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Constructing Sets of Uniformly Tighter Linear Approximations for a Chance Constraint

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  • Yrjö Seppälä

    (Operaatiotutkimustoimisto Seppäläky, Helsinki, Finland)

Abstract

The aim of this paper is to construct sets of uniformly tighter linear constraints to replace a chance constraint, in order to be able to solve the chance-constrained programming problem by the simplex method. The chance constraints are first diagonalized by a linear orthonormal transformation. Uniformly tighter linear constraints can then be formed to replace the chance constraint. The developed multistage linear programming problem can also be solved using the Dantzig-Wolfe decomposition technique. Approximation errors of our method and one of Hillier's [8] are compared.

Suggested Citation

  • Yrjö Seppälä, 1971. "Constructing Sets of Uniformly Tighter Linear Approximations for a Chance Constraint," Management Science, INFORMS, vol. 17(11), pages 736-749, July.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:11:p:736-749
    DOI: 10.1287/mnsc.17.11.736
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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. 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.
    4. Bitran, Gabriel R. & Leong, Thin-Yin., 1990. "Distribution-free, uniformly-tighter linear approximations for chance-constrained programming," Working papers 3111-90., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Qiushi Chen & Lei Zhao & Jan C. Fransoo & Zhe Li, 2019. "Dual-mode inventory management under a chance credit constraint," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 147-178, March.

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