Operational Research II

Learning Outcomes

Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

• Work successfully within in a group

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Appreciate the types of problems that can be solved with OR methods
• Show understanding of the use of models in OR;

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Appreciate both the capabilities and the limitations of OR techniques
• Fomulate and construct a mathematical model of a real life situation
• Solve OR problems, both non-standard as well as standard, using appropriate OR techniques

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Produce well-structure assignment reports describing problem formulation and solution

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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Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.