss some of the more important advantages and disadvantages of animation, and to provide information about some of the available simulation model development software supporting animation capabilities.
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Le Roux NJ, Bothma A & Botha HL, 2004, Statistical properties of indicators of first-year performance at university, ORiON, 20(2), pp. 161-178.
Abstract. Appraisal of admission procedures is a matter of urgency for South African universities, as well as for schools producing the prospective students. In this article the focus is on how various statistical procedures can be used to assess admission measures. Properties of the statistical distributions related to school results, access test results and first-year university performance are vital for decision-makers in schools preparing the prospective students and for those who wish to refine university admission procedures. These properties are scrutinised for the 1999, 2000 and 2001 intake groups required to write access tests before being admitted to Stellenbosch University. Using kernel density estimates the univariate distributions of all variables concerned are described in detail. Bagplots are proposed for visual displays of important features like location, spread, correlation, skewness, outliers and tails of bivariate distributions composed of university average performance and a school result or access test variable. Evidence is provided that certain access tests (Mathematics, Science and Numeracy Skills) have statistical distributions similar to that of average first-year university performance, but that average school marks could not be trusted to discriminate between potentially successful and unsuccessful university students.
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Ltter DP, Nieuwoudt I & Van Vuuren JH, 2013, A multiobjective approach towards weapon assignment in a ground-based air defence environment, ORiON, 29(1), pp. 31-54.
Abstract. A typical ground-based air defence (GBAD) environment comprises defended assets on the ground which require protection from enemy aircraft entering the defended airspace. Protection against these aircraft is afforded by means of pre-deployed ground-based weapon systems that are assigned to engage these enemy aircraft according to some pre-specified criterion or set of criteria. The conditions under which human operators have to propose assignments of weapon systems to engage these aircraft are severely stressful since time is a critical factor and there is no room for error. Some progress has already been made with respect to the design of computerised threat evaluation and weapon assignment (TEWA) decision support systems (DSSs) within the context of a GBAD system. However, the weapon assignment (WA) component within such a TEWA DSS is typically based on a single criterion (objective). The aim in this paper is to model the WA problem as a multiobjective decision problem. A list of relevant factors (related to objectives) is identified by means of feedback received from a WA questionnaire which was completed by a number of military experts. For illustrative purposes, two objectives, namely the cost of assigning weapon systems for engagement and the accumulated survival probabilities of observed threats as a result of these engagements, were isolated from these factors in order to derive a bi-objective WA model. This model is solved in the context of a simulated, but realistic, GBAD environment by means of an existing multiobjective solution technique called the Nondominated Sorting Genetic Algorithm II.
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Ltter DP & Van Vuuren JH, 2016, A tri-objective, dynamic weapon assignment model for surface-based air defence ORiON, 32(1), pp. 1-22.
Abstract. In a military surface-based air defence environment, a fire control officer typically employs a computerised weapon assignment decision support subsystem to aid him in the assignment of available surface-based weapon systems to engage aerial threats in an attempt to protect defended surface assets - a problem known in the military operations research literature as the weapon assignment problem. In this paper, a tri-objective, dynamic weapon assignment model is proposed by modelling the weapon assignment problem as a multi-objective variation of the celebrated vehicle routing problem with time windows. A multi-objective, evolutionary metaheuristic for solving the vehicle routing problem with time windows is used to solve the model. The workability of this modelling approach is illustrated by solving the model in the context of a simulated, surface-based air defence scenario.
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Loubser JS, Visagie SE & Pienaar WJ, 2002, Logistiese beplanning met behulp van simulasiemodellering: 'n gevallestudie, ORiON, 18(1/2), pp. 1-19.
Abstract. This article gives an overview of the combined use of object-oriented programming and simulation, with the objective of analysing and planning the logistic functions of a firm. An object-oriented simulation approach is used to evaluate the reception and distribution function of a courier firm. Both the reception of and operations (sorting) on the parcels in the plant were simulated. The first objective of the firm was to analyse the productivity of the conveyer belts and workers in the sorting plant of the courier firm. The firm's utilisation of most of its resources is fairly good, but it is possible to obtain a more efficient process by restructuring its activities. Results from the simulation study showed an imbalance in the capacities of the workstations. Some of the workers, especially those to the end of the conveyer belts, spent almost all of their time waiting for parcels to reach them, while those at the beginning were working at maximum capacity. This is mainly due to the layout and structure of the system. The biggest bottleneck in the system was the capacity of the coupling between two of the conveyer belts. The conclusion was that the firm should seriously consider redesigning the plant. This is the first computer model of the firm's business activities that can be used as a planning tool, and fills a gap in its current planning function. This simulation can be used to determine where and how workers should be applied in the sorting process. The complete simulation model reaches its potential when used as a strategic operational tool, by forecasting the expected results from changing operations and plant layout. A new plant layout has been proposed to the firm, which the model shows to result in substantial improvements in the productivity of the workers, allowing a reduction in their numbers.
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Love CE, Bird WW, Horsfall RJ & Kingwill J, 1991, Airline seat inventory control benefitting from currency differentials to enhance revenues, ORiON, 7(2), pp. 71-94.
Abstract. The purpose of this paper is to develop an airline seat inventory control model which will capitalise on currency differentials that exist between city pairs. The approach taken here is to maximise Expected Marginal Seat Revenues as proposed by Belobaba for non-nested fare classes. the basic Expected Marginal Seat Revenue model is extended to explicitly include the effects of overbooking. Data from the South African Airways return flight between Cape Town and London is utilised to demonstrate the model.
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Lynch JP, 1996, Numbers for the RDP: The role of the CSS, ORiON, 12(1/2), pp. 15-20.
Abstract. Not available.
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Manson NJ, 2006, Is operations research really research?, ORiON, 22(2), pp. 155-180.
Abstract. This paper takes a philosophical look at the Research in Operations Research. First, the questions "What is Research?" and "What is Operations Research?" are discussed. Next, the paper discusses why it is important to have a clear definition of research, especially in academia. The paper then discusses a research paradigm called 'Design Research'. Design Research is defined and compared with other research paradigms. Seven guidelines for understanding, executing, and evaluating Design Research are presented. As examples, three recently published papers on Operations Research are evaluated using these guidelines. Finally, conclusions are presented discussing why it can be advantageous to understand, execute

and evaluate Operations Research projects within the Design Research paradigm.

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Matthews J & Visagie SE, 2015, SKU assignment to unidirectional picking lines using correlations ORiON, 31(2), pp. 61-76.
Abstract. A real life order picking system consisting of a set of unidirectional picking lines is investigated. Batches of stock keeping units (SKUs) are processed in waves defined as a set of SKUs and their corresponding store requirements. Each wave is processed independently on one of the parallel picking lines as pickers walk in a clockwise direction picking stock. Once all the orders for a wave are completed a new mutually exclusive set of SKUs are brought to the picking line for a new wave. SKUs which differ only in size classification, for example small, medium and large shirts, are grouped together into distributions (DBNs) and must be picked in the same wave. The assignment of DBNs to available picking lines for a single day of picking is considered in this paper. Different assignments of DBNs to picking lines are evaluated using three measures, namely total walking distance, the number of resulting small cartons and work balance. Several approaches to assign DBNs to picking lines have been investigated in literature. All of these approaches seek to minimise walking distance only and include mathematical formulations and greedy heuristics. Four different correlation measure are introduced in this paper to reduce the number of small cartons produced and reduce walking distance simultaneously. These correlation measures are used in a greedy insertion algorithm. The correlation measures were compared to historical assignments as well as a greedy approach which is known to address walking distances effectively. Using correlation measures to assign DBNs to picking lines reduces the total walking distance of pickers by 20% compared to the historical assignments. This is similar to the greedy approach which only considers walking distance as an objective, however, using correlations reduced the number of small cartons produced by the greedy approach.
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Meyer DH, 1993, Modelling in support of decision-making for South African extensive beef farmers, ORiON, 9(2), pp. 37-54.
Abstract. In this study it is shown that it is possible to build a decision support system for the use of South African extensive beef farmers. Initially models for the key variables which affect extensive beef farmers are developed. These key variables include rainfall, beef, veal and weaner prices and the condition of the veld. This last key variable is monitored using the voluntary lick intake of the cattle and is modelled in terms of rainfall and stocking intensity. Particular attention is paid to the interrelationships between the key variables and to the distribution of modelling errors. The next stage of the study concerns the use of these models as a decision-support tool for extensive beef farmers. It is shown that Monte Carlo simulations and dynamic programming analyses can use these models to suggest how gross margins can be increased. At the same time these methods can be used to monitor the effect of management decisions on mean lick intake and, hence, the effect of these decisions on the condition of the veld. In particular the decisions of "what stocking intensity", "what cattle system", "when to sell" and "when to make a change" are addressed.
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Miller J & De Vries L, 1992, Computerized routing: Its time has come, ORiON, 8(1), pp. 12-32.
Abstract. The costs of commercial fleet management in South Africa continue to rise ahead of the inflation rate. Computerised routing and scheduling promises to alleviate the situation provided it is judiciously applied. This article describes the nature of the routing problem and ways to cope with its complexity. Some results of research into South African firms are presented and this leads to a discussion of computer-based routing and scheduling. The authors offer a framework for assessing routing situations and apply it to cases in South Africa. The relative benefits of the application of computer solutions are discussed and recommendations are made.
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Monabbati E, 2013, Uncapacitated facility location problem with self-serving demands, ORiON, 29(2), pp. 169-180
Abstract. In classical uncapacitated facility location problems (UFLP) the goal is to satisfy requirements of some demand points by setting up some servers, among potential facility locations, such that the total cost including service costs and fixed costs are minimized. In this paper a generalization of UFLP is considered in which some demand points, called self-serving, could be served exclusively by a new server at that point. Numerical experiments show that near optimal solutions are achieved by the proposed method.
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Montgomery DC, 2000, The future of industrial statistics, ORiON, 16(1), pp. 1-21.
Abstract. The field of industrial statistics traces its origins from the early part of the previous century. The last 20 years have seen significant advances in both applications of the tools of industrial statistics and in the development of new methodology. The use of statistics in industry, including applications in new product design and development, optimization, and control of manufacturing processes, and in service industries continues to expand at a rapid rate. Consequently, the field of industrial statistics has emerged as an important branch of modern statistical science. These growing applications of statistics in industry have created opportunities and needs for methodological research, and many new challenges have arisen. This paper identifies some areas in which statisticians may contribute to the methodology of industrial statistics and discusses some of the educational and implementation challenges that we confront today.
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Mphahlele MI, Olugbara OO, Ojo SO & Kourie DG, 2011, Cross-impact analysis experimentation using two techniques to revise marginal probabilities of interdependent events, ORiON, 27(1), pp. 1-15.
Abstract. Cross-impact analysis relies on decision makers to provide marginal probability estimates of interdependent events. Generally, these have to be revised in order to ensure overall system coherency. This paper describes cross-impact analysis experimentation in which a Monte Carlo based approach and a difference equation approach, respectively, were used to revise these marginal probabilities. The objective of the study was to determine the consequences of such revisions on the expected impact rankings of these events. A cross-impact analysis system was developed and used to conduct the experiments. The experiments show that the impact ranking of interdependent events may indeed depend on the technique used for revising event marginal probabilities. Moreover, the Monte Carlo technique generates a world view closer to the one of the decision makers, while the world view generated by the difference equation technique differs from that of the decision makers.
