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 module will introduce the concepts and applications of simulation. This component will include 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 module then focuses on linear and integer programming Particular emphasis will be placed on forming linear programming models to represent real-life problems. The Simplex method for solving linear programming problems will be outlined, together with some of its variants. Branch and bound approaches for solving integer programming problems will be developed. Appropriate computer packages will be used to solve these problems.

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 complex problems, heuristic methods may be utilised, and design principles of heuristics and local search methods will be explained.

• demonstrate foundational knowledge and understanding of the core areas of simulation, mathematical modelling and optimisation in the field of operational research;
• comprehend problems in the field of mathematical programming and formulate them mathematically;
• solve optimisation problems by identifying appropriate, tools, techniques, models and algorithms from the syllabus
• use appropriate algorithms, performing steps and calculations with precision;

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 to support the learning (e.g. videos, exercise sheets, lecture notes, quizzes)

Students are also expected to undertake at least 100 hours of self-guided study throughout the duration of the module, including preparation of formative assessments.

O.R. and analytics: simulation of stochastic systems; formulation and solution of optimisation problems.

Mathematical reasoning: understanding the theory and assumptions that underpin optimisation algorithms.

Use of simulation and optimisation computer packages.

Written communication skills.

1. Simulation. Concepts of the modelling approach, simulation approaches, static/dynamic, continuous/discrete. Monte Carlo, Discrete Event, System Dynamics.

2. Linear Programming. Forming models of real-life problems. Construction, standard and normal forms of LP problems, Simplex method, two-phase method. Sensitivity analysis, case studies.

3. Integer Programming. Branch and Bound, binary variables, problem formulation, examples of IP problems.

4. Dynamic Programming. Terminology, practical examples, stochastic dynamic programming.

5. Scheduling. Scheduling models, constraints, rules, Moore’s algorithm, Johnson’s algorithm.

6. Heuristics. Design of heuristics, complexity, greedy algorithms, local search, genetic algorithms.