Computational complexity of stochastic programming problems

• Published in: Mathematical programming Vol. 106; no. 3; pp. 423 - 432
• Main Authors: Dyer, Martin, Stougie, Leen
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.07.2006; Springer Nature B.V
• Subjects: Applied sciences; Exact sciences and technology; Integer programming; Linear programming; Mathematical programming; Operational research and scientific management; Operational research. Management science; Optimization; Optimization techniques; Phase transitions; Random variables; Stochastic models; Studies; Uncertain system; Probabilistic approach; Computational complexity; Distributed parameter system; Mathematical programming; Stochastic programming
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-005-0597-0

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. [PUBLICATION ABSTRACT]