The University of Southampton
Courses

# MATH2013 Operational Research II

## 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.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

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

• Show understanding of the use of models in OR;
• Appreciate the types of problems that can be solved with OR methods
##### 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
##### 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
##### Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

• Work successfully within in a group

### 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

.

TypeHours
Independent Study102
Teaching48
Total study time150

A.M. LAW and W.D. KELTON (1991). Simulation Modeling and Analysis.

F.S.HILLIER and G.J. LIEBERMAN (2010). Introduction to Operations Research.

W.L. WINSTON (2004). Operations Research: Applications and Algorithms.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 50%
Written assessment 50%

#### Referral

MethodPercentage contribution
Written assessment 100%

#### Repeat Information

Repeat type: Internal & External

Prerequisites: MATH1024 AND MATH1048 AND (MATH1058 OR MATH1002) AND (MATH1059 OR MATH1056)

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Recommended texts for this module may be available in limited supply in the University Library and students may wish to purchase reading texts as appropriate.

There are no additional compulsory costs associated with the module

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.