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On Chance Constrained Programming Problems with Joint Constraints

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  • Vijay S. Bawa

    (Bell Telephone Laboratories, Inc., Holmdel, New Jersey)

Abstract

In this paper we consider chance constrained programming problems with joint constraints shown in the literature to be equivalent deterministic nonlinear programming problems. Since most existing computational methods for solution require that the constraints of the equivalent deterministic problem be concave, we obtain a simple condition for which the concavity assumption holds when the right-hand side coefficients are independent random variables. We show that it holds for most probability distributions of practical importance. For the case where the random vector has a multivariate normal distribution, nonexistence of any efficient numerical methods for evaluating multivariate normal integrals necessitates the use of lower bound approximations. We propose an approximation for the case of positively correlated normal random variables.

Suggested Citation

  • Vijay S. Bawa, 1973. "On Chance Constrained Programming Problems with Joint Constraints," Management Science, INFORMS, vol. 19(11), pages 1326-1331, July.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:11:p:1326-1331
    DOI: 10.1287/mnsc.19.11.1326
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    Cited by:

    1. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    2. Sergey S. Rabotyagov & Adriana M. Valcu-Lisman & Catherine L. Kling, 2016. "Resilient Provision of Ecosystem Services from Agricultural Landscapes: Trade-offs Involving Means and Variances of Water Quality Improvements," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(5), pages 1295-1313.
    3. Rashed Khanjani-Shiraz & Salman Khodayifar & Panos M. Pardalos, 2021. "Copula theory approach to stochastic geometric programming," Journal of Global Optimization, Springer, vol. 81(2), pages 435-468, October.
    4. Zhen, Chen & Zheng, Xiaoyong, 2015. "Measuring the Informational Value of Interpretive Shelf Nutrition Labels to Shoppers," 2016 Allied Social Sciences Association (ASSA) Annual Meeting, January 3-5, 2016, San Francisco, California 212812, Agricultural and Applied Economics Association.
    5. Willis, David B. & Whittlesey, Norman K., 1998. "The Effect Of Stochastic Irrigation Demands And Surface Water Supplies On On-Farm Water Management," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 23(1), pages 1-19, July.
    6. Zahra Mashayekhi Zadeh & Esmaile Khorram, 2012. "Convexity of chance constrained programming problems with respect to a new generalized concavity notion," Annals of Operations Research, Springer, vol. 196(1), pages 651-662, July.

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