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Mubiru PK, 2010, A Markov decision model for optimising economic production lot size under stochastic demand, ORiON, 26(1), pp. 45-52.
Abstract. Traditional approaches towards determining the economic production lot (EPL) size in manufacturing applications assume deterministic demand, often at a constant rate. In this paper, an optimisation model is developed for determining the EPL size that minimises production and inventory costs of a periodic review production-inventory system under stochastic demand. Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces an optimal lot sizing policy, as well as the corresponding total production and inventory costs.
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Munapo E, Jones BC & Kumar S, 2008, A minimum incoming weight label method and its application in CPM networks, ORiON, 24(1), pp. 37-48.
Abstract. An efficient approach towards finding a directed, shortest path or a directed longest path from the source to all other nodes in a directed network is described in this paper. Application of this approach with respect to CPM project networks is also considered. The approach is based on a minimum incoming weight labelling method and determines a critical path for a given project activity network. Although many algorithms exist in the operational research literature that may be used to find critical paths, the method discussed in this paper has an interesting application in determining optimal crash limits for various activities in a CPM network. In case of network topology changes due to any reason, such as that an activity has to be completed in crash duration or the actual duration of an activity takes longer than scheduled, a new critical path and new associated floats can be computed without analyzing the complete network all over again. This is achieved by recycling part of the available information. The algorithm presented in this paper is illustrated by means of numerical examples.
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Nel JH & Hattingh JM, 1992, Techniques that strive to combat the influence of degeneracy in linear programming problems, ORiON, 8(2), pp. 69-89.
Abstract. Degeneracy can cause enormous problems when solving large scale linear programming problems. This is not only because there is a possibility that the problem can cycle, but also because a large number of iterations can be executed that do not improve the objective. In this article a procedure which utilises derived reduced costs is discussed. The derived reduced cost of a non- basic variable is defined in such a way that it makes the introduction to the non-basic variable into the basis unattractive if such a decision fails to improve the objective. The procedure deliberately strives to combat degeneracy using derived reduced costs, but it also utilises the advantageous properties of the classical gradient methods.
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Nel JH, Krygsman SC & De Jong T, 2008, The identification of possible future provincial boundaries for South Africa based on an intramax analysis of journey-to-work data, ORiON, 24(2), pp. 131-156.
Abstract. National census data contain information on place of residence and place of work. It is possible to combine this information and create journey-to-work flows. The process of establishing these flows is presented in this paper. The intramax method is explained and used to identify functional regions based upon these flows. Interesting applications, such as the demarcation of regions in South Africa are considered and solutions to disputed areas are put forward. The process of the creation of the current provincial boundaries is discussed. New boundaries, based on the intramax analysis of the journey-to-work data are proposed for four or five new provinces. Results compare favourably with those from a principal component and cluster analysis, which has previously been used to demarcate the South African space economy into a hierarchy of development regions.
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Nevin JM & Swart J, 1995, A model to compare a defined benefit pension fund with a defined contribution provident fund, ORiON, 11(1/2), pp. 19-40.
Abstract. During 1994 universities and certain other institutions were given the option of setting up private retirement funds as an alternative to the AIPF. Because of the underfundedness of the AIPF only a substantially reduced Actuarial Reserve Value could be transferred to the new fund on behalf of each member. Employees at these institutions had to make the difficult decision of whether to remain a member of the AIPF or to join a new fund. Several institutions created defined contribution funds as an alternative to the AIPF. In such funds the member carries the investment risk and most institutions felt the need to provide some form of top-up of the Transfer Value. A simple mathematical model is formulated to aid in the comparison of expected retirement benefits under the AIPF and a private fund and to investigate the management problem of distributing additional top-up funds in a fair manner amongst the various age groups within the fund.
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Ntene N & Van Vuuren JH, 2008, A survey and comparison of heuristics for the 2D oriented on-line strip packing problem, ORiON, 24(2), pp. 157-183.
Abstract. The two dimensional oriented on-line strip packing problem requires items to be packed, one at a time, into a strip of fixed width and infinite height so as to minimise the total height of the packing. The items may neither be rotated nor overlap. In this paper, ten heuristics from the literature are considered for the special case where the items are rectangles. Six modifications to some of these heuristics are proposed, along with two entirely new shelf algorithms. The performances and efficiencies of all the algorithms are compared in terms of the total packing height achieved and computation time required in each case, when applied to 542 benchmark data sets documented in the literature.
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Nyirenda JC, 2001, Relationship between the modified due date rule and the heuristic of Wilkerson and Irwin, ORiON, 17(1/2), pp. 101-111.
Abstract. In this paper, we consider the problem of scheduling N jobs on a single machine to minimise total tardiness. Both the modified due date (MDD) rule and the heuristic of Wilkerson and Irwin (W-I) are very effective in reducing total tardiness. We show that in fact the MDD rule and the W-I heuristic are strongly related in the sense that both are based on the same local optimality condition for a pair of adjacent jobs, so that a sequence generated by these methods cannot be improved by any further adjacent pair-wise interchange.
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Nyirenda JC, 2006, A rescheduling heuristic for the single machine total tardiness problem, ORiON, 22(1), pp. 77-87.
Abstract. In this paper, we propose a rescheduling heuristic for scheduling N jobs on a single machine in order to minimise total tardiness. The heuristic is of the interchange type and constructs a schedule from the modified due date (MDD) schedule. Unlike most interchange heuristics that consider interchanges involving only two jobs at a time, the newly proposed heuristic uses interchanges that may involve more than two jobs at any one time. Experimental results show that the heuristic is effective at reducing total tardiness producing schedules that either similar or better than those produced by the MDD alone. Furthermore, when applied to some test problems the heuristic found optimal schedules to all of them.
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Oberholzer JA, Hattingh JM & Steyn T, 2014, Efficient waste reduction algorithms based on alternative underestimates for the modified Wang method ORiON, 30(2), pp. 73-83.
Abstract. This paper is concerned with wastage reduction in constrained two-dimensional guillotine-cut cutting stock problems, often called trim loss problems. A number of researchers report in the literature on algorithmic approaches to find exact solutions for the trim loss problem. Alternative heuristic functions are investigated and applied to the modified Wang method. This involves the sharpening of underestimates used in the methods heuristic function. Two aspects of these solution approaches are considered and some empirical results are given. The first part considers the feasibility to construct more informed heuristic functions. The second part investigates the role of more informedness on the computational cost of these search processes.
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Oladele OS & Bradfield D, 2016, Low volatility sector-based portfolios: a South African case ORiON, 32(1), pp. 55-78.
Abstract. Portfolios and indices that have been specifically constructed to have low risk attributes have received increasing interest in the recent international literature. It has been found that portfolios constructed by targeting low risk assets have predominantly outperformed portfolios constructed to have higher risks. This anomaly has led to renewed interest in constructing low volatility portfolios by practitioners. This study analyses a variety of low volatility portfolio construction methodologies using sectors as building blocks in the South African environment. The empirical results from back-testing these portfolios show significant promise in the South African setting when compared with a market capitalization-weighted benchmark. In the empirical analysis in the South African environment two techniques stand out as being superior low volatility construction techniques amongst the seven techniques assessed. Furthermore, the low volatility portfolios are blended with typical general equity portfolios (using the Shareholder-Weighted Index (SWIX) as a proxy). It was found that these blended portfolios have useful features which lead to enhanced performance and therefore can serve as effective portfolio strategies.
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Ormerod RJ, 1993, The role of OR in strategy development, ORiON, 9(2), pp. 71-88.
Abstract. Reflecting on the experiences of applying OR approaches in a variety of contexts, the paper draws attention to some of the ways that OR can be brought to bear on strategic issues. Perhaps most frequently the strategic contribution derives from projects aimed at operational issues which have strategic implications. The paper argues that OR practitioners cannot expect to be given a role in strategy questions as of right, nor is there an "OR solution" to strategic questions. However, many OR scientists do have the skills, approaches and methods that can be usefully deployed, if they develop the confidence to do so.
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Ortmann FG, Van Vuuren JH & Van Dyk FE, 2006, Modelling the South African fruit export infrastructure: A case study, ORiON, 22(1), p.35-57.
Abstract. A description is provided of work performed as part of the fruit logistics infrastructure project commissioned by the South African Deciduous Fruit Producers� Trust and coordinated by the South African Council for Scientific and Industrial Research, as described in [Van Dyk FE & Maspero E, 2004, An analysis of the South African fruit logistics infrastructure, ORiON, 20(1), pp. 55�72]. After a brief introduction to the problem, two models (a single-commodity graph theoretic model and a multi-commodity mathematical programming model) are derived for determining the maximal weekly flow or throughput of fresh fruit through the South African national export infrastructure. These models are solved for two extreme seasonal export scenarios and the solutions show that no export infrastructure expansion is required in the near future � observed bottlenecks are not fundamental to the infrastructure and its capacities, but are rather due to sub-optimal management and utilisation of the existing infrastructure.
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Ortmann FG & Van Vuuren JH , 2010, Modified strip packing heuristics for the rectangular variable-sized bin packing problem, ORiON, 26(1), pp. 21-44.
Abstract. Two packing problems are considered in this paper, namely the well-known strip packing problem (SPP) and the variable-sized bin packing problem (VSBPP). A total of 252 strip packing heuristics (and variations thereof) from the literature, as well as novel heuristics proposed by the authors, are compared statistically by means of 1170 SPP benchmark instances in order to identify the best heuristics in various classes. A combination of new heuristics with a new sorting method yields the best results. These heuristics are combined with a previous heuristic for the VSBPP by the authors to find good feasible solutions to 1357 VSBPP benchmark instances. This is the largest statistical comparison of algorithms for the SPP and the VSBPP to the best knowledge of the authors.
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Ouwehand P, 2010, A simple proof of Debreu's Gap Lemma, ORiON, 26(1), pp. 17-20.
Abstract. Debreu's Gap Lemma is central to the proof of his fundamental result on the existence of continuous utility functions. A short proof based on a standard textbook construction of utility functions on countable linearly ordered sets is presented here. The proof is accessible to students with limited mathematical background, thus making it suitable for inclusion in elementary texts on utility theory.
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Passy U, 1990, Optimal design of network distribution systems, ORiON, 6(2), pp. 64-78.
Abstract. The problem of finding the optimal distribution of pressure drop over a network is solved via an unconstrained gradient type algorithm. The developed algorithm is computationally attractive. Problems with several hundred variables and constraints were solved.
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Paterson AE, 1986, Decision management - projects subject to uncertainty, ORiON, 2(2), pp. 100-125.
Abstract. The human mind is normally unable to grasp more than five to nine aspects relating to the same decision circumstances simultaneously. It has been demonstrated that only between four and eight variables significantly affect return on engineering projects (at the 90% level) irrespective of scale. The most powerful means of isolating these significant variables is by computer simulation. This is demonstrated through the application of the interactive CASPAR programme to a simulated mining project. The significant variables are separated into controllable, influence able and uncontrollable categories for decision and control purposes since the nature of the speculative risk differs. The managerial treatment of each category is discussed.
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Pembridge TJ, 1985, A holistic approach to planning agricultural development: A comparative study of Taiwan and Transkei, ORiON, 1(1), pp. 16-27.
