Deterministic order-up-to level strategies for the minimization of the logistic costs in distribution systems

We consider a distribution problem in which a product has to be shipped from a supplier to several retailers on a given time horizon. Shipments from the supplier to the retailers are performed by using a vehicle of given transportation capacity and cost. Each retailer determines a minimum and a maximum level of the inventory of the product. Every time a retailer is visited, the quantity delivered by the supplier is such that the maximum level of the inventory is reached at the retailer; in other words, a deterministic order-up-to level strategy is applied. The problem is to determine for each discrete time instant the retailers to be visited and the route that the vehicle has to travel. Various objective functions are considered which correspond to different decision strategies and possibly to different decision-makers. For this problem we present a heuristic algorithm and compare the solutions obtained with different objective functions on a set of randomly generated problem instances.