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Chance-Constrained Programming with 0-1 or Bounded Continuous Decision Variables

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  • Fredrick S. Hillier

    (Stanford University)

Abstract

This paper considers the chance-constrained programming problem where the decision variables can be either bounded and continuous or restricted to be either zero or one, and where some or all of the parameters are random variables that may be statistically dependent. Both exact and approximate solution procedures are presented, where most of these are based on several linear inequalities that permit this problem to be approximated by a number of ordinary (integer or noninteger) linear programming problems. Either zero-order or linear decision rules are allowed for the continuous variables, and a general method of making "second-stage decisions" with either continuous or 0-1 variables is developed.

Suggested Citation

  • Fredrick S. Hillier, 1967. "Chance-Constrained Programming with 0-1 or Bounded Continuous Decision Variables," Management Science, INFORMS, vol. 14(1), pages 34-57, September.
    • Handle: RePEc:inm:ormnsc:v:14:y:1967:i:1:p:34-57
    DOI: 10.1287/mnsc.14.1.34
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    Cited by:

    1. Bitran, Gabriel R. & Leong, Thin-Yin., 1989. "Deterministic approximations to co-production problems with service constraints," Working papers 3071-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Poojari, Chandra A. & Varghese, Boby, 2008. "Genetic Algorithm based technique for solving Chance Constrained Problems," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1128-1154, March.
    3. Bilsel, R. Ufuk & Ravindran, A., 2011. "A multiobjective chance constrained programming model for supplier selection under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1284-1300, September.
    4. Zare M., Yahia & Daneshmand, Ahmad, 1995. "A linear approximation method for solving a special class of the chance constrained programming problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 213-225, January.
    5. John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie, 2022. "An introduction to stochastic bin packing-based server consolidation with conflicts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 296-331, July.

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