Mathematical Programming and Optimisation

BMAN60101 Mathematical Programming and Optimisation 15 Semester 1 Postgraduate Taught Level 7 Dong-Ling Xu Unit coordinator Alliance Manchester Business School 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 Mathematical modelling and optimization are critical to production planning, service design, and decision-making at operational, managerial, and strategic levels. They are also the foundation of machine learning and artificial intelligence. This course provides students with a solid understanding of the techniques and skills that underpin the business data analytics industry. Through real-world examples, students will learn how academic theory applies to practice, enhancing their ability to make informed decisions in workplace environments and management consulting roles. The module also highlights the importance of optimization techniques in addressing contemporary challenges such as minimizing costs, reducing waste, and mitigating the environmental impact of business activities.  Mathematical modelling and optimization are critical to production planning, service design, and decision-making at operational, managerial, and strategic levels. They are also the foundation of machine learning and artificial intelligence. This course provides students with a solid understanding of the techniques and skills that underpin the business data analytics industry. Through real-world examples, students will learn how academic theory applies to practice, enhancing their ability to make informed decisions in workplace environments and management consulting roles. The module also highlights the importance of optimization techniques in addressing contemporary challenges such as minimizing costs, reducing waste, and mitigating the environmental impact of business activities. The aim of this unit is to equip students with key concepts and algorithms of mathematical programming and demonstrate how to apply them in the context of resource management for business. The course covers linear, non-linear, integer, and dynamic programming, including problem formulation, solution techniques, solution interpretation, sensitivity analysis, and metaheuristics. Students will gain an understanding of the algorithms used to find optimal solutions and learn to apply these algorithms both manually and using software tools like Excel Solver, OpenSolver, and other optimization software packages. At the end of the unit students should be able to understand the main optimization approaches and their applications for solving managerial decision problems. Students should be able to critically analyse and model appropriate decision problems and solve them analytically, or by using optimization software. They will learn to present solutions and arguments in textual and oral forms, both individually and in groups.  Identify various types of decision-making problems and formulate them as appropriate mathematical programs.  Apply suitable algorithms and procedures to solve these problems, finding optimal solutions both manually (for small-scale problems) and using software tools such as Excel, Python, or other relevant software packages Interpret the optimal solutions and analyze resource utilization, conducting sensitivity analysis where applicable. Construct abstract mathematical models from concrete problem statements Design, analyse, and apply step-by-step procedures (algorithms) to solve problems, both manually or through computer programming, effectively and efficiently.  Analyse the impact of market fluctuations or resource availability on decision making and performance Apply mathematical programming techniques to solve problems in areas such as resource allocation, scheduling, production planning, or supply chain management. Use software tools like Excel Solver, OpenSolver, Python, MATLAB, or other optimization packages to solve mathematical programs, and understand how the programs work.  Decide whether and how an optimal business plan should be adjusted when there is fluctuations in market condition or resource availability, to ensure optimal decision-making under uncertainty.  Break down complex decision-making scenarios into manageable components and identify their essential features, and frame real-world problems as mathematical formulations, enabling structured solutions.  Focus on optimising business objectives when planning and allocating resources.  Translate mathematical models and solutions into actionable business decisions for managers, and communicating the implications and resource status associated with implementing optimal plans.  Formal Contact MethodsMinimum Contact hours: 20 Delivery format: Lecture and Workshops  0 Other 100% 50% Exam 50% Coursework  • Informal advice and discussion during lectures and office hours. • Written and/or verbal comments on assessed or non-assessed work. • Responses to student frequently asked questions via Canvas or emails. • Generic feedback posted on Canvas regarding overall examination performance. BMAN60101 Programme Req: BMAN60101 is only available as a core unit to students on MSc Business Analytics and as an elective to students on MSc Data Science (Business & Management pathway) N The CORE text is:HILLIER, F and LIEBERMAN, G (2004 or any later edition), Introduction to Operations Research with CD-Rom, McGra HillTaha, H.A. Operations Research, An Introduction (1997, 5th Edition or later), MacmillanHastings, N.A.J (1988) Dynamic Programming with Management Applications, The Butterworth Group, EnglandThe most important chapter of the book can be accessed from this link: <a href="https://contentstore.cla.co.uk/secure/link?id=224f1b5d-22af-e711-80cb-005056af4099" target="_blank">https://contentstore.cla.co.uk/secure/link?id=224f1b5d-22af-e711-80cb-005056af4099</a> (It will ask you to login first; after login, you may see an error message, but if you come here to click on this link again, it should workTALBI, El-Ghazali (2009), Metaheuristics: from design to implementation (e-book available through the library)Other readings:Smith, D.K (1991) Dynamic Programming, A Practical Introduction, Ellis Horwood Assessment written exam 2 Lectures 33 0 115 Informal Contact MethodOffice hoursPeer Assisted Study Sessions