Landelijk Netwerk Mathematische Besliskunde
Course SP: "Stochastic Programming"
Time: 
Monday 15.15 – 17.00 (February 24  April 6, April 20, May 4  May 11). 
Location: 
Hans Freudenthalgebouw, Room 611AB, Budapestlaan, Utrecht (De Uithof). 
Lecturer: 
Dr. W. Romeijnders (University of Groningen). 
Course description:
Stochastic programming (see also http://stoprog.org) is a framework for
modelling optimization problems that involve uncertainty. Whereas
deterministic optimization problems are formulated with known
parameters, real world problems almost invariably include some unknown
parameters. When the parameters are known only within certain bounds,
one approach to tackling such problems is called robust optimization.
Here the goal is to find a solution which is feasible for all such data
and optimal in some sense. Stochastic programming models are similar in
style but take advantage of the fact that probability distributions
governing the data are known or can be estimated. The goal here is to
find some policy that is feasible for all (or almost all) the possible
data instances and maximizes the expectation of some function of the
decisions and the random variables. More generally, such models are
formulated, solved analytically or numerically, and analyzed in order
to provide useful information to a decisionmaker.
The most widely applied and studied stochastic programming
models are twostage linear programs. Here the decision maker takes
some action in the first stage, after which a random event occurs
affecting the outcome of the firststage decision. A recourse decision
can then be made in the second stage that compensates for any bad
effects that might have been experienced as a result of the firststage
decision. The optimal policy from such a model is a single firststage
policy and a collection of recourse decisions (a decision rule)
defining which secondstage action should be taken in response to each
random outcome.
The following subjects are discussed:
 Concepts and examples of stochastic programming.
 Stochastic linear programming.
 Recourse models.
 Chance constraints.
 SP calculus (e.g. convexity; approximation of distributions).
 Algorithms.
 Stochastic integer programming.
 Multistadia recourse models.
 Case study.
Prerequisites:
 Basic knowledge of probability theory: S.M. Ross, Introduction to
probability models, 8th edition, Academic Press, 2003 (chapters 13).
 Basic knowledge of linear programming: V. Chvatal, Linear
programming, Freeman, 1983.
Literature:
 W.K. Klein Haneveld, M.H. van der Vlerk, and W. Romeijnders, Stochastic Programming  Modeling Decision Problems Under Uncertainty, Graduate Texts in Operations Research, Springer, 2020. Link to book
Examination:
Take home problems, case study.
Address of the lecturer:
Dr. W. Romeijnders
Faculteit Economie en Bedrijfskunde, Operations , University of
Groningen, P.O. Box 800, 9700 AV Groningen.
Phone: 050  3638613.
Email: w.romeijnders@rug.nl
