Operational Research II

Learning Outcomes

Decisions under Uncertainty. Review of Probability: sample space, axioms of probability; conditional probability; Law of Total Probability; Bayes Law; discrete random variables and their expectation; Law of the Unconscious Statistician; examples. Single-stage optimal decisions; emphasis on the maximum expected value approach. Multi-stage optimal decisions via finite decision trees. Examples. Stochastic Simulation. Continuous random variables in one dimension: probability density function; cumulative distribution function; inverse of the distribution function. Independence of random variables. Introduction to random sampling: independent uniform random variables as the source of randomness; sampling general (non-uniform) random variables via the inversion method. Network models: (1) definition of networks and the min-cost network flow formulations for modelling transportation and supply-chain problems; (2) basics of dynamic programming, Dijkstra’s and Bellman-Ford algorithms; (3) the Critical Path Method for time and resource management of complex multi-task projects. Markov Chains. A rigorous introduction to the theory and application of this special class of stochastic systems. Includes: (I) Basic definitions and properties; (II) Communicating classes; (III) Limiting behaviour; and (IV) Absorbing chains. With plenty of exercises in different areas of application. Game theory: the study of strategic interactions between decision makers, with many illustrations in different areas of application. Includes: (I) Strategy games, dominance and best response, iterative deletion, common knowledge, Nash equilibria, mixed strategies, (II) Sequential games, backward induction, information sets, (III) Cooperative games, Core and Shapley, computer implementations.

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