On solving two stage stochastic linear problems by using a new approach, Cluster Benders Decomposition

The optimization of stochastic linear problems, via scenario analysis, based on Benders decomposition requires to appending feasibility and/or optimality cuts to the master problem until the iterative procedure reaches the optimal solution. The cuts are identified by solving the auxiliary submodels attached to the scenarios. In this work, we propose a so-called scenario cluster decomposition approach for dealing with the feasibility cut identification in the Benders method for solving large-scale two stage stochastic linear problems. The scenario tree is decomposed into a set of scenario clusters and tighter feasibility cuts are obtained by solving the auxiliary submodel for each cluster instead of each individual scenario. Then, this scenario cluster based scheme allows us to define tighter feasibility cuts that yield feasible second stage decisions in reasonable time consuming. Some computational experience by using the free software COIN-OR is reported to show the favorable performance of the new approach over traditional Benders decomposition.