Introductory description

Uncertainty plays a significant role in a wide range of real-world applications, especially in science and engineering, such as manufacturing, transportation, telecommunication, finance, agriculture, and energy etc. Uncertainty modelling is therefore an important issue in solving real-life optimisation problems with data uncertainty.
Stochastic programming is concerned with optimal decision making under uncertainty. The module focuses on several aspects of uncertainty modelling and stochastic programming. In general, the module provides an introduction to models, basic theory and computational methods for optimisation problems under uncertainty as well as a broad overview of its applications in various sectors. It basically focuses on modelling and solving methods as well as real life applications including power generation, financial planning, network resource utilisation, supply chain management, revenue and inventory management.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The content of module includes the following topics:

• introduction: decision making under uncertainty and its application areas,
• uncertainty modelling,
• two-stage stochastic optimisation models,
• computational software (AMPL),
• computational and practical aspects of two-stage models and their applications,
• robust optimisation,
• chance-constrained models,
• multi-stage modelling and scenario based approaches, and
• real-life applications in multi-stage stochastic programming.

Learning outcomes

By the end of the module, students should be able to:

• Identify key theoretical concepts and methods used for robust and optimal decision making under uncertainty.
• Understand the capabilities and limitations of stochastic models.
• Develop modelling and solving skills for stochastic optimization problems.
• Understand a range of optimization techniques to model and solve stochastic programming problems arising in wide applications.
• Be aware of complex decision making problems and advanced modelling approaches.

Indicative reading list

A. J. King and S. W. Wallace. Modeling with Stochastic Programming. Springer, 2012.
A. Ben-Tal, L. El Ghaoui, and A. Nemirovski. Robust Optimization. Princeton University Press, Princeton, NJ, 2009.
A. Shapiro, D. Dentcheva, and A., Ruszczynski, Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia, 2009. Ebook Downloadable: http://www2.isye.gatech.edu/people/faculty/Alex_Shapiro/SPbook.pdf
P. Kall and J. Mayer. Stochastic Linear Programming: Models, Theory, and Computation. International Series in Operations Research & Management Science, Vol. 156, Springer, 2011, Edition 2.
S. W. Wallace and W. T. Ziemba (Eds.), Applications of Stochastic Programming, MPS-SIAM Book Series on Optimization 5, 2005.
A. Ruszczynski and A. Shapiro (Eds.), Stochastic Programming, Handbooks in Operations Research and Management Science, Vol. 10, Elsevier, 2003.

Subject specific skills

Model and solve stochastic optimisation model using AMPL.
Learn complex decision-making problems.

Transferable skills

Identify and incorporate uncertainty into decision making process.
Recognise and formulate a practical problem as tochastic program.
Be able to solve the stochastic model using an appropriate method.