The University of Southampton
Courses

# MATH6004 Stochastic OR Methods

## Module Overview

The Stochastic OR Techniques part introduces the concepts and applications of the following four topics: queuing systems, inventory systems, reliability theory and decision theory. Models and examples are also given to demonstrate applications of the topics. Discrete event simulation is taught separately via lectures and computer workshops. One of the pre-requisites for MATH6013

### Aims and Objectives

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• demonstrate knowledge and understanding of the concepts and applications of the following five topics: queuing systems, inventory systems, reliability theory, decision theory and simulation.
• demonstrate skills in technical report writing.
• demonstrate practical skills in decision analysis, modelling queueing and inventory systems and calculating the reliability of systems.
• demonstrate skills in team working.
• understand how to implement and analyse a discrete event simulation model using Simul8 software.
• demonstrate gained skills in using computer software and programming.

### Syllabus

Queuing Systems: Basic elements of a queue and applications of queuing systems. Inventory System: EOQ models, newsboy models, inventory model with stochastic demand. Reliability Theory: Reliability of a component, reliability of a system, maintenance models, reliability and economics. Decision Theory: Bayes’ rule, value of information, Decision trees, and utility. Simulation: The emphasis is on simulation computing skills, which are developed in computer labs based on the SIMUL8 package. Lectures cover: the concept of randomness; and sampling from probability distributions including discrete and continuous models.

### Learning and Teaching

#### Teaching and learning methods

Twelve 2-hour OR techniques lectures Twelve 1-hour OR techniques tutorial sessions Three 2-hour simulation lectures Six 1-hour simulation computer sessions

TypeHours
Independent Study102
Teaching48
Total study time150

#### Resources & Reading list

Schaum. Outline of Operations Research.

Winston, WL. Operations Research: Applications and Algorithms.

Ross, SM. Applied Probability Models with Optimization Applications.

Hillier, F. Introduction to Operations Research.

Nelson, BL. Stochastic Modeling: Analysis & Simulation.

### Assessment

#### Assessment Strategy

The summative coursework assessment will be on Simulation (one individual assignment & one group assignment) The referral/repeat assessment includes both coursework and examination. If the coursework was previously passed, it is not retaken.

#### Summative

MethodPercentage contribution
Coursework 50%
Written assessment 50%

#### Referral

MethodPercentage contribution
Written assessment 100%

#### Repeat Information

Repeat type: Internal & External

### 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.

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.