This module aims to equip students with the essential skills and knowledge needed to apply operations research (OR) techniques in decision-making processes. Through the study of mathematical optimisation, specifically focusing on multivariate functions, students will gain a solid understanding of how to approach complex real-world problems with a solid analytical framework. The module, in its updated form, will complement the students' curriculum in multivariate calculus, which is critical for formulating and solving complex real-world optimisation problems. 

The following syllabus is indicative of the content to be addressed in this module. 1. Model building and the methods of operations research. 2. Linear programming in operations research - graphical interpretation, simplex method and sensitivity analysis. Duality and the dual simplex method. 3. Applications of linear programming - transportation and assignment algorithms, zero-sum games. 4. Dynamic programming and decision analysis in operations research - decision trees, expected value, utility, decision-making under uncertainty (Bayesian approach). 5. An introduction to unconstrained optimisation - line search methods. 6. An introduction to constrained optimisation - necessary and sufficient conditions for optimality (including the KKT conditions and the method of Lagrange multipliers).

On successful completion of this module, students will be able to: 1. apply the geometrical interpretation of a linear programming problem in operations research to solve linear programming problems with two variables;  2. formulate real life problems as linear programming problems, then apply appropriate algorithms to solve such linear programming problems, including transport and assignment problems; 3. apply a Bayesian approach to decision theory problems in operations research; 4. examine both unconstrained and constrained optimisation problems in operations research and apply the methods of multivariate calculus to solve them.

On successful completion of this module, students will be able to: 1. value the importance of the operations research method of linear programming in real-world applications; 2. advocate the key role of optimisation methods in operations research and, more widely, in applied mathematics.

The module will be taught by introducing an environment for the students that is experiential, collaborative and challenge-driven, beyond the conventional lecture format. Students will develop advanced skills in writing the algorithms of linear programming and optimisation of interest in real-world operations research applications. Simple real-life problems will be used to illustrate each step used in the algorithms presented.  The module, embedded in a number of research-led undergraduate programmes, will provide the students with research-led skills in operations research, including linear programming and optimisation, that reflect the CHALLENGE-DRIVEN & EXPERIENTIAL nature of the module and the programmes.  The module, embedded in a number of COLLABORATIVE & CROSS-DISCIPLINARY programmes, will encourage students to think critically and to collaborate across the scientific disciplines of mathematics, statistics, economics, artificial intelligence and machine learning. It will offer authentic learning experiences drawn from real-world examples. Tutorials will provide real-world examples that build upon the material covered in the lectures. These sessions are designed to help students apply what they've learned by solving practical problems and addressing areas of difficulty. This hands-on approach ensures that students not only reinforce their understanding but also gain valuable experience in tackling complex issues. The module will provide a learning experience for the students that will stimulate the students to stay CURIOUS (think logically, analytically and critically and demonstrate strong problem-solving skills); to be COURAGEOUS (can undertake complex problems with diligent organisation and resilience, and communicate abstract concepts and highly technical problems effectively in a wide variety of contexts); to be ARTICULATE (can work and communicate effectively and efficiently on trans- and inter-disciplinary projects and teams); to be AGILE (can take a high-level view of a problem and formulate relevant models and mathematical strategies that are flexible and generalisable to a wide variety of settings); to be RESPONSIBLE (able to challenge and question the appropriate use of operations research and optimisation techniques and the responsible implementation of these).