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Application of the polyblock method to special integer chance constrained problem

Bellahcene Fatima

Operations Research and Decisions

2019

Vol. 29, No. 4

23--40

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.