Operational Research (also known as OR or Management Science) is an important field that under-graduates often have not come across.  It is concerned with providing advice, analysis and support to decision-makers.  Often this takes the form of developing a model of a system under-consideration and then using the model to ask Where? How? What? and When? 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

• 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.

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.

Improves skills involved in problem solving, logical thinking and mathematical formulation of problems.  Also provides knowledge and use of simulation software.  All sought after skills in the management and business world.

Formative assessment is carried out by means of regular tutorial 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 combination of homeworks, a test and 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 but normally short.  Section B has a choice of three from four equally weighted questions.

• Queueing Theory
  • Kendall's queueing notation. 
  • Differential-difference equation approach to M/M/1 and M/M/C queues. 
  • 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. 
  • Discrete event and continuous time simulations. 
  • Fixed time step models. 
  • Event-to-event models. 
  • Random number generation.  
  • Random variable generation. 
  • Verification and validation. 
  • Construction of simple simulation models.

• 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.
  • Solution methods for these problems and their derivation.

Not applicable.

Operational Research: analysis and applications, Wilkes, F., M., McGraw-Hill, 1989

Operations Research: an introduction, Taha, H., A., Prentice Hall, 1997