Stochastic maximum weight forest problem

In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some insight about the complexity of this problem. We introduce an L‐shaped decomposition approach for the polynomial formulation, thus allowing the optimal solution of large scale instances with up to 90 nodes. Finally, we propose a Kruskal based variable neighborhood search (VNS) metaheuristic to compute near optimal solutions with significantly less computational effort. Our numerical results show that the VNS approach provides tight near optimal solutions with a gap less than 1% for most of the instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 289–305 2015