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An Integer Programming and Decomposition Approach to General Chance-Constrained Mathematical Programs

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Integer Programming and Combinatorial Optimization (IPCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

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Abstract

We present a new approach for exactly solving general chance constrained mathematical programs having discrete distributions. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and currently available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained two-stage problem arising in call center staffing indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. Thus, the strength of this approach results from the successful merger of stochastic programming decomposition techniques with integer programming techniques for finding strong valid inequalities.

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Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    James Luedtke

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  1. James Luedtke
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Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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Luedtke, J. (2010). An Integer Programming and Decomposition Approach to General Chance-Constrained Mathematical Programs. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_21

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

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