Abstract. The study discusses the application of a systems approach model to agricultural development in Taiwan and Transkei in determining development needs and priorities. The model consists of the interactions between and within four groups of factors: (i) physical and ecological, (ii) institutional and operational, (iii) the human potential, and (iv) the agri-milieu.
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Phala JM, 1988, A university course timetabling problem, ORiON, 4(2), pp. 92-102.
Abstract. This paper addresses a university course timetabling problem. The problem as experienced at Unibo is formulated in such a way that simple heuristics can be used to achieve the objective of finding either an 'optimal' or a feasible practical solution. the problem is divided into three phases, namely grouping of courses into course groups, allocation of lecture rooms to courses within groups, and finally, scheduling of periods to course groups. Heuristic algorithms are proposed to solve this problem. The computerised algorithms which have been integrated into Unibo's Student Management System are fully implemented.
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Pienaar WJ, 2005, Operations Research: An indispensable toolkit for the logistician, ORiON, 21(1), pp. 77-91.
Abstract. This paper traces the origin of the word logistics, outlines its conceptual evolution, and explains its meaning in contemporary usage. The background that led to the introduction of Logistics Management and Operations Research (OR) as undergraduate fields of study at the University of Stellenbosch is sketched. The concept of Logistics Management is described and its strategic, tactical and operational tiers, as well as the different activities that form part of the logistics supply chain process are identified. The role and necessity of OR in decision-making within each activity and in the coordination between the various activities are outlined. OR techniques most pertinent to the field of logistics are identified and the analytical competencies that a logistician should possess are indicated.
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Pienaar WJ & Nel JH, 2009, Mathematical principles of road congestion pricing, ORiON, 25(1), pp. 45-51.
Abstract. This paper briefly considers the objectives of road congestion pricing and identifies prerequisites to the successful application of such a pricing scheme. The paper is divided into two sections. In the first section, a mathematical analysis of the constituents of an optimal road congestion price is offered. The eliminated inefficiency loss achieved by the introduction of a congestion levy is usually evaluated by means of an integral involving marginal trip cost, travel demand and average trip cost in two-dimensional (travel time, traffic flow)-space. In this section we show that this loss may, in fact, be evaluated more easily for a general marginal trip cost function and a linear demand function as the difference between the areas of a rectangle (representing the part of road agency revenue that lies below the original trip cost) and a triangle (representing the loss of consumer surplus of the reduced traffic) in (travel time, traffic flow)-space, eliminating the need to use integration. The next section deals with the application of the illustrated mathematical principles and proofs to a hypothetical case study relating to road congestion pricing in Cape Town.
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Potgieter L, Van Vuuren JH & Conlong DE, 2012, Modelling the effects of the sterile insect technique applied to Eldana saccharina Walker in sugarcane, ORiON, 28(2), pp. 59-84.
Abstract. A mathematical model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The model describes the population growth of and interaction between normal and sterile E.saccharina moths in a temporally variable, but spatially homogeneous environment. The model consists of a deterministic system of difference equations subject to strictly positive initial data. The primary objective of this model is to determine suitable parameters in terms of which the above population growth and interaction may be quantified and according to which E.saccharina infestation levels and the associated sugarcane damage may be measured. Although many models have been formulated in the past describing the sterile insect technique, few of these models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these models consider the technique when fully sterile females and partially sterile males are being released. The model formulated is also the first to describe the technique applied specifically to E.saccharina, and to consider the economic viability of applying the technique to this species. Pertinent decision support is provided to farm managers in terms of the best timing for releases, release ratios and release frequencies.
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Quinn NW, Green CM, Hearne JW & Whitfield AK, 1998, Decision support systems for environmental management: A case study, ORiON, 14(1/2), pp. 17-35.
Abstract. In situations to do with the management of natural resources in the public domain there are often many 'interested and affected parties'. The opinions of how a given resource should be managed are as diverse as the parties themselves. Debates are frequently unproductive. We argue that in these situations the development of a decision support system (DSS) is a constructive way forward towards sound management practices. This approach enables existing knowledge to be integrated into a form that can be used immediately in decision-making. Furthermore, research can be optimally prioritised should greater accuracy or improvement in the initial DSS be required. We illustrate this approach by considering the problem of determining the freshwater requirements of estuaries. The pattern of freshwater flow into estuary of a river that has been impounded is a management decision. This inflow pattern influences the state of an estuary. This in turn affects the fish that use the estuary. In this illustration we focus on these fish in developing a DSS. The DSS is then applied in a case study of the Krom River in the Eastern Cape.
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Raad DN, Sinske A & Van Vuuren JH, 2011, Water distribution systems design optimisation using metaheuristics and hyperheuristics, ORiON, 27(1), pp. 17-43.
Abstract. The topic of multi-objective water distribution systems (WDS) design optimisation using metaheuristics is investigated, comparing numerous modern metaheuristics, including several multi-objective evolutionary algorithms, an estimation of distribution algorithm and a recent hyperheuristic named AMALGAM (an evolutionary framework for the simultaneous incorporation of multiple metaheuristics), in order to determine which approach is most capable with respect to WDS design optimisation. Novel metaheuristics and variants of existing algorithms are developed, for a total of twenty-three algorithms examined. Testing with respect to eight small-to-large-sized WDS benchmarks from the literature reveal that the four top-performing algorithms are mutually non-dominated with respect to the various performance metrics used. These algorithms are NSGA-II, TAMALGAMJ_ndu, TAMALGAM_ndu and AMALGAMS_ndp (the last three being novel variants of AMALGAM). However, when these four algorithms are applied to the design of a very large real-world benchmark, the AMALGAM paradigm outperforms NSGA-II convincingly, with AMALGAMS_ndp exhibiting the best performance overall.
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Raghavjee R & Pillay N, 2015, A genetic algorithm selection perturbative hyper-heuristic for solving the school timetabling problem ORiON, 31(1), pp. 39-60.
Abstract. Research in the domain of school timetabling has essentially focused on applying various techniques such as integer programming, constraint satisfaction, simulated annealing, tabu search and genetic algorithms to calculate a solution to the problem. Optimization techniques like simulated annealing, tabu search and genetic algorithms generally explore a solution space. Hyper-heuristics, on the other hand, search a heuristic space with the aim of providing a more generalized solution to the particular optimisation problem. This is a fairly new technique that has proven to be successful in solving various combinatorial optimisation problems. There has not been much research into the use of hyper-heuristics to solve the school timetabling problem. This study investigates the use of a genetic algorithm selection perturbative hyper-heuristic for solving the school timetabling problem. A two-phased approach is taken, with the first phase focusing on hard constraints, and the second on soft constraints. The genetic algorithm uses tournament selection to choose parents, to which the mutation and crossover operators are applied. The genetic algorithm selection perturbative hyper-heuristic (GASPHH) was applied to five different school timetabling problems. The performance of the hyper-heuristic was compared to that of other methods applied to these problems, including a genetic algorithm that was applied directly to the solution space. GASPHH performed well over all five different types of school timetabling problems.
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Ramanath K & Lakshmi P, 2006, Modelling M/G/1 queueing systems with server vacations using stochastic Petri nets, ORiON, 22(2), pp. 131-154.
Abstract. The theory of non-Markovian stochastic Petri nets is employed in this paper to derive an alternative method for studying the steady state behaviour of the M/G/1 vacation queueing system with a limited service discipline. Three types of vacation schemes are considered, and sytems with both a finite population and those with an infinite population (but finite capacity) are considered. Simple numerical examples are also provided to illustrate the functionality of the methods and some useful performance measures for the system are obtained.
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Rand GK, 2009, The life and times of the Savings Method for Vehicle Routing Problems, ORiON, 25(2), pp. 125-145.
Abstract. Forty five years ago, an academic and practitioner from the north of England published a method of tackling the vehicle routing problem (VRP) in an American journal. Little could they have realised how the method they devised would still be a significant part of the research agenda nearly half a century later. Adaptations of their method are significant components in the analysis of the many different extensions to the problem that have been investigated. This paper provides the historical background to the development of the savings method and subsequent proposed variations to the basic savings formula and other improvements, and then charts the role the savings method has played in the investigation of VRPs with additional constraints. Some interesting examples of practical applications of the savings method are reported. Finally, comments are made on the use of the savings method in commercial routing packages.
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Rodtook S, Makhanov SS & Vanderperre EJ, 2005, A filter bank for rotationally invariant image recognition, ORiON, 21(2), pp. 125-138.
Abstract. We present new rotation moment invariants based on multiresolution filter bank techniques. The multiresolution pyramid motivates our simple but efficient feature selection procedure based on the fuzzy C-mean clustering methodology combined with the Mahalanobis distance measure. The proposed procedure verifies an impact of random noise as well as an interesting, less known impact of noise due to spatial transformations. The recognition accuracy of the proposed technique has been tested with the Zernike moments, the Fourier-Mellin moments as well as with wavelet based schemes. The numerical experiments, with more than 30 000 images, demonstrate a tangible accuracy increase of about 3% for low level noise, 8% for the average level noise and 15% for high level noise.
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Roos E, 2004, A bio-economic application to the Cape Rock Lobster resource using a delay difference modelling approach, ORiON, 20(1), pp. 7-28.
Abstract. In many species, like the Cape Rock Lobster (Jasus lalandii), the life cycles of males and females differ. This may motivate the use of two-sex models in a stock-assessment analysis. It is also true for this resource, that juveniles do not reach sexual maturity immediately. Therefore a delay-difference model is appropriate. In this study we follow a bio-economic approach and use a two-sex delay-difference model to determine a maximum economic yield strategy. Thus we determine an economic optimum steady state solution at which to harvest this resource subject to the biological constraints of the species.
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Rosenhead J, 1996, Enabling analysis: Across the development divide, ORiON, 12(1/2), pp. 69-103.
Abstract. It is argued in this paper that a least certain strands of operational research (OR) carried out in less developed countries have intriguing similarities with community operational research. It follows that community OR, which is still short of accounts of actual practice, might learn from OR aimed at promoting the self-reliance of communities in developing countries. The paper starts with community operational research - its origin, nature, clientele, and methods. This is followed by a parallel discussion of the characteristics of operational research aligned with third-world community development. A final section explores the common themes between the two literatures and practices.
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Rossouw JA, 1993, Comparing the performance of weapon systems in terms of an application role, ORiON, 9(1), pp. 21-35.
Abstract. A method is presented for assigning a figure of merit to a weapon system, based on the weapon's suitability for a particular application role. The procedure involves correlating expected scenario parameter distributions with functions depicting the weapon system's dependence on these parameters. The procedure was motivated by the need for a choice between weapons to fulfil a role for which none of them were originally intended. The method is, however, suitable for any comparison where the application scenario plays a major role.
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Rossouw RF, Coetzer RJL & Pretorius PD, 2010, Simulation experiments for maximising the availability of a commercial octene production facility, ORiON, 26(1), pp. 53-77.
Abstract. Overall availability of a chemical process is of critical importance in industry. In this paper we evaluate the process design factors that influence the availability of a new chemical production facility by performing computer experiments on a stochastic simulation model. Experimental designs commonly used in the Design and Analysis of Computer Experiments (DACE) and Classical Design of Experiments (DOE) are evaluated and compared for application by means of simulation experiments. Furthermore, response surface and kriging models are evaluated for the approximation of the input-output relationships. The most accurate experimental design by approximation model combination is used to explore the design space, both in terms of the overall availability and the percentage time offline. We illustrate how the design and analysis of simulation experiments (DASE) are used for minimizing the risks in the design of a new 1-octene production facility in terms of maximising the overall availability and minimizing the percentage time offline simultaneously.
