The stochastic inventory routing problem with direct deliveries

Vendor managed inventory replenishment is a business practice in which vendors monitor their customers' inventories, and decide when and how much inventory should be replenished. The inventory routing problem addresses the coordination of inventory management and transportation. The ability to solve the inventory routing problem contributes to the realization of the potential savings in inventory and transportation costs brought about by vendor managed inventory replenishment. The inventory routing problem is hard, especially if a large number of customers is involved. We formulate the inventory routing problem as a Markov decision process, and we propose approximation methods to find good solutions with reasonable computational effort. Computational results are presented for the inventory routing problem with direct deliveries.