An Optimization-Simulation Approach to Chance-Constraint Programming

Abstract

This paper considers a stochastic programming problem with a number of random parameters in the set of constraints. The method used for solving the problem is the iterative optimization- simulation approach. It consists of two phases: optimization phase, which includes solving a deterministic counterpart of the original chance-constrained problem, and a simulation phase in which the original constraints are checked using Monte Carlo simulation. One iteration corresponds to one scenario. If the decision maker is dissatisfied with the results, a new scenario is generated in which the deterministic values of stochastic parameters are changed in the direction that will provide a more robust solution. The deterministic counterpart in the new scenario is formulated depending on the result of the previous iteration. To that end, different heuristics are considered. The main goal is to provide a good insight on the optimization problem under uncertainty by performing a relatively small number of iterations. The general approach and results of the proposed framework are illustrated on an example of advertisement placement.