On the collection depots location problem

In this paper we investigate the problem of locating a new facility servicing a set of demand points. A given set of collection depots is also given. When service is required by a demand point, the server travels from the facