This refers to an optimization problem with uncertain or random parameters, the realizations of which are revealed progressively over successive time periods (or stages). For a k-stage instance, the set of decision variables is decomposed into (x 1 , y 1 , x 2 , y 2 , . .., x k , y k ); in any stage t, the decision variables x t have to be fixed knowing the realizations of the uncertain or random parameters in stages 1, 2, … t-1, but prior to getting any information about the realization of the uncertain or random parameters in stage t and in subsequent stages; the decision variables y t can be adjusted after observing the realized values of the uncertain or random parameters in stages 1, 2, .., t.
Published in Chapter:
Robust Two-Stage and Multistage Optimization: Complexity Issues and Applications
Michel Andre Minoux (University P. and M. Curie, France)
Copyright: © 2016
|Pages: 41
DOI: 10.4018/978-1-4666-9644-0.ch002
Abstract
This chapter is intended as an overview of robust optimization models related to optimization problems subject to uncertain data, with special focus on the case when uncertainty impacts the right-hand side coefficients in the constraints. Two-stage as well as multistage models are addressed, emphasizing links with applications and computational complexity issues. A class of multistage robust optimization problems for which exact optimal strategies can be efficiently computed (via a robust dynamic programming recursion) is discussed. An application to a multiperiod energy production planning problem is presented into detail, and computational results are reported.