Single-period cutting planes for inventory routing problems

IRP involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a limited amount of stock. The product is shipped through a distribution network by one or more vehicles of limited capacity. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. In this paper we present reformulations of IRP, under the Maximum Level replenishment policy, derived from a single-period substructure. We define a generic family of valid inequalities, and then introduce two specific subclasses for which the separation problem of generating violated inequalities can be solved effectively. A basic Branch-and-Cut algorithm has been implemented to demonstrate the strength of the single-period reformulations. Computational results are presented for the benchmark instances with 50 clients and three periods and 30 clients and six periods.