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Simulation-Based Optimality Tests for Stochastic Programs

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Stochastic Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 150))

Abstract

Assessing whether a solution is optimal, or near-optimal, is fundamental in optimization. We describe a simple simulation-based procedure for assessing the quality of a candidate solution to a stochastic program. The procedure is easy to implement, widely applicable, and yields point and interval estimators on the candidate solutions optimality gap. Our simplest procedure allows for significant computational improvements. The improvements we detail aim to reduce computational effort through single- and two-replication procedures, reduce bias via a class of generalized jackknife estimators, and reduce variance by using a randomized quasi-Monte Carlo scheme.

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Acknowledgments

The authors thank Georg Pflug for valuable discussions, particularly with respect to Example 3.2. This research was supported by the National Science Foundation under grants CMMI-0653916 and EFRI-0835930.

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Authors and Affiliations

  1. Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Güzin Bayraksan

  2. Graduate Program in Operations Research, The University of Texas at Austin, Austin, TX, 78712, USA

    David P. Morton & Amit Partani

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  1. Güzin Bayraksan
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  2. David P. Morton
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  3. Amit Partani
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Correspondence to Güzin Bayraksan .

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  1. Dept. Management Science & Engineering, Stanford University, Stanford, 94305, California, USA

    Gerd Infanger

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Bayraksan, G., Morton, D.P., Partani, A. (2010). Simulation-Based Optimality Tests for Stochastic Programs. In: Infanger, G. (eds) Stochastic Programming. International Series in Operations Research & Management Science, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1642-6_3

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