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
The authors are grateful to the anonymous referees for their thoughtful comments which substantially improved the paper. This research was supported by the Swiss National Science Foundation Grant BSCGI0_157733 and the EPSRC Grants EP/M028240/1 and EP/M027856/1.
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