A Benders’ Decomposition Approach for the Stochastic CPs with Linear Recourse

We adopt Benders’ decomposition algorithm to solve scenariobased Stochastic Constraint Programs (SCPs) with linear recourse. Rather than attempting to solve SCPs via a monolithic model, we show that one can iteratively solve a collection of smaller sub-problems and arrive at a solution to the entire problem. In this approach, decision variables corresponding to the initial stage and linear recourse actions are grouped into two sub-problems. The sub-problem corresponding to the recourse action further decomposes into independent problems, each of which is a representation of a single scenario. Our computational experience on stochastic versions of the well-known template design and warehouse location problems shows that, for linear recourse SCPs, Benders’ decomposition algorithm provides a very efficient solution method.