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Roux JN & Van Vuuren JH, 2007, Threat evaluation and weapon assignment decision support: A review of the state of the art, ORiON, 23(2), pp. 151-187.
Abstract. In a military environment an operator is typically required to evaluate the tactical situation in real-time and protect defended assets against enemy threats by assigning available weapon systems to engage enemy craft. This environment requires rapid operational planning and decision making under severe stress conditions, and the associated responsibilities are usually divided between a number of operators and computerized decision support systems that aid these operators during the decision making processes. The aim in this paper is to review the state of the art of this kind of threat evaluation and weapon assignment decision support process as it stands within the context of a ground based air defence system (GBADS) at the turn of the twenty first century. However, much of the contents of the paper may be generalized to military environments other than a GBADS one.
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Roux JN & Van Vuuren JH, 2008, Real-time threat evaluation in a ground based air defence environment, ORiON, 24(1), pp. 75-101.
Abstract. In a military environment a ground based air defence operator is required to evaluate the tactical situation in real-time and protect Defended Assets (DAs) on the ground against aerial threats by assigning available Weapon Systems (WSs) to engage enemy aircraft. Since this aerial environment requires rapid operational planning and decision making in stress situations, the associated responsibilities are typically divided between a number of operators and computerized systems that aid these operators during the decision making processes. One such a Decision Support System (DSS), a threat evaluation and weapon assignment system, assigns threat values to aircraft (with respect to DAs) in real-time and uses these values to propose possible engagements of observed enemy aircraft by anti-aircraft WSs. In this paper a design of the threat evaluation part of such a DSS is put forward. The design follows the structured approach suggested in [Roux JN & van Vuuren JH, 2007, Threat evaluation and weapon assignment decision support: A review of the state of the art, ORiON, 23(2), pp. 151-187], phasing in a suite of increasingly complex qualitative and quantitative model components as more (reliable) data become available.
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Saaty TL, 1988, The negotiation and resolution of the conflict in South Africa: The AHP, ORiON, 4(1), pp. 3-25.
Abstract. The theory of retributive conflict solution with regard to the problem in South Africa is illustrated in this article. It is assumed that there are only two parties in the conflict: Blacks and the Whites. A set of feasible concessions is derived for both sides to solve the problem over the short, medium and long term. The decision model of the negotiator in both cases is discussed and tables are included. It was found from this preliminary exercise that it is possible to derive an equitable solution according to the demands being made by both sides. A major limitation has been the use which had to be made of surmised hierarchies and judgements gleaned from available literature. It would be preferable were the parties to the conflict to do this themselves. The analysis of this paper is concerned with a negotiated solution of the conflict in South Africa with the aid of a mediator, if necessary.
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Sandrock K, 1987, Two simple tools for industrial OR, ORiON, 3(1), pp. 23-41.
Abstract. At the 1985 Annual Congress of the South African Production & Inventory Control Society it was pointed out that the productivity growth rate for South Africa is completely out of kilter with that for the western industrialised nations. The latter all display positive rates (some as high as that of Japan) whereas the rate for South Africa is - NEGATIVE. Partly as a result of this situation, more and more attention is being given to quality control and reliability engineering by our industrialists in their attempts to improve productivity. This is going hand in hand with the introduction of better techniques and better use of the latest technology. We should also give attention to analytical tools that may be used in a simple inexpensive way to improve our methods of analysing industrial data, and in this way to improve our performance at little or no additional cost. To this end two tools are discussed. They are by means new. But it does seem as though they could be more widely applied in the industrial milieu.
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Sandrock K, 1991, A TQC philosophy, ORiON, 7(1), pp. 38-56.
Abstract. There has been a recent upsurge in the quest for world class manufacturing. Tremendous amounts of effort are being exerted to attain Total quality Control (TQC) - so as to be able to produce "the best". The EEC has stated categorically that it will only support accredited suppliers, and this has been partly responsible for the recent fixation on techniques for excellence. These techniques often fail to produce results. This paper presents a systems based philosophy for working towards world class levels of manufacturing.
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Scholtz E, Bekker J & Du Toit D, 2012, Multi-objective optimisation with stochastic discrete-event simulation in retail banking: A case study, ORiON, 28(2), pp. 117-135.
Abstract. The cash management of an autoteller machine (ATM) is a multi-objective optimisation problem which aims to maximise the service level provided to customers at minimum cost. This paper focus on improved cash management in a section of the South African retail banking industry, for which a decision support system (DSS) was developed. This DSS integrates four Operations Research (OR) methods: the vehicle routing problem (VRP), the continuous review policy for inventory management, the knapsack problem and stochastic, discrete-event simulation. The DSS was applied to an ATM network in the Eastern Cape, South Africa, to investigate 90 different scenarios. Results show that the application of a formal vehicle routing method consistently yields higher service levels at lower cost when compared to two other routing approaches, in conjunction with selected ATM reorder levels and a knapsack-based notes dispensing algorithm. It is concluded that the use of vehicle routing methods is especially beneficial when the bank has substantial control over transportation cost.
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Scogings CJ & Uys PW, 1995, Optimising of resource utilisation at a university - an allocation problem, ORiON, 11(1/2), pp. 5-17.
Abstract. Student enrolment at the University of Natal has been increasing steadily over the years. Moreover additional new courses are introduced from time to time. Despite this State subsidies are declining in real terms. These factors imply escalating demands on physical resources. Historically, at this university, lecture rooms have been used only during the mornings and laboratories only during the afternoons. An obvious solution to meet the demand for accommodation is to double up on the number of timetabled periods so that the lecture rooms are in use the whole day. Since there are many classes which are in fact too large to be accommodated in any one room it is also necessary to split these classes into separate lecture groups. Likewise classes have to be divided up into several smaller groups for laboratory and tutorial sessions. The policy at this university is to encourage students to choose curricula including courses selected from as wide a range as possible. The above timetable strategy apparently facilitates this. In practice, however, to ensure that student numbers are evenly distributed across alternative sessions for a given course and to do this for all courses simultaneously while avoiding clashes is not a simple matter.
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Scott L, 2005, Unpacking developmental local government using Soft Systems Methodology and MCDA tools, ORiON, 21(2), pp. 173-195.
Abstract. This paper presents two different analytical approaches that may be useful in developing an understanding of developmental local government (DLG). DLG implies a significant commitment with respect to poverty relief at the local administrative level as well as strong emphasis on participation and accountability to communities. This paper attempts to apply Soft Systems Methodology (SSM) to clarify the activities that DLG implies for local authorities and focuses specifically on their ability to be developmental and to effectively impact upon poverty. An expected product of this approach will be the identification of specific indicators of (inter alia) poverty that may be used to monitor the effectiveness of local government from a constitutional and developmental perspective. Indicators may also be generated from the perspective of community needs and this paper reports on a case study which identifies the needs of a small community, Pniel, in the South African Western Cape, using a Multi-Criteria Decision Analysis approach. This approach allows for both the identification and prioritisation of issues from the perspective of the community. Further, it is suggested that the SSM approach can be used to provide a context within which community needs may be considered. This framework clarifies what it is that local government have the aims, powers and functions to perform. Viewing the community needs within this framework provides a mechanism for realistically linking the community needs to the local authority�s budget. A process of ongoing monitoring and evaluation of DLG, using the two sets of indicators, can assist to focus the functioning of local government on effective poverty relief.
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Seegmuller DM, Visagie SE, De Kock HC & Pienaar WJ, 2007, Selection and scheduling of jobs with time-dependent duration, ORiON, 23(1), pp. 17-28.
Abstract. In this paper two mathematical programming models, both with multiple objective functions, are proposed to solve four related categories of job scheduling problems. All four of these categories have the property that the duration of the jobs is dependent on the time of implementation and in some cases the preceding job. Furthermore, some jobs (restricted to subsets of the total pool of jobs) can, to different extents, run in parallel. In addition, not all the jobs need necessarily be implemented during the given time period.
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Sharma NK, Kumar S & Singh MP, 2009, Conjugate descent formulation of backpropagation error in feedforward neural networks, ORiON, 25(1), pp. 69-86.
Abstract. The feedforward neural network architecture uses backpropagation learning to determine optimal weights between different interconnected layers. This learning procedure uses a gradient descent technique applied to a sum-of-squares error function for the given input-output pattern. It employs an iterative procedure to minimise the error function for a given set of patterns, by adjusting the weights of the network. The first derivates of the error with respect to the weights identify the local error surface in the descent direction. Hence the network exhibits a different local error surface for every different pattern presented to it, and weights are iteratively modified in order to minimise the current local error. The determination of an optimal weight vector is possible only when the total minimum error (mean of the minimum local errors) for all patterns from the training set may be minimised. In this paper, we present a general mathematical formulation for the second derivative of the error function with respect to the weights (which represents a conjugate descent) for arbitrary feedforward neural network topologies, and we use this derivative information to obtain the optimal weight vector. The local error is backpropagated among the units of hidden layers via the second order derivative of the error with respect to the weights of the hidden and output layers independently and also in combination. The new total minimum error point may be evaluated with the help of the current total minimum error and the current minimised local error. The weight modification processes is performed twice: once with respect to the present local error and once more with respect to the current total or mean error. We present some numerical evidence that our proposed method yields better network weights than those determined via a conventional gradient descent approach.
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Sigauke C & Chikobvu D, 2010, Daily peak electricity load forecasting in South Africa using a multivariate non-parametric regression approach, ORiON, 26(2), pp. 97-111.
Abstract. Accurate prediction of daily peak load demand is very important for decision makers in the energy sector. This helps in the determination of consistent and reliable supply schedules during peak periods. Accurate short term load forecasts enable effective load shifting between transmission substations, scheduling of startup times of peak stations, load flow analysis and power system security studies. A multivariate adaptive regression splines (MARS) modelling approach towards daily peak electricity load forecasting in South Africa is presented in this paper for the period 2000 to 2009. MARS is a non-parametric multivariate regression method which is used in high-dimensional problems with complex model structures, such as nonlinearities, interactions and missing data, in a straight forward manner and produces results which may easily be explained to management. The models developed in this paper consist of components that represent calendar and meteorological data. The performances of the models are evaluated by comparing them to a piecewise linear regression model. The results from the study show that the MARS models achieve better forecast accuracy.
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Sinclair M, 1985, The assignment of workers to tasks - An example from an academic department, ORiON, 1(2), pp. 49-69.
Abstract. A description is given of the application of Operations Research techniques to the problem of assigning lecturers to tasks in an academic department. All the steps in the approach are described - from the collection of the data through the building of a mathematical model to the implementation of the solution. Two approaches to obtaining a solution are described. Firstly a heuristic method is shown which can be done with pencil and paper. The solution obtained with this method can be used for implementation, or it can be used as a starting solution for the computer package used for the solution of the mathematical model.
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Sinclair M, 1989, A case study in value design, ORiON, 5(2), pp. 59-67.
Abstract. The design of a special type of valve gave rise to a problem which lead the mechanical engineers who designed the valve to call in the help of the author. The final solution to the problem may not be mathematically sophisticated (in fact, it may seem trivial to some readers), but the steps through which the design team struggled and the final approach which resulted in a practically feasible solution may be of interest to other practitioners.
