Issue: 2019/Vol.29/No.4, Pages 23-40
APPLICATION OF THE POLYBLOCK METHOD TO SPECIAL INTEGER CHANCE CONSTRAINED PROBLEM
Fatima Bellahcene
Cite as: F. Bellahcene. Application of the polyblock method to special integer chance constrained problem. Operations Research and Decisions 2019: 29(4), 23-40. DOI 10.37190/ord190402
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.
Keywords: stochastic programming, integer nonlinear programming, monotone optimization, polyblock method
Received: 9 March 2019, Accepted: 11 January 2020