The Stochastic Inventory Routing Problem

This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers’ inventories, and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation in such a way that the cost is minimized over the long run. In a recent paper (Kleywegt, Nori and Savelsbergh 1999), we formulated the inventory routing problem as a Markov decision process, and proposed approximation methods to find good solutions with reasonable computational effort for the inventory routing problem with direct deliveries. In this paper we propose solution methods for the inventory routing problem in which multiple customers can be visited on a route. ∗Supported by the National Science Foundation under grant DMI-9875400.