Computational complexity of stochastic programming problems

Authors:
Martin Dyer;Leen Stougie
Affiliations:
School of Computing, University of Leeds, United Kingdom;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven and CWI, Amsterdam, The Netherlands
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theoretical complexity of a variety of stochastic programming problems studied in this literature. Under the assumption that the stochastic parameters are independently distributed, we show that two-stage stochastic programming problems are ♯P-hard. Under the same assumption we show that certain multi-stage stochastic programming problems are PSPACE-hard. The problems we consider are non-standard in that distributions of stochastic parameters in later stages depend on decisions made in earlier stages.