MAT001 - OR Methods
This course will introduce to students a range of fundamental Operational Research (OR) techniques, both stochastic and deterministic in nature. Students will additionally gain experience in using commercial software packages to support learning and connect theoretical understanding with solving practical problems.
The stochastic part will introduce the concepts and applications of the following five topics: decision theory, reliability theory, inventory systems, queueing theory and simulation. Models and examples will be provided to demonstrate applications of the topics. The simulation component will include the main approaches in this topic: Monte Carlo, Discrete Event, System Dynamics, and Agent Based Simulation. Computer workshops will introduce the students to a range of simulation software covering the different approaches taught in the lectures.
The deterministic part focuses on linear and integer programming, dynamic programming, scheduling, project networks and heuristics. Following an explanation and illustrations of the standard simplex method, some of its variants will be introduced and the concepts of duality explained. Computer workshops will train the students in the use of software for linear programming. Branch and bound approaches for solving integer programming problems will be developed. For tackling sequential problems, dynamic programming will be introduced. Scheduling problems will be discussed and the students will be introduced to a number of algorithms for developing efficient schedules. For project networks, the representation of projects as networks and methods for analysing such networks will be covered. For complex problems, heuristic methods may be utilised, and design principles of heuristics and local search methods will be explained.
The following books are recommended texts for this module:-
Winston WL. Operations Research: Applications and Algorithms (Duxbury).
Hillier FS and Lieberman GJ. Introduction to Operations Research (McGraw-Hill)
Pidd M. Computer Simulation in Management Science (Wiley).
Robinson S. Simulation: The Practice of Model Development and Use (Wiley).
Law M and Kelton WD. Simulation Modelling and Analysis (McGraw-Hill).
Williams HP. Model Building in Mathematical Programming (Wiley).
Williams HP. Model Solving in Mathematical Programming (Wiley).
Winston WL and Venkataramanan M. Introduction to Mathematical Programming (Duxbury).
Pinedo M. Scheduling: Theory, Algorithms and Systems (Prentice Hall).