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Distribution-Free Approximations for Chance Constraints

Author

Listed:
  • F. M. Allen

    (Western Electric Engineering Research Center, Princeton, New Jersey)

  • R. N. Braswell

    (Armament Development and Test Center, Air Force Systems Command, Eglin Air Force Base, Florida)

  • P. V. Rao

    (University of Florida, Gainesville, Florida)

Abstract

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used, it is not possible to relate the accuracy of sample-based assumptions to actual constraint satisfaction. The methods presented here employ the concept of a distribution-free tolerance region to construct various sets whose elements have the common property of satisfying the chance constraint with a preassigned level of confidence. The sample size required to meet the desired confidence is readily available in tabular or graphical form.

Suggested Citation

  • F. M. Allen & R. N. Braswell & P. V. Rao, 1974. "Distribution-Free Approximations for Chance Constraints," Operations Research, INFORMS, vol. 22(3), pages 610-621, June.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:3:p:610-621
    DOI: 10.1287/opre.22.3.610
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    Cited by:

    1. Raffaello Seri & Christine Choirat, 2013. "Scenario Approximation of Robust and Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 590-614, August.
    2. 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.
    3. Bitran, Gabriel R. & Leong, Thin-Yin., 1989. "Co-production of substitutable products," Working papers 3097-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    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.

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