Module overview
A variety of OR techniques are covered in lectures and assessed by examination.
Workshops develop skills with computer modelling software (discrete-event simulation and linear programming). Other skills that are developed within the module are group work, report writing and oral presentation. These skills are assessed by coursework assignments.
Linked modules
Prerequisites: MATH1024 AND MATH1048 AND (MATH1058 OR MATH1002) AND (MATH1059 OR MATH1056)
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- 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
- Appreciate both the capabilities and the limitations of OR techniques
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;
Disciplinary Specific Learning Outcomes
Having successfully completed this module you will be able to:
- Work successfully within in a group
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Produce well-structure assignment reports describing problem formulation and solution
- Present models and solutions orally
Syllabus
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.
Project Networks, or the mathematics to help with the time and resource management of complex multi-task projects. Includes: modelling a project as a directed acyclic graph; topological sorting algorithm; critical path method; time complexity; managerial use of float information; ALAP and ASAP Gantt charts; computer implementation, applications and exercises.
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.
Learning and Teaching
Teaching and learning methods
.
Type | Hours |
---|---|
Independent Study | 102 |
Teaching | 48 |
Total study time | 150 |
Resources & Reading list
Textbooks
A.M. LAW and W.D. KELTON (1991). Simulation Modeling and Analysis. McGraw-Hill.
W.L. WINSTON (2004). Operations Research: Applications and Algorithms. Thomson Brooks/Cole.
F.S.HILLIER and G.J. LIEBERMAN (2010). Introduction to Operations Research. McGraw-Hill.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Written exam | 50% |
Coursework | 50% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Written exam | 100% |
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.
Method | Percentage contribution |
---|---|
Written exam | 100% |
Repeat Information
Repeat type: Internal & External