On distributionally robust multiperiod stochastic optimization

Bita Analui () and Georg Pflug ()

Computational Management Science, 2014, vol. 11, issue 3, 197-220

Abstract: This paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider “ambiguity neighborhoods” around this tree as alternative models which are close to the baseline model. Closeness is defined in terms of a distance for probability trees, called the nested distance. This distance is appropriate for scenario models of multistage stochastic optimization problems as was demonstrated in Pflug and Pichler (SIAM J Optim 22:1–23, 2012 ). The ambiguity model is formulated as a minimax problem, where the the optimal decision is to be found, which minimizes the maximal objective function within the ambiguity set. We give a setup for studying saddle point properties of the minimax problem. Moreover, we present solution algorithms for finding the minimax decisions at least asymptotically. As an example, we consider a multiperiod stochastic production/inventory control problem with weekly ordering. The stochastic scenario process is given by the random demands for two products. We determine the minimax solution and identify the worst trees within the ambiguity set. It turns out that the probability weights of the worst case trees are concentrated on few very bad scenarios. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Multistage stochastic optimization; Distributional robustness; Model ambiguity; Nested distance; Inventory management (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10287-014-0213-y

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