MA2601: Operational Research

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA2601
External Subject Code 100404
Number of Credits 20
Level L5
Language of Delivery English
Module Leader Mr Geraint Palmer
Semester Spring Semester
Academic Year 2022/3

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 Year Three modules in OR.

Recommended Modules: MA1500 Introduction to Probability Theory and 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

Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:

  • Weekly face to face classes (e.g. labs, lectures, exercise classes)
  • Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)

Students are also expected to undertake self-guided study throughout the duration of the module.

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

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 80 Operational Research 3
Written Assessment 20 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.

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