The University of Southampton
Courses

# MATH2013 Introduction to Operational Research

## Module Overview

Various OR techniques are described within the module, the most important being linear programming (LP)/inter programming (IP) and simulation modelling. The use of computer software for solving LP/IP models and for developing simulation models is covered within computer workshop sessions. Other skills that are developed within the module are group-working, report writing and oral presentation. These are assessed by coursework assignments involving the use of LP/IP and simulation modelling.

### Aims and Objectives

#### Module Aims

To provide an appreciation of how operational research (OR) is useful for solving various practical decision-making problems. The importance of the use of models within OR is conveyed, as well as the wide range of application areas of OR

#### 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 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
##### 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

### Syllabus

Simulation modelling: Motivation via the single-server queue. State variables and discrete events. Next-event time-advance mechanism. Pseudo-random numbers and their generation. Generation of non-uniform random variables by inversion Decision analysis: Introduction to decision making under uncertainty. Linear and Integer Programming. Assumptions of LP/IP models. Geometry of LPs and the graphical solution of 2-dimensional LPs. Examples of different classes of LP/IP problems; static vs dynamic models. Simplex method: standard form of LPs; phase 2 of simplex method; sensitivity analysis. Project networks: Drawing project networks. Analyzing project networks by computing the critical path. Evaluating the sensitivity to changes in activity durations. Dynamic programming: Introduction to principles of dynamic programming. Developing recursion equations for solving problems. Inventory control: Economic order quantity model and its variants. Wagner-Whitin dynamic model

### Learning and Teaching

TypeHours
Independent Study109
Teaching41
Total study time150

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

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

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

### Assessment

#### Summative

MethodPercentage contribution
Closed book Examination 60%
Coursework 40%

#### Referral

MethodPercentage contribution
Exam %

#### Repeat Information

Repeat type: Internal & External

Prerequisites: MATH1048 and MATH1024 and MATH1050 (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

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.