Inventory/routing: Reduction from an annual to a short‐period problem

The inventory‐routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Given a central supplier, the objective is to minimize the annual delivery costs while attempting to insure that no customer runs out of the commodity at any time. In this article we present a procedure for reducing the long‐term version of this problem to a single‐period problem, which can be attacked using standard routing algorithms. The reduction procedure involves the definition of single‐period costs that reflect long‐term costs, the definition of a safety stock level and a specification of the customer subset to be considered during a single period.