MA0261: Operational Research
School | Cardiff School of Mathematics |
Department Code | MATHS |
Module Code | MA0261 |
External Subject Code | 100404 |
Number of Credits | 20 |
Level | L5 |
Language of Delivery | English |
Module Leader | Dr Jonathan Thompson |
Semester | Spring Semester |
Academic Year | 2015/6 |
Outline Description of Module
Operational Research (OR) is the application of advanced analytical methods to help make better decisions. Often this takes the form of developing a mathematical model of a system under-consideration and then using the model to examine and quantify “What if?” type questions in order to improve its performance.
This double module provides an introduction to a number of topics in OR, viz Queueing Theory, Simulation, Linear Programming and Network Analysis. These topics are orientated towards applications of mathematics in real-life situations. This module is a prerequisite to certain third level modules in OR.
Prerequisite Modules: MA1500 Introduction to Probability Theory
Recommended Modules: MA1501 Statistical Inference
On completion of the module a student should be able to
- understand the notation of Queueing Theory.
- set up simple stochastic models of queueing situations and derive analytic solutions to such models.
- undertake cost analyses associated with queueing systems and understand the decision making processes involved.
- understand the concepts of simulation procedures.
- generate samples from commonly occurring distributions.
- undertake simple simulation exercises.
- formulate linear programming models of resource allocation problems, transportation problems.
- understand the basic form of the simplex method for solving resource allocation problems and understand the stepping stone method for solving the transportation problem.
- formulate network graph models of shortest route problems, critical path problems, maximum flow problems.
- derive and use basic solution methods for finding the shortest route, critical path, and maximum flow in a network.
How the module will be delivered
54 - 50 minute lectures (including practical classes)
Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.
Students are also expected to undertake at least 100 hours private study including preparation of solutions to given exercises.
Skills that will be practised and developed
The skills developed in this module are essential in the management and business world. Thy include:
- Problem solving
- Logical thinking
- Mathematical formulation of problems
- Knowledge and use of simulation software
How the module will be assessed
Formative assessment is carried out by means of regular exercises. Feedback to students on their solutions and their progress towards learning outcomes is provided during lectures.
Summative assessment is by coursework and the written examination at the end of the module. The coursework consists of a simulation exercise. The examination gives students the opportunity to demonstrate their overall achievement of learning outcomes. It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.
The examination paper has two sections of equal weight. Section A contains a number of compulsory questions of variable length. Section B has a choice of three from four equally weighted questions.
Assessment Breakdown
Type | % | Title | Duration(hrs) |
---|---|---|---|
Exam - Spring Semester | 90 | Operational Research | 3 |
Written Assessment | 10 | Coursework | N/A |
Syllabus content
- Queueing Theory
- Kendall's queueing notation.
- Differential-difference equation approach to M/M/1 and M/M/C queues.
- Introduction to Markov processes.
- Derivation of summary measures, distribution of waiting times, mean busy period.
- Cost analysis in queueing theory.
- Case studies.
- Simulation
- Basic ideas of simulation processes, particularly Monte Carlo methods.
- Random number and variable generation.
- Verification and validation.
- Construction of simple simulation models.
- Optimization
- Formal introduction to continuous and discrete optimisation problems.
- Linear and non-linear optimisation.
- Iterative methods, descent.
- Convexity.
- Global and local optima.
- Linear Programming and Transportation
- Introduction to elementary linear programming problems.
- Simplex method of solving these and its rationale.
- Transportation problems.
- Networks
- Introduction to shortest route problem, critical path problem maximum flow problem.
- Dynamic programming.
- Solution methods for these problems and their derivation.
Essential Reading and Resource List
Not applicable.
Background Reading and Resource List
Taha, H.A., Operations Research: An Introduction, Prentice Hall, 1997
Winston, W.L, Operations Research: Applications and Algorithms, Brooks/Cole, 1998