Module overview
Optimisation under uncertainty concerns the modelling and solution of decision-making problems in which some input data are not known with certainty at the time decisions must be made. Such uncertainty is inherent in most real-world systems and arises in applications including energy systems, logistics, transportation, scheduling, healthcare, finance, and machine learning.
This module introduces the principal mathematical frameworks for optimisation under uncertainty and real-world examples using the mathematical frameworks. Students will study stochastic programming and robust optimisation. Students will learn how uncertainty can be represented mathematically and how these representations influence both modelling choices and solution approaches. The module also briefly highlights how these frameworks interact with modern data-driven methods and emerging computational technologies such as AI and quantum computing.
The course develops both theoretical foundations and practical methodologies. Core topics include two-stage, multi-stage and multi-horizon stochastic programming, risk-sensitive optimisation, dynamic decision-making models. Attention is given to scalable solution techniques, such as decomposition algorithms and value function approximation methods, that enable large-scale problems to be solved efficiently. Where appropriate, links to recent developments in areas such as machine learning and quantum computing are discussed.
The module integrates analytical development with computational implementation. Through lectures and interactive workshops, students will formulate and implement optimisation models motivated by real-world applications. By the end of the module, students will be able to model uncertainty rigorously and apply advanced optimisation tools to support robust and informed decision-making in complex problems, preparing them to competently apply optimisation under uncertainty methodologies in their future careers.