A comment on “computational complexity of stochastic programming problems”
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Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Program A 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is governed by independent uniform distributions. We show that Dyer and Stougie’s proof is not correct, and we offer a correction which establishes the stronger result that even the approximate solution of such problems is #P-hard for a sufficiently high accuracy. We also provide new results which indicate that linear two-stage stochastic programs with random recourse seem even more challenging to solve.
KeywordsStochastic programming Complexity theory Two-stage problems
Mathematics Subject Classification90C15
- 11.Ruszczyński, A., Shapiro, A. (eds.): Stochastic Programming, Volume 10 of Handbooks in Operations Research and Management Science. Elsevier, Amsterdam (2003)Google Scholar