Warehouse location problem with concave costs : heuristics and exact method

The purpose of facility location models is to select a set of facilities (warehouses, plants, public facilities, antennas, etc.) to be implanted over a given area in order to satisfy the needs of the customers within this area. In this article, we consider a warehouse location problem with round trip distribution. The objective is to minimize the sum of the costs of investment, storage and distribution. In this paper we consider a new type of facility location model, in which the incurred cost is a concave function of the quantity q delivered by the facility. We introduce some properties of an optimal solution and derive heuristic algorithms and a branch and bound method from these properties. Numerical examples illustrate this approach.