Deterministic Order-Up-To Level Policies in an Inventory Routing Problem

We consider a distribution problem in which a set of products has to be shipped from a supplier to several retailers in a given time horizon. Shipments from the supplier to the retailers are performed by a vehicle of given capacity and cost. Each retailer determines a minimum and a maximum level of the inventory of each product, and each must be visited before its inventory reaches the minimum level.

Every time a retailer is visited, the quantity of each product delivered by the supplier is such that the maximum level of the inventory is reached at the retailer. The problem is to determine for each discrete time instant the retailers to be visited and the route of the vehicle. Various objective functions corresponding to different decision policies, and possibly to different decision makers, are considered.

We present a heuristic algorithm and compare the solutions obtained with the different objective functions on a set of randomly generated problem instances.