Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities

We study a complex class of stochastic programming problems involving a joint chance constraint with random technology matrix and stochastic quadratic inequalities. We present a basic mixedinteger nonlinear reformulation based on Boolean modeling and derive several variants of it. We present detailed empirical results comparing the various reformulations and several easy to implement algorithmic ideas that improve performances of the mixed-integer nonlinear solver Couenne for solving these problems. Guidelines on how to tune the solver and selecting reformulations are presented. The test instances are epidemiology and disaster management facility location models and cover the three types of stochastic quadratic inequalities, namely product of two variables that are (i) both binary, (ii) binary and continuous, or (iii) both continuous.