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This paper considers the vehicle routing problem with stochastic demands(VRPSD) under optimal restocking. We develop an exact algorithm that iseffective for solving instances with many vehicles and few customers per route.In our experiments, we show that in these instances solving the stochasticproblem is most relevant (i.e., the potential gains over the deterministicequivalent solution are highest). The proposed branch-price-and-cut algorithmrelies on an efficient labeling procedure, exact and heuristic dominance rules,and completion bounds to price profitable columns. Instances with up to 76nodes could be solved in less than 5 hours, and instances with up to 148 nodescould be solved in long-runs of the algorithm. The experiments also allowed newfindings on the problem. Solving the stochastic problem leads to solutions upto 10% superior to the deterministic equivalent solution. When the number ofroutes is not fixed, the optimal solutions under detour-to-depot and optimalrestocking are nearly equivalent. Opening new routes is a good strategy toreduce restocking costs, and in many cases results in solutions with lesstransportation costs. For the first time, scenarios where the expected demandin a route is allowed to exceed the capacity of the vehicle were also tested,and the results indicate that superior solutions with lower cost and fewerroutes exist.

New Exact Algorithm and Solution Properties for the Vehicle Routing Problem with Stochastic Demands