Sample approximation technique for mixed-integer stochastic programming problems with several chance constraints

Abstract

The paper deals with sample approximation applied to stochastic programming problems with chance constraints. We extend results on rates of convergence for problems with mixed-integer bounded sets of feasible solutions and several chance constraints.

We derive estimates on the sample size necessary to get a feasible solution of the original problem using sample approximation. We present an application to a vehicle routing problem with time windows, random travel times, and random demand.

Keywords

• Chance constrained problems
• Sample approximation
• Rate of convergence
• Sample size
• Stochastic vehicle routing problem