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Decomposition algorithms for two-stage chance-constrained programs

Abstract

We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility cuts to solve this class of problems. Computational results on a chance-constrained resource planing problem indicate that our algorithms are highly effective in solving these problems compared to a mixed-integer programming reformulation and a naive decomposition method.

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Acknowledgments

We are grateful to the two anonymous referees and Dave Morton for their comments on an earlier version.

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Correspondence to Simge Küçükyavuz.

Additional information

Simge Küçükyavuz and Xiao Liu are supported by the National Science Foundation (NSF) under Grant CMMI-1055668.

James Luedtke is supported by NSF under Grant CMMI-0952907 and by the Applied Mathematics activity, Advance Scientific Computing Research program within the DOE Office of Science under a contract from Argonne National Laboratory.

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Liu, X., Küçükyavuz, S. & Luedtke, J. Decomposition algorithms for two-stage chance-constrained programs. Math. Program. 157, 219–243 (2016). https://doi.org/10.1007/s10107-014-0832-7

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  • DOI: https://doi.org/10.1007/s10107-014-0832-7

Keywords

  • Two-stage stochastic programming
  • Chance constraints
  • Benders decomposition
  • Cutting planes

Mathematics Subject Classification

  • 90C15
  • 90C10