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Sinclair M & Esterhuyzen DG, 1991, Allocating conference delegates to workshops: A special timetabling problem, ORiON, 7(2), pp. 95-103.
Abstract. The problem of assigning delegates to workshops at a conference can be formulated as a timetabling problem. Such an assignment must take into account the preferences of the delegates, as well as the number of participants each workshop can accommodate. This paper will report on a heuristic solution technique for a special case of such a problem. An implementation of the method for the solution of a real world problem will also be reported.
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Sinclair M & Winstanley MM, 1994, A heuristic solution for the stability problem in conventional submarines, ORiON, 10(1/2), pp. 33-43.
Abstract. Seafaring vessels must meet a few very obvious conditions in order to be of any use. The one condition is that they should stay afloat when loaded. The other condition is that they should float upright and with a level keel. The technical terms for these conditions are gravitational stability and trim. In practice some very precise numerical values are calculated for certain parameters in order to describe these conditions. After each refit of a submarine, the numerical values for the parameters referred to above must be recalculated. In the conventional submarines used by the South African Navy these new values must then be translated into the physical redistribution of weights housed in bays in the keel of the submarine. This paper discusses the problem of how this redistribution must be done in order to minimise the amount of work necessary. A heuristic algorithm is proposed by means of which a satisfactory redistribution may economically be computed.
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Sivakumar B, Anbazhagan N & Arivarignan G, 2005, A two-commodity perishable inventory system, ORiON, 21(2), pp. 157-172.
Abstract. We present a two-commodity perishable stochastic inventory system under continuous review at a service facility with a finite waiting room. The maximum storage capacity for the i-th item is fixed as Si (i = 1,2). We assume that a demand for the i-th commodity is of unit size. The arrival instants of customers to the service station constitutes a Poisson process with parameter lambda. The customer demands for these commodities are assumed to be in the ratio p1 : p2. An individual customer is issued a demanded item after a random time of service with a negative exponential distribution. The items are perishable in nature and the life time of items of each commodity is assumed to be exponentially distributed. Both commodities are supposed to be substitutable in the sense that at the instant of any zero-stock, the other item may be used to meet the demand. A joint reordering policy is adopted with a random lead time for orders with exponential distribution. The joint probability distribution of the number of customers in the system and the inventory levels are obtained in both the transient and steady states. We also derive some stationary performance measures. The results are illustrated by means of a numerical example.
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Smit CF, 1996, An analysis of key RDP issues and proposed support by the statistical profession, ORiON, 12(1/2), pp. 42-53.
Abstract. Not available.
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Steel SJ & Uys DW, 2007, Variable selection in multiple linear regression: The influence of individual cases, ORiON, 23(2), pp. 123-136.
Abstract. The influence of individual cases in a data set is studied when variable selection is applied in multiple linear regression. Two different influence measures, based on the Cp criterion and Akaike�s information criterion, are introduced. The relative change in the selection criterion when an individual case is omitted is proposed as the selection influence of the specific omitted case. Four standard examples from the literature are considered and the selection influence of the cases is calculated. It is argued that the selection procedure may be improved by taking the selection influence of individual data cases into account.
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Stewart TJ, 1989, A review of simple multiple criteria decision making analytic procedures which are implementable on spreadsheet packages, ORiON, 5(1), pp. 24-51.
Abstract. A number of modern multi-criteria decision making aids for the discrete choice problem, are reviewed, with particular emphasis on those which can be implemented on standard commercial spreadsheet packages. Three broad classes of procedures are discussed, namely the analytic hierarchy process, reference point methods, and outranking methods. The broad principles are summarised in a consistent framework, and on a spreadsheet. LOTUS spreadsheets implementing these are available from the author.
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Stewart TJ, 1998, Measurements of risk in fisheries management, ORiON, 14(1/2), pp. 1-15.
Abstract. An important goal in many fisheries management problems is perceived to be minimisation of risk. This paper examines the problem of measuring risk by means of meaningful attributes or surrogate measures, for use in multiple criteria decision support systems. It is found that exponential utility functions, which are associated in this context with geometric discounting of the future, give a poor fit in many cases relative to power functions. The implication is that conventional mean-variance measures of risk may be less appropriate than cumulative probability measures.
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Stewart TJ, 2007, The essential multiobjectivity of linear programming, ORiON, 23(1), pp. 1-15.
Abstract. It is argued that any non-trivial real world problems involve multiple objectives. The simplistic approach of combining objectives in linear form can generate highly misleading and biased results, and is poor operational research practice. Such biases are illustrated by means of a simple example, and it is demonstrated that two simple approaches based on goal programming and piecewise linear value functions can largely resolve these problems. These methods require careful attention to problem structuring but are easily implemented by use of standard linear programming (LP) packages.
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Steyn T & Hattingh JM, 2015, An exact algorithm for the N-sheet two dimensional single stock-size cutting stock problem ORiON, 31(2), pp. 77-94.
Abstract. The method introduced in this paper extends the trim-loss problem or also known as 2D rectangular SLOPP to the multiple sheet situation where N same size two-dimensional sheets have to be cut optimally producing demand items that partially or totally satisfy the requirements of a given order. The cutting methodology is constrained to be of the guillotine type and rotation of pieces is allowed. Sets of patterns are generated in a sequential way. For each set found, an integer program is solved to produce a feasible or sometimes optimal solution to the N-sheet problem if possible. If a feasible solution cannot be identified, the waste acceptance tolerance is relaxed somewhat until solutions are obtained. Sets of cutting patterns consisting of N cutting patterns, one for each of the N sheets, is then analysed for optimality using criteria developed here. This process continues until an optimal solution is identified. Finally, it is indicated how a given order of demand items can be totally satisfied in an optimal way by identifying the smallest N and associated cutting patterns to minimize wastage. Empirical results are reported on a set of 120 problem instances based on well known problems from the literature. The results reported for this data set of problems suggest the feasibility of this approach to optimize the cutting stock problem over more than one same size stock sheet. The main contribution of this research shows the details of an extension of the Wang methodology to obtain and prove exact solutions for the multiple same size stock sheet case.
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Stock JR, 2009, A research review of supply chain management: Developments and topics for exploration, ORiON, 25(2), pp. 147-160.
Abstract. There have been advances in the understanding of supply chain management (SCM) since its inception in the early-1980s. However, there are still some basic issues of SCM that remain unresolved. Much of the research that has been conducted takes one or more of the following three perspectives: (1) development of methods and techniques to study SCM and its components/processes; (2) developing solutions or answers to specific supply chain-related problems or challenges; and/or (3) measuring the results or outcomes of supply chain strategies and tactics. Each of these three perspectives is briefly examined, with selected examples from the literature cited to illustrate the type of research that has been conducted. Some potential areas of research exploration are presented. The areas examined include: theory development, and SCM processes and functions.
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Swan WH, 1986, The use of visual interactive simulation techniques for production scheduling, ORiON, 2(2), pp. 34-51.
Abstract. During the last decade visual interactive simulation has become established as a useful new tool for solving real life problems. It offers the Operational Research professional the opportunity to impact beneficially on important new decision making areas of business and industry. As an example, this paper discusses its application to the scheduling of production on batch chemical plants, which to date has remained largely a manual activity. Two different approaches are introduced, and it is concluded that while discrete event simulation is most useful as an aid to learning at a time of change, bar chart simulation is preferred for the day to day scheduling. The technique has been implemented on a number of plants and has led to significant improvements in their performance. Some areas for further development are identified.
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Swart J, 1990, Sensitivity of a mathematical model used to optimize revenue in a predation-competative farming environment, ORiON, 6(1), pp. 37-52.
Abstract. Sheep farmers in the Cape Midlands region of South Africa frequently sustain stock losses through predation by caracal lynx. Further losses are incurred when hyrax compete with sheep for available pasture. Hyrax constitute the natural prey for lynx with the result that culling either hyrax or lynx has complicated feedback effects. In order to investigate the spill-over problems from the natural predator-prey system on farming revenue, a differential equations model was previously formulated, comprising the sectors Hyrax, Lynx, Sheep, Pasture and Revenue and an optimisation procedure was used to determine the optimal culling rate policy for farmers. The purpose of this paper is to investigate the numerical, behavioural and policy sensitivity of this model to parameter uncertainty.
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Swart J, 1999, Optimising investment performance through international diversification, ORiON, 15(1/2), pp. 1-24.
Abstract. International portfolio diversification is often advocated as a way of enhancing portfolio performance particularly through the reduction of portfolio risk. Portfolio managers in Europe have for decades routinely invested a substantial portion of their portfolios in securities that were issued in other countries. During the last decade US investors have held a significant amount of foreign securities with over a trillion dollars invested in foreign assets by 1994. South African institutions have been allowed some freedom to diversify internationally since mid 1995 and individual investors since July 1997. In this paper the potential diversification benefits for South African investors are considered. The stability over time of the correlation structure is investigated and simple ex-ante investment strategies are formulated and evaluated.
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Tapson DR, 1985, Constraints to optimal land use in Ciskei, ORiON, 1(2), pp. 83-104.
Abstract. Against the background of a definition of optimal land-use it is shown that a wide gap exists between the consumption and production of agricultural products in Ciskei. This condition is not due to a paucity of agricultural resources but the outcome of their sub-optimal use resulting from a series of institutional rather than technical constraints.
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Taylor D & Woolsey RED, 1989, Shrink stope design using an inventory model, ORiON, 5(2), pp. 68-74.
Abstract. This paper addresses the fact that current practice in shrink-stoping in hard rock mining invariably ignores the inventory holding cost of the blasted ore. We believe, and show by example, that ignoring this cost could make the difference between profit and loss in an industry that, at present, needs all the help it can get.
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Terblanche SE & Bley A, 2015, An improved formulation of the underground mine scheduling optimisation problem when considering selective mining ORiON, 31(1), pp. 1-16.
Abstract. The use of mixed integer programming is a modelling approach well suited to formulate the mine scheduling optimisation problem for both open pit and underground mining. The resolution applied for discretising the problem, however, has a direct effect on both the level of selectivity that can be applied to improve profitability, as well as the computational feasibility. The proposed model allows for a balance in reducing the resolution used in discretising the underground mine scheduling problem, while maintaining enough detail that will allow the generation of mine production schedules that improve profitability through selective mining. As a secondary contribution, an improved formulation set within a resource production/consumption framework is presented, which can potentially simplify notation used in formulating underground mine scheduling optimisation problems.
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Terblanche SE & De la Rey T, 2014, Credit price optimisation within retail banking ORiON, 30(2), pp. 85-102.
Abstract. The willingness of a customer to pay for a product or service is mathematically captured by a price elasticity model. The model relates the responsiveness of customers to a change in the quoted price. In addition to overall price sensitivity, adverse selection could be observed whereby certain customer segments react differently towards price changes. In this paper the problem of determining optimal prices to quote prospective customers in credit retail is addressed such that the interest income to the lender will be maximised while taking price sensitivity and adverse selection into account. For this purpose a response model is suggested that overcomes non-concavity and unrealistic asymptotic behaviour which allows for a linearisation approach of the non-linear price optimisation problem. A two-stage linear stochastic programming formulation is suggested for the optimisation of prices while taking uncertainty in future price sensitivity into account. Empirical results are based on real data from a financial institution.
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Terblanche SE & Van Vuuren JH, 2017, A note on flow-based formulations for solving resource constrained scheduling problems ORiON, 33(1), pp. 21-34.
