by Hans Ittmann
Up to the 70s and early 80s many mining companies in South Africa had dedicated OR groups. Mining was possibly one of the first areas where OR was used and applied in a considerable “big” way in the country. Most, if not all, of these early groups have disappeared creating the impression that OR is no longer considered as a critical discipline within the South African mining industry.
It was therefore very surprising, and pleasing, when ORSSA organised and scheduled a Webinar with the title: OR approaches in Mine Planning. The Webinar was scheduled on 14 April 2022 by ORSSA with Prof Fanie Terblanche of North-West University as presenter. The ORSSA Head of Events, Jess Rees was the host of this event.
The presentation focussed on underground mining and started with the explanation of mining concepts and terminology. These included sloping blocks and sloping panels with tunnels and the shaft to get the mined ore body to the surface. Every mine is different with infinite mine layout combinations, with no blueprint for a mine and many different mining methods. Furthermore, excavation is expensive and there in uncertainty in the marketplace as prices can fluctuate. The primary planning problem is what the layout of the mine should be and then how to excavate the mine in the most economic way. To complicate matters further safety is of utmost importance with many unplanned events during the mining operation.
The assumption is there is a mine layout, and the planning then focusses on which part of the mine should be excavated, when, to ensure profitability and sustainability. Various issues need to be considered in this process such as the location and grade of the mineral deposits, ventilation requirements, shaft and tunnel capacities, size of the work force, etc. What this leads to is a mine scheduling optimization problem. A small conceptual model was used to illustrate this approach. Various mining activities are identified, and the challenge is how to sequence these activities. This problem can be formulated as the classic Resource Constraint Scheduling Model. The mathematical model formulation was outlined in detail. The objective and all the constraints required was shown and discussed as well as the variables required. In this model the decision variable denotes the start time of an activity.
Reasons were presented why this conceptual model cannot be used as-is and more explicit formulations where presented. Time discretization is required and a binary decision variable equal to 1 indicating the start of an activity is introduced. All activities need to start at discreet time periods. The formulation and model that captures this was then presented as an Integer Linear Programming (ILP) model. A further, more refined model, namely a resource flow Mixed Integer Linear Programming (MILP) model was the next formulation that was discussed. The insights gained from the empirical evaluations of these two approaches lead to adaptations resulting in performance improvements especially in the case of the resource flow MILP approach. Applying this to real-world mining problems still proved inadequate. This in turn lead to considering heuristics. The issues resulting from using heuristics and how it had to be treated were then discussed as well.
The presentation was concluded by considering improvements at how these problems can be addressed in the future, both from a modelling and algorithmic perspective. There are many opportunities for further work. Mine planning is complex since there are multiple uncertainties that need to be considered. In the end the mining must be profitable and result in a positive net present value. This remains a huge challenge.
As the presentation was scheduled on the eve of the Easter weekend there were not many participants, which is unfortunate. Mining is still an important industry in our country and this webinar gave one not only an insight into the intricacies of mining but also how OR can contribute. It was an excellent webinar.