Using scenario trees and progressive hedging for stochastic inventory routing problems

The Stochastic Inventory Routing Problem is a challenging problem, combining inventory management and vehicle routing, as well as including stochastic customer demands. The problem can be described by a discounted, infinite horizon Markov Decision Problem, but it has been showed that this can be effectively approximated by solving a finite scenario tree based problem at each epoch. In this paper the use of the Progressive Hedging Algorithm for solving these scenario tree based problems is examined. The Progressive Hedging Algorithm can be suitable for large-scale problems, by giving an effective decomposition, but is not trivially implemented for non-convex problems. Attempting to improve the solution process, the standard algorithm is extended with locking mechanisms, dynamic multiple penalty parameters, and heuristic intermediate solutions. Extensive computational results are reported, giving further insights into the use of scenario trees as approximations of Markov Decision Problem formulations of the Stochastic Inventory Routing Problem.