Abstract. The resource constrained scheduling problem involves the scheduling of a number of activities over time, where each activity consumes one or more resources per time period. For a feasible solution to exist, the total resource consumption per time period must not exceed the available resources. In addition, the order in which activities may be scheduled is determined by a precedence graph. In this paper, valid inequalities proposed for the resource flow-based formulation in previous studies are investigated to determine what effect they may have on computing times. It is shown empirically that improved computing times may be obtained if these valid inequalities are, in fact, omitted from the resource flow-based formulation. In addition, a heuristic is proposed for the generation of initial starting solutions and for estimating the extent of the scheduling horizon which, in turn, is required to calculate the latest starting times of activities. The computational results are based on well-known problem test instances as well as new randomly generated problem instances.
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Theron P & Van den Honert RC, 2003, A mathematical approach to increasing the long-term wealth of an agricultural enterprise, ORiON, 19(1/2), pp. 53-74.
Abstract. This study focuses on developing an agricultural investment model based upon proven financial investment portfolio techniques. The model can be used as a tool to diversify agricultural risk over the long-term by optimising the proportion of land allocated to each of the agricultural products, resulting in increased value of the agricultural enterprise. Sensitivity analysis allows the strategist to understand the impact that future prices, gross margins and land availability may have on the long-term sustainability of the farming enterprise.
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Thomson R, 2001, Assets, liabilities and risks, ORiON, 17(1/2), pp. 29-54.
Abstract. Financial economists and actuaries do not always talk the same language. One particular difference of concern to actuaries is the method of treatment (or non-treatment) of the liabilities of an investor in the portfolio selection problem. Another difference relates to the way in which liabilities are valued. In this paper, these differences are discussed and possible way forward are suggested.
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Turpin SM & Marais MA, 2004, Decision-making: Theory and practice, ORiON, 20(2), pp. 143-160.
Abstract. This paper compares a number of theoretical models of decision-making with the way in which senior managers make decisions in practice. Six prominent decision-makers were interviewed about their own decision-making style, as well as their use of decision support technology. Significant variation was found in personal decision-making styles. However, some central themes emerged, such as the importance of sensitivity to the decision-making context, attention to the presentation of information, and the use of intuition. In terms of the use of decision support technology, the use of self-help tools, such as o�ce software, was clearly favoured.
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Van den Berg F, Holloway JP, Pienaar M, Koen R, Elphinstone CD & Woodborne S, 2008, A comparison of various modelling approaches applied to Cholera case data, ORiON, 24(1), pp. 17-36.
Abstract. The application of a methodology that proposes the use of spectral methods to inform the development of statistical forecasting models for cholera case data is explored in this paper. The seasonal behaviour of the target variable (cholera cases) is analysed using singular spectrum analysis followed by spectrum estimation using the maximum entropy method. This seasonal behaviour is compared to that of environmental variables (rainfall and temperature). The spectral analysis is refined by means of a cross-wavelet technique, which is used to compute lead times for co-varying variables, and suggests transformations that enhance co-varying behaviour. Several statistical modelling techniques, including generalised linear models, ARIMA time series modelling, and dynamic regression are investigated for the purpose of developing a cholera cases forecast model fed by environmental variables. The analyses are demonstrated on data collected from Beira, Mozambique. Dynamic regression was found to be the preferred forecasting method for this data set.
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Van den Honert RC & Westvig K, 1993, A simulation of the finish-line system of a major running race, ORiON, 9(2), pp. 55-69.
Abstract. The finish-line system of a major road race is investigated by means of a simulation model. In an attempt to help race management identify conditions that may lead to congestion of runners at this point. Based on the results of the model, race management was presented with a simple tool which could be used in situ to analyse a given situation, identify if congestion was likely to occur, and then consider corrective action.
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Van den Honert RC, 1997, Junk food or genuine nourishment: The nutritional value of some of South African fast-food chains, ORiON, 13(1/2), pp. 1-17.
Abstract. Integer programming is used to test the nutritional completeness of two fast-food chains operating in South Africa. McDonald's and Kentucky Fried Chicken. It is shown that a fully nutritional and varied daily diet can be made up from McDonald's menu items, but the same is not true for Kentucky Fried Chicken. This exercise is highly suited to introduce students to mathematical programming: skills learned include formulating mathematical programming problems, mastering linear programming software and exploring the Internet for relevant data.
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Van der Merwe A, Van Dyk FE & Van Vuuren JH, 2011, Decision support for grape harvesting at a South African winery, ORiON, 27(2), pp. 83-100.
Abstract. Recent technological advances have had a major impact on the management of traditional wineries, giving rise to the prospect of computerised decision support with respect to a range of complex harvesting and wine making decisions which have to be taken routinely. In this paper, two nested scheduling problems are considered. The first, referred to as the active cellar scheduling problem, is concerned with making good scheduling decisions within a winery (i.e. optimal assignments of grape intake batches to different processor sets inside the active part of the cellar). The harvest scheduling problem, on the other hand, refers to the larger, over-arching problem of selecting the best possible dates on which to harvest the respective vineyard blocks in order to preserve grape quality. A nested tabu search approach is presented to solve these two scheduling problems simultaneously. This solution approach has been implemented as a computerised decision support tool, called VinDSS, and the practical workability of this tool is demonstrated by means of a special case study at a winery in the South African Western Cape.
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Van der Merwe CJ & Conradie WJ, 2012, Calculation aspects of the European rebalanced basket option using Monte Carlo methods: Valuation, ORiON, 28(1), pp. 1-18.
Abstract. Extra premiums may be charged to a client to guarantee a minimum payout of a contract on a portfolio that gets rebalanced back to fixed proportions on a regular basis. The valuation of this premium can be seen as that of the pricing of a European put option with underlying rebalanced portfolio. This paper finds the most efficient estimators for the value of this path-dependent multi-asset put option using different Monte Carlo methods. With the help of a refined method, computational time of the value decreased significantly. Furthermore, variance reduction techniques and Quasi-Monte Carlo methods delivered more accurate and faster converging estimates as well.
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Van der Merwe DJ & Hattingh JM, 2010, Solving the Extended Tree Knapsack Problem with fixed cost flow expansion functions, ORiON, 26(1), pp. 1-16.
Abstract. Parts of the Local Access Telecommunication Network planning problem may be modelled as an Extended Tree Knapsack Problem. The Local Access Telecommunication Network can contribute up to 60% of the total network costs. This paper presents partitioning algorithms that use standard off-the-shelf software coupled with enhanced modelling. Enhancements to the algorithms and empirical results for both the Tree Knapsack Problem and Extended Tree Knapsack Problem are presented.
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Van der Merwe JEG, Kruger PS & Van Heerden JS, 1986, A simulation model for evaluating aircraft system operational availability, ORiON, 2(2), pp. 126-132.
Abstract. The cost effective utilisation and acquisition of equipment is vitally important to the air force of any national defence force. This paper describes a simulation model which was developed to aid the decision makers of such an air force in determining aircraft system requirements for carrying out specific missions within different conflict scenarios. Comprehensive validation of the model has not been completed.
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Van Deventer PJU & Manna ZG, 2009, An easy and low cost option for economic statistical process control using Excel, ORiON, 25(1), pp. 1-15.
Abstract. In this paper, a user-friendly, Excel program is developed to search for the optimal values of the parameters in minimizing the total cost function in both economic and economic statistical designs of the X-control chart. Two assumptions are considered in the development and use of the economic or economic statistical models. These assumptions are potentially critical. It is assumed that the time between process shifts can be modelled by means of the exponential distribution. It is further assumed that there is only one assignable cause. Based on these assumptions, economic or economic statistical models are derived using a total cost function per unit time as proposed by a unified approach. In this approach the relationship between the three-control chart parameters as well as the three types of costs are expressed in the total cost function. The optimal parameters are usually obtained by the minimization of the expected total cost per unit time. Nevertheless, few practitioners have tried to optimize the design of their X-control charts. One reason for this is that the cost models and their associated optimization techniques are often too complex and difficult for practitioners to understand and apply. Therefore, a user-friendly Excel program has been developed in this paper and the numerical examples illustrated are executed on this program. The optimization procedure is easy-to-use, easy-to-understand, and easy-to-access. Moreover, and not least important, it is a low cost option unlike previous approaches which can be found in expensive software packages only. The results and the execution times of all numerical examples show that our optimization procedure using Excel is accurate and efficient.
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Van Dyk FE & Maspero E, 2004, An analysis of the South African fruit logistics infrastructure, ORiON, 20(1), pp. 55-72.
Abstract. This paper gives an overview of a study that was done on the logistics infrastructure used by the South African fruit industry. Given the increasing production and export volumes, development of new markets and the shortage of logistics infrastructure capacity during peak seasons, the SA fruit industry identified the need to investigate the optimal usage of existing infrastructure on a national level and to make recommendations with regards to the development of additional infrastructure. Some background on the SA fresh fruit industry and its export supply chain are provided. This is followed by a description of the four project phases and their deliverables. The paper is concluded with the key findings of the study.
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Van Eck L, Visagie SE & De Kock HC, 2005, Fairness of seat allocation methods in proportional representation, ORiON, 21(2), pp. 93-110.
Abstract. In this paper the fairness of some methods of allocating seats in a proportional representation (PR) voting system is investigated. Different PR systems are in use throughout the democratic world, but the primary focus here is the method used in South Africa, namely the largest remainder method with a Droop quota. It is shown that as the number of parties increases, the number of lost votes (votes not used to allocate seats) increases when using this method. Other existing allocation methods are discussed and compared with each other as well as with three optimisation methods (based on mathematical programming) introduced in this paper. Applying these mathematical programming methods results in allocations that are more fair than the existing methods of seat allocation, if South African voting data are used. These mathematical models attempt to minimise a number of different measures of the deviation between the actual percentage of votes received and the percentage of seats allocated to a certain party. Ideally this deviation should be zero, but due to the discrete nature of seats this is virtually impossible to achieve.
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Van Loggerenberg SP, Grobler MJ & Terblanche SE, 2015, Heuristic approach to the passive optical network with fibre duct sharing planning problem ORiON, 31(2), pp. 95-110.
Abstract. Similar to the constrained facility location problem, the passive optical network (PON) planning problem necessitates the search for a subset of deployed facilities (splitters) and their allocated demand points (optical network units) to minimise the overall deployment cost. A mixed integer linear programming formulation stemming from network flow optimisation is used to construct a heuristic based on limiting the total number of interconnecting paths when implementing fibre duct sharing. A disintegration heuristic is proposed based on the output of a centroid, density-based and a hybrid clustering algorithm to reduce the time complexity while ensuring close to optimal results. The proposed heuristics are then evaluated using a large real-world dataset, showing favourable performance.
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Van Vuuren JH & Huddlestone GE, 1999, Seeking optimality in fruit pulping schedules: a case study, ORiON, 15(1/2), pp. 25-51.
Abstract. The process of scheduling fruit pulping for the production of fruit juices is of great importance in the beverage industry. Decisions have to be made regarding available processing time, the disposal of fruit that will not be pulped before stock loss due to spoilage, the fulfilment of customer demand and an optimal financial position. Sheduling depends on the capacity of the work force, pulping machine limitations and delivery deadlines. However, the situation is often encountered where the plant manager has to decide which fruit batches (usually from stock piles of overwhelming proportions during the harvesting season) are to be pulped in order to minimize losses due to fruit deterioration. Such decisions are usually done manually, based on intuition and experience. A mathematical model is presented here which constructs a pulping strategy while minimising cascading financial losses associated with fruit grade drops within the stock pile. It is shown in particular that a minimisation of fruit losses is not a good criterion for optimality, and that substantial financial gains may be accomplished when minimising financial losses in stead of fruit losses, which is currently standard practice at most fruit pulping plants.
