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Approximation in stochastic integer programming

Author

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  • Stougie, Leen
  • Vlerk, Maarten H. van der

    (Groningen University)

Abstract

Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions. However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality. Only recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.

Suggested Citation

  • Stougie, Leen & Vlerk, Maarten H. van der, 2003. "Approximation in stochastic integer programming," Research Report 03A14, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:03a14
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    File URL: http://irs.ub.rug.nl/ppn/248283359
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    References listed on IDEAS

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    Cited by:

    1. Maarten Vlerk, 2010. "Convex approximations for a class of mixed-integer recourse models," Annals of Operations Research, Springer, vol. 177(1), pages 139-150, June.
    2. Retsef Levi & Martin Pál & Robin O. Roundy & David B. Shmoys, 2007. "Approximation Algorithms for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 284-302, May.

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