A stochastic inventory routing problem with stock-out

In this paper, we study an inventory routing problem in which a supplier has to serve a setof retailers. For each retailer, a maximum inventory level is defined and a stochasticdemand has to be satisfied over a given time horizon. An order-up-to level policy is appliedto each retailer, i.e. the quantity sent to each retailer is such that its inventory level reachesthe maximum level whenever the retailer is served. An inventory cost is applied to anypositive inventory level, while a penalty cost is charged and the excess demand is not backloggedwhenever the inventory level is negative. The problem is to determine a shippingstrategy that minimizes the expected total cost, given by the sum of the expected totalinventory and penalty cost at the retailers and of the expected routing cost. A hybrid rolloutalgorithm is proposed for the solution of the problem and its performance is evaluatedon a large set of randomly generated problem instances.