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Vanderperre EJ, 2005, A Sokhotski-Plemelj problem related to a renewable T-cell, ORiON, 21(2), pp. 147-155.
Abstract. We analyse the long-run availability of a technical device subjected to inspections and repair. All statistical distributions involved are general. In order to describe the random behaviour of the system, we employ a stochastic process endowed with stationary measures satisfying coupled Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions. As an example, we consider the particular case of Coxian inspections.
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Venter L & Visagie SE, 2016, On the solution of petrochemical blending problems with classical metaheuristics ORiON, 32(2), pp. 79-104.
Abstract. In this paper a comparison of classical metaheuristic techniques over different sizes of petrochemical blending problems is presented. Three problems are taken from the literature and used for initial comparisons and parameter setting. A fourth instance of real world size is then introduced and the best performing algorithm of each type is then applied to it. Random search techniques, such as blind random search and local random search, deliver fair results for the smaller instances. Within the class of genetic algorithms the best results for all three problems were obtained using ranked fitness assignment with tournament selection. Good results are also obtained by means of continuous tabu search approaches. A simulated annealing approach also yielded fair results. Comparisons of the results for the different approaches shows that the tabu search technique delivers the best results with respect to solution quality and execution time for all of the three smaller problems under consideration. However, simulated annealing delivers the best result with respect to solution quality and execution time for the introduced real world size problem.
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Venter G & Wolvaardt JS, 2005, 'n Algoritme vir die minimum van die konkawe knapsakprobleem, ORiON, 21(1), pp. 13-31.
Abstract. This paper addresses the problem of resource allocation among activities where the cost of each is described by a concave function. There is a single linear constraint (limited resource) and each activity has an upper and lower bound (maximum and minimum resource allocations). The objective is to minimise the sum of the functions. The problem with convex functions is well-studied and since a local minimum is also global, this problem was tamed early by Luss and Gupta [Luss H & Gupta SK, 1975, Allocation of effort resources among competing activities, Operations Research, 23, pp. 360�366], and by Bitran and Hax [Bitran GR & Hax AC, 1979, On the solution of convex knapsack problems with bounded variables, pp. 357�367 in Prekopa A (Ed.), Survey of Mathematical Programming]. In contrast the minimisation of a sum of concave functions has received less attention and then the emphasis has often been on an objective function which is nonseparable quadratic, and on the complexity of finding a true local minimiser (e.g. More and Vavasis [More JJ & Vavasis SS, 1991, On the solution of concave knapsack problems, Mathematical Programming, 49, pp. 397�411]). We are concerned with the computational problem of finding the global optimum for a (separable) sum of nondecreasing general concave functions and the approach is via the Kuhn-Tucker necessary conditions. These are improved by using the result that a minimiser must be an extreme point, which means that all but one variable (at most) is at an upper or lower bound. (More and Vavasis base their CKP algorithm on this property.) The improved necessary conditions form the basis of the method of greatest differences (GVA), our algorithm to improve a feasible solution. A greedy heuristic to produce a first feasible solution is also proposed. Using four groups of 10 instances, each from the four classes of concave functions of Luss and Gupta, one thousand different runs for incremental values of the resource were made for both the CKP and our GVA. While the CKP often found a globally suboptimal answer for functions which intersect, the GVA found the correct answer in all 16 000 runs. This is no guarantee that a method based on necessary conditions will always find the global maximum but the GVA is numerically promising and it masters a class of problems that the CKP does not. The greedy first feasible solution was found to be optimal more frequently (64% to 49%, and 73% to 40%) than that proposed by Mor�e and Vavasis. The GVA does not depend on the kind of function, requiring only that the functions be nondecreasing and concave. With minor alterations it can be used for the maximisation of the sum of nondecreasing convex functions. It is much faster than dynamic programming on problems with up to 10 functions and should be superior when tested on large problems.
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Vermeulen PJ, 1985, Assessment of technologies in a global energy system, ORiON, 1(2), pp. 105-122.
Abstract. A limited research and development budget usually implies that decisions must be made regarding the distribution of the available funds among the most promising R & D projects. The MARKAL model is used to describe a national energy system where existing and new energy conversion and process technologies compete for a market share in satisfying exogenously specified demand patterns. A measure is introduced which may be used to rank the relative importance of a technology in the energy system. Several scenarios depicting different restrictions on the energy system are used in the analysis.
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Vermeulen PJ & Snyman JA, 1992, A unified feasible direction interior approach to the minimization of linear and general objective functions subject to linear constraints, ORiON, 8(2), pp. 90-107.
Abstract. A modification of Snyman's interior feasible direction method for linear programming is proposed and the method is also extended to problems where the objective function is non-linear. The method attempts to identify the optimal bounding set of active constraints. In the modified algorithm the successive interior steps in the identifying cycle are no longer constrained to be in the place of constant objective function value, but are computed to ensure improvement in the objective function for any non-zero step taken within the cycle. The method is also extended to non-linear objective functions by allowing for line searches within the interior and along bounding hypersurfaces. A formal unified algorithm is presented and the method is illustrated by its successful application to a number of simple problems from different categories.
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Verster A, Chikobvu D & Sigauke C, 2013, Analysis of the same day of the week increases in peak electricity demand in South Africa, ORiON, 29(2), pp. 125-136.
Abstract. Modelling of the same day of the week increases in peak electricity demand using the Generalized Pareto-type (GP-type) distribution is discussed. The GP-type distribution discussed in this paper has one parameter to estimate and as such, it is referred to as the Generalized Single Pareto (GSP). The data is from Eskom, South Africa's power utility company and is for the years 2000 to 2011. A comparative analysis is done with a Generalized Pareto Distribution (GPD). Although both the GSP and the GPD fit the data, the use of the GSP is easier since it has only one parameter to estimate instead of two as is the case with the GPD. Modelling of the same day of the week increases in peak electricity demand improves the reliability of a power network if an accurate assessment of the level and frequency of future extreme load forecasts is carried out.
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Viljoen H & Steel SJ, 2013, Identifying secondary series for stepwise common singular spectrum analysis, ORiON, 29(2), pp. 155-167
Abstract. Common singular spectrum analysis is a technique which can be used to forecast a primary time series by using the information from a secondary series. Not all secondary series, however, provide useful information. A first contribution in this paper is to point out the properties which a secondary series should have in order to improve the forecast accuracy of the primary series. The second contribution is a proposal which can be used to select a secondary series from several candidate series. Empirical studies suggest that the proposal performs well.
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Von Collani E, 2000, Integrated and objective-oriented statistical process control, ORiON, 16(1), pp. 23-45.
Abstract. Global competition and increased environmental concern have emphasized the significance of process quality for an economic success. Statistical Process Control (SPC) is considered as one of the major tools for better quality. However, there are many opinions about the nature, the role and the results of SPC in industry. If SPC is understood and implemented correctly, then it should not only lead to "a reduction of waste, shorter throughput times and greater reliability of supply, but also in a better understanding of the processes and their variation" as Does, Roes and Trip formulated it. SPC should ultimately lead to "an operational management of the continuous improvement of processes." The aim of an industrial production process is to make profit, thus quality should be measured by process profitability. From a more operational point of view highest quality, i.e. highest profitability, is reached by producing with high conformance to an appropriately selected target value, and quality improvement means further reduction of variation around the target value. Thus, understanding the inherent variation represents the key for controlling "profitability" and for being able to implement a system of continuous "quality improvement". The inherent variations reflect the complex relations between everything concerning the production process and results in uncertainty about the future development. Exactly at this point stochastics, the science of uncertainty, enters the stage. For controlling profitability the relations and the resulting variations have to be taken appropriately into account by an integrated and objective-oriented stochastic approach.
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Visagie SE, 2004, Prysverlagings op voorraad met �n dalende vraag, ORiON, 20(2), pp. 125-142.
Abstract. Hierdie artikel stel �n heuristiese benadering voor om die verliese op voorraad met �n dalende vraag en onbekende tydshorison te minimeer. Die twee metodes wat voorgestel word, gebruik �n benaderde vraagkromme om die verwagte verliese te voorspel. Albei heuristieke gebruik hierdie vooruitskatting om te bepaal wanneer die prys van items in voorraad afgemerk moet word ten einde verkope te versnel om verliese te vermy wat as gevolg van lang omsettye ontstaan. �n Gevallestudie wat die werklike data van �n CD-winkel simuleer, word gebruik om die twee heuristieke se prestasie relatief tot die huidige afmerkstrategie van die bestuur.
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Visagie, 2008, On the efficient solvability of a simple class of nonlinear knapsack problems, ORiON, 24(1), pp. 1-15.
Abstract. In this paper the efficient solvability of a class of nonlinear knapsack problems is investigated by means of the problem's necessary and sufficient conditions. It is shown that, from the general theory, it is impossible to determine sufficient conditions for a solution to be globally optimal. Furthermore, it is shown that even for the smallest possible instance of this problem it is, in general, possible to have an arbitrary large number of solutions for which the necessary conditions hold. These results are then generalised to larger instances of the problem. A possible solution approach is applied to sets of randomly generated problems that utilises the necessary conditions together with the branch-and-bound technique in an attempt to limit the search space. This approach solves mixed 0/1 knapsack problems in order to find all possible solutions satisfying the necessary conditions. Due to the large number of solutions satisfying the necessary conditions the proposed solution approach takes substantially longer than existing branch-and-bound algorithms together with linear enveloping when applied to the same set of problems. This result renders the proposed approach not very efficient.
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Visagie SE, De Kock HC & Ghebretsadik AH, 2004, Optimising an integrated crop-livestock farm using risk programming, ORiON, 20(1), pp. 29-54.
Abstract. Numerous studies have analysed farm planning decisions focusing on producer risk preferences. Few studies have focussed on the farm planning decisions in an integrated croplivestock farm context. Income variability and means of managing risk continues to receive much attention in farm planning research. Different risk programming models have attempted to focus on minimising the income variability of farm activities. This study attempts to identify the optimal mix of crops and the number of animals the farm needs to keep in the presence of crop production risk for a range of risk levels. A mixed integer linear programming model was developed to model the decision environment faced by an integrated crop-livestock farmer. The deviation of income from the expected value was used as a measure of risk. A case study is presented with representative data from a farm in the Swartland area. An investigation of the results of the model under different constraints shows that, in general, strategies that depend on crop rotation principles are preferred to strategies that follow mono-crop production practices.
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Wagenaar EA & Van Vuuren JH, 2001, Quantifying the role of personal management style in the success of investment portfolios, ORiON, 17(1/2), pp. 13-28.
Abstract. It is extremely difficult to quantify the effect of different management styles of portfolio managers upon the success of their portfolios. Various mathematical models in the literature attempt to predict the risk and returns of portfolios according to changes in the economic arena, but these models usually do not take into account the personal styles of portfolio managers. The aim of this paper is a modest attempt at quantifying the effect of different managerial styles upon decisions regarding portfolios. This is accomplished by the formulation of a mathematical performance index that portrays the influence of a portfolio manager's personal and managerial characteristics on the success of his portfolio.
