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Application of the polyblock method to special integer chance constrained problem

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  • Fatima Bellahcene

Abstract

The focus in this paper is on a special integer stochastic program with a chance constraint in which, with a given probability, a sum of independent and normally distributed random variables is bounded below. The objective is to maximize the expectation of a linear function of the random variables. The stochastic program is first reduced to an equivalent deterministic integer nonlinear program with monotonic objective and constraints functions. The resulting deterministic problem is solved using the discrete polyblock method which exploits its special structure. A numerical example is included for illustration and comparisons with LINGO, COUENNE, BONMIN and BARON solvers are performed.

Suggested Citation

  • Fatima Bellahcene, 2019. "Application of the polyblock method to special integer chance constrained problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(4), pages 23-40.
    • Handle: RePEc:wut:journl:v:4:y:2019:p:23-40:id:1445
    DOI: 10.37190/ord190402
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    References listed on IDEAS

    as
    1. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, March.
    2. D. Li & X.L. Sun & M.P. Biswal & F. Gao, 2001. "Convexification, Concavification and Monotonization in Global Optimization," Annals of Operations Research, Springer, vol. 105(1), pages 213-226, July.
    3. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    4. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
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