## Typical areas of study within OR

The following areas of interest are often studied under the general banner of Operations Research:

Decision making

Utility · Decision trees · Bayes' rule

Discrete optimisation problems

Knapsack & capital budgeting problems · Set packing, covering & partitioning problems · Assignment & matching problems · Travelling salesman & other vehicle routing problems · Machine scheduling problems

Dynamic programming

Recursive equation modelling approach · Forward & backward computations · Dimensionality & complexity · Solving linear programming problems via dynamic programming

Forecasting

Moving average methods · Exponential smoothing · Trends and seasonality · Holt's method & Winter's method · Linear & multiple regression

Game theory

Minimax and maximin criteria · Game representations · Pure & mixed strategies · Core of a game · Strategy domination and Nash equilibria · Solving games via linear programming · Shapley index

Goal programming

Pareto optimality · Preemptive optimisation · Weighted sums approach · trade-off curves & efficient frontiers

Inventory theory

Economic order quantities (EOQs) · Lead time · EOQ models under fixed, deterministic or stochastic demand · Order quantities when discounts apply · Back-ordering · Marginal analysis · (r, q) and (s, S) models · Periodic review policies · ABC Classification · Material requirements planning · Just-in-time approach

Local search (meta)heuristics

Improving search heuristics · Tabu search · Simulated Annealing

Integer programming

Rounding of solutions · Linear programming, Lagrange and other relaxations · Branch & bound methodology · Implicit enumeration & Balas' zero-one algoritm · Cutting plane methods of Gomory · Valid inequalities · Strong formulations · Formulations with exponentially many variables/constraints

Linear programming

Feasibility & optimality · Graphical solutions · Artificial variables · Extreme point searches · Simplex & revised simplex algorithm · Degeneracy · Convergence & cycling · Interior point methods · Duality · Dual simplex method · Karmarkar's method · Sensitivity

Metaheuristics

Ant colony optimisation · Genetic algoritms · Particle swarm optimisation

Multiple criteria decision analysis

Problem structuring · Preference modelling (measurement theory, utility theory, aspiration levels, ranking, relative importance) · Value function methods · Analytic hierarchy process · ELECTRE & PROMETHEE methods

Network flow problems

Cycle directions · Search algorithms · Integrality constraints · Transportation & assignment models · Network simplex algorithm for optimal flows · Cycle cancelling algorithms · Multi-commodity and gain/loss flows

Nonlinear programming

Extremal points · Convexity and local/global optima · Karush-Kuhn-Tucker optimality conditions · Gradient search methods · Newton's method · Nelder-Mead methods · Convex programming · Separation of variables · Quadratic programming · Geometric programming · Lagrange multiplier methods · Penalty & barier methods · Reduced gradient methods

Probability theory

Events & sample spaces · Laws of probability · Random variables & probability distributions · Joint probability distributions · Expectation and moments of a random variable · Moment generating functions · Central limit theorem · Convolutions · Stochastic processes

Project scheduling

Network representations · Critial path calculation · Gantt charts · Resource levelling · Sensitivity, probability & cost considerations

Queuing theory

Kendall-Lee notation · Arrival and departure processes · Poisson vs non-Poisson queuing models · Priorities of service · Queues in series vs queues in parallel · Markov chains · Simulation techniques