| CODE | SOR3311 | ||||||||
| TITLE | Stochastic Programming | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 6 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | - Examples of modelling under uncertainty - Underlying program formulation and deterministic equivalent choice - Here-and-Now (HN) and Wait-and-See (WS) approaches - Random objective functions - Expected Value of Perfect Information (EVPI) and Value of Stochastic Solution (VSS) measures - Chance (or probabilistic) constraints - Recourse models - Two-stage stochastic programs and their properties - L-shaped decomposition method - Multi-stage stochastic programs - Stochastic integer programs - Monte Carlo sampling methods for stochastic optimization problems - Introduction to stochastic dynamic programming Study-Unit Aims: Stochastic programming is a framework for modelling optimization problems that involve parameters which are uncertain at the time the decisions are made and for which probability distributions are known or can be estimated. Such problems arise in a variety of areas such as transportation, finance, agriculture, manufacturing, healthcare, energy and telecommunications, amongst others. This study unit aims at covering the basic theory, modelling, applications and solution methods of this optimization field. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - demonstrate the use of stochastic programming in several real-life settings; - distinguish between here-and-now and wait-and-see decisions; - analyse the theoretical properties of stochastic programs; - identify decision making situations in which several decision stages and/or recourse actions are required; - describe verbally and apply the L-shaped decomposition method to different stochastic optimization problems; - recognise the usefulness of Monte Carlo sampling in stochastic optimization; - have a basic understanding of stochastic dynamic programming. 2. Skills: By the end of the study-unit the student will be able to: - formulate real-life optimization problems with uncertain input data as stochastic programs; - handle randomness in objective functions; - compare solutions from different deterministic equivalents; - handle chance (or probabilistic) constraints; - model and solve two-stage stochastic programs, multi-stage stochastic programs and stochastic integer programs; - model and solve stochastic dynamic programs. Main Text/s and any supplementary readings: Birge, J. R., & Louveaux, F. (2011). Introduction to Stochastic Programming. New York, NY: Springer New York. Kall, P., & Mayer, J. (2011). Stochastic linear programming: Models, theory, and computation. New York: Springer. Kall, P., & Wallace, S. W. (1994). Stochastic programming. Chichester: John Wiley & Sons. Klein Haneveld, W. K., van der Vlerk, M. H., & Romeijnders, W. (2020). Stochastic programming: Modeling decision problems under uncertainty. Cham, Switzerland: Springer. Prékopa, A. (1995). Stochastic programming. Dordrecht: Kluwer Academic. Ruszczyński, A. P., & Shapiro, A. (2003). Stochastic programming. Amsterdam: Elsevier. Shapiro, A., Dentcheva, D., & Ruszczyński, A. P. (2014). Lectures on stochastic programming: Modeling and theory. Philadelphia, PA: SIAM. |
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| RULES/CONDITIONS | Before TAKING THIS UNIT YOU MUST TAKE SOR1310 AND TAKE SOR1320 AND TAKE SOR2330 AND TAKE SOR3350 | ||||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Monique Sciortino |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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