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Walls MR, 1995, An examination of risk propensities in an orginizational context: differences by discipline and position, ORiON, 11(1/2), pp. 41-57.
Abstract. Previous studies of risk-taking suggest there are significant variations across individuals' willingness to take financial risk within the organisational context. For example, a decision maker's propensity to take risk may be more aligned with his unique planning horizon. Previous research also suggests that division and lower level managers are typically more risk averse than top managers in the organisation. In this case study we investigate differences in risk propensity across managerial and functional designations in a major oil company, BP Exploration, Inc. We present a model for measuring risk propensity, examine the results of a survey of 39 staff and supervisory personnel, and explore the implications of a divergence between individual risk propensities and the firm's corporate risk policy.
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Walters IS & Le Roux NJ, 2008, Monitoring gender remuneration inequalities in academia using biplots, ORiON, 24(1), pp. 49-73.
Abstract. Gender remuneration inequalities at universities have been studied in various parts of the world. In South Africa, the responsibility largely rests with individual higher education institutions to establish levels of pay for male and female academic staff members. The multidimensional character of the gender wage gap includes gender differentials in research output, age, academic rank and qualifcations. The aim in this paper is to demonstrate the use of modern biplot methodology for describing and monitoring changes in the gender remuneration gap over time. A biplot is considered as a multivariate extension of an ordinary scatterplot. Our case study includes the permanent fulltime academic staff at Stellenbosch University for the period 2002 to 2005. We constructed canonical variate analysis (CVA) biplots with 90% alpha bags for the five-dimensional data collected for males and females in 2002 and 2005 aggregated over faculties as well as for each faculty separately. The biplots illustrate, for our case study, that rank, age, research output and qualifications are related to remuneration. The CVA biplots show narrowing, widening and constant gender remuneration gaps in different faculties.
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Watson NM, Stewart TJ & Scott L, 2014, Decision support for Foodbank South Africa ORiON, 30(1), pp. 1-18.
Abstract. This paper employs a combined 'soft-hard' OR approach to aid decision making in the area of allocation at a not-for-profit organization, Foodbank South Africa (FBSA), that represents the largest hunger-relief network in South Africa. Two problem-structuring tools, causal mapping and root definitions (RDs) are utilized. Causal mapping is used to identify areas for useful research within FBSA, and gain a greater understanding of the organization in terms of its goals and consequently a good appreciation of the context in which decisions are made. Root definitions are employed to acquire a better understanding of the 'decision-issues' within the allocation system at the Cape Town warehouse. A simulation model is developed to imitate daily allocation decisions, with the end-objective of assisting decision-making by developing a range of allocation policies. A decision support system (DSS) is developed to help FBSA manage their agency database, automate some of the daily allocation decisio
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Woolsey RED, 1995, How to market OR successfully, ORiON, 11(1/2), pp. 1-3.
Abstract. It was with considerable amusement that I noticed a recent flyer from ORSSA for a one day workshop on "Marketing Operations Research". The brochure contained some amusing but painful truths such as "Most O.R. Practitioners experience difficulty in marketing O.R." For those of you who did not attend the course, but would like some advice for free, here it is. As this is a precis of what I have been saying (and doing) for over twenty years, I also provide (with my usual humility) a bibliography of my (personally tested) suggestions for successfully marketing O.R.
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Woolsey RED & Lienert CE, 1985, A comparison of economic decision making using net present value analysis versus present value ratio combined with a minimum hurdle rate, ORiON, 1(1), pp. 43-48.
Abstract. The authors will show that using present value ratio combined with a minimum hurdle rate for economic decision making can lead to erroneous economic conclusions. Two examples are presented.
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Woolsey RED & Sandrock K, 1986, 'n Vinnige en kragtig benadering tot kapitaal beleggingsbesluitneming, ORiON, 2(1), pp. 26-32.
Abstract. This paper describes a 'Quick and Dirty' (but powerful) approach to the capital investment problem. The idea is to leave the reader with a pro-forma based methodology for capital investment decision-making within the framework of the taxation laws of the Republic.
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Yadavalli VSS, Adendorf K, Erasmus G, Chandrasekhar P & Deepa SP, 2004, Confidence limits for expected waiting time of two queuing models, ORiON, 20(1), pp. 1-6.
Abstract. A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected waiting time per customer in the queues of M|M|1|infinity and M|M|1|N are obtained.
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Yadavalli VSS & Botha M, 2000, Stochastic analysis of a two unit system with vacation for the repair facility after M repairs, ORiON, 16(2), pp. 139-148.
Abstract. Stochastic analysis of a two unit system with vacation period for the repair facility after the completion of m repairs is studied. All the underlying distributions are assumed to be non-Markovian. The reliability and availability analysis for such a system is studied. A numerical illustration is given.
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Yadavalli VSS & Jeganathan K, 2016, A finite source perishable inventory system with second optional service and server interruptions ORiON, 32(1), pp. 23-53.
Abstract. In this article, a service facility inventory system with server interruptions and a finite number of sources are considered. The inventory is replenished according to (s,S) ordering policy. Using the matrix methods, the stationary distribution of the stock level, server status and waiting area level is obtained in the steady state case. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Many impartment system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.
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Yadavalli VSS, Labeodan MMO, Udayabaskaran S & Forche N, 2010, Modelling T4 cell count as a marker of HIV progression in the absence of any defense mechanism, ORiON, 26(2), pp. 113-123.
Abstract. The T4 cell count, which is considered one of the markers of disease progression in an HIV infected individual, is modelled in this paper. The World Health Organisation has recently advocated that countries encourage HIV infected individuals to commence antiretroviral treatments once their T4 cell count drops below 350 cells per ml of blood (this threshold was formerly 200 cells per ml of blood). This recommendation is made because when the T4 cell count is low, the T4 cells are unable to mount an effective immune response against antigens and any such foreign matters in the body, and consequently the individual becomes susceptible to opportunistic infections and lymphomas. A stochastic catastrophe model is developed in this paper to obtain the mean, variance and covariance of the uninfected, infected and lysed T4 cells. The amount of toxin produced in an HIV infected person from the time of infection to a later time may also be obtained from the model. Numerical illustrations of the correlation structures between uninfected and infected T4 cells, and between the infected and lysed T4 cells are also presented.
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Yadavalli VSS, Labeodan MMO, Udayabaskaran S & Mwanga Y, 2009, A stochastic model for the dynamics of HIV under a combination therapeutic intervention, ORiON, 25(1), pp. 17-30.
Abstract. Drug resistance to single therapeutic treatment in HIV infected individuals has promoted research into combined treatments. In this paper we propose a stochastic model under combined therapeutic treatment by extending the model of HIV pathogenesis under treatment by anti-viral drugs given in [Perelson AS, Neumann AU, Markowits M, Leonard JM & Ho DD, 1996, HIV-1 dynamics in vivo virion clearance rate, infected cell life span, and viral generation time, Science New Series, 271, pp. 1582-1586]. Variance and co-variance structures of variables are obtainable via this approach in addition to the mean numbers of free HIV, infectious free HIV and non-infectious free HIV that were obtained by Perelson et al. Comparing simulated data for before and after treatment indicates the importance of combined treatment and its overall effect(s).
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Yadavalli VSS & Muller MAE, 2005, A stochastic model for an urea decomposition system, ORiON, 21(2), pp. 139-146.
Abstract. Availability is an important measure in describing the performance of a system. The availability of a decomposition process in an urea production system in the fertilizer industry is considered in this paper. The system contains four subsystems and is supported by a standby unit. An estimation study of the steady state availability of the system is performed and illustrated by means of a numerical example.
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Yadavalli VSS, Singh N & Boraine H, 2002, Distribution-free approach to the evaluation of reliability of complex systems, ORiON, 18(1/2), pp. 59-74.
Abstract. In the industrial community it is well known that the failure rate of the manufactured units vary with time due to a variety of causes, namely, engineering design, manufacturing process, maintenance and quality inspection procedures and various assignable and non-assignable factors. Such failure rates invariably exhibit changes in both level and slope and at times exhibit periodic patterns as well. Therefore it would be quite inappropriate and erroneous to analyze such stochastic series of observations using the usual failure distribution approach. Since such data can be construed as time series, we suggest in this paper the time series techniques including the Kalman filter for their analysis. Other advantages of using the latter techniques are that the periodicities, if any, can be taken into account and short-term forecasts can be made which otherwise would not have been possible.
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Yadavalli VSS, Sivakumar B & Arivarignan G, 2007, Stochastic inventory management at a service facility with a set of reorder levels, ORiON, 23(2), pp. 137-149.
Abstract. We consider a continuous review perishable inventory system at a service facility with a finite waiting capacity. The maximum inventory level is fixed and the customers arrive according to a Markov arrival process. The life time of each item and the service time are assumed to have independent exponential distributions. Unlike the conventional method of placing an order at a prefixed level, we consider a set of reorder levels with a specified probability for placing an order at a particular reorder level. This allows the modelling of a situation in which the decision maker may advance or postpone the placement of reorder as a result of his/her memory on the past supply behaviour. The reordering quantity depends upon the reorder level at which an order was triggered and the lead time is distributed as negative exponential. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state. We also derive some stationary system performance measures and compute the total expected cost rate under a cost structure. We also present a numerical illustration.
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Yadavalli VSS, Van Schoor CdeW, Strasheim JJ & Udayabaskaran S, 2004, A single product perishing inventory model with demand interaction, ORiON, 20(2), pp. 109-124.
Abstract. The paper describes a single perishing product inventory model in which items deteriorate in two phases and then perish. An independent demand takes place at constant rates for items in both phases. A demand for an item in Phase I not satisfied may be satisfied by an item in Phase II, based on a probability measure. Demand for items in Phase II during stock-out is lost. The re-ordering policy is an adjustable (S, s) policy with the lead-time following an arbitrary distribution. Identifying the underlying stochastic process as a renewal process, the probability distribution of the inventory level at any arbitrary point in time is obtained. The expressions for the mean stationary rates of lost demand, substituted demand, perished units and scrapped units are also derived. A numerical example is considered to highlight the results obtained.
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Yoon M, Bekker J & Kroon S, 2017, New reinforcement learning algorithm for robot soccer ORiON, 33(1), pp. 1-20.
Abstract. Reinforcement Learning (RL) is a powerful technique to develop intelligent agents in the field of Artificial Intelligence (AI). This paper proposes a new RL algorithm called the Temporal-Difference value iteration algorithm with state-value functions and presents applications of this algorithm to the decision-making problems challenged in the RoboCup Small Size League (SSL) domain. Six scenarios were defined to develop shooting skills for an SSL soccer robot in various situations using the proposed algorithm. Furthermore, an Artificial Neural Network (ANN) model, namely Multi-Layer Perceptron (MLP) was used as a function approximator in each application. The experimental results showed that the proposed RL algorithm had effectively trained the RL agent to acquire good shooting skills. The RL agent showed good performance under specified experimental conditions.
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Zionts S & Lofti V, 1989, Recent developments in multiple criteria decision making, ORiON, 5(1), pp. 1-23.
Abstract. Problems involving more than one criterion abound. To help in the solution of such problems, a field of management science and operations research known as multiple criteria decision making (MCDM) has emerged to help solve such problems. In this paper we discuss some recent developments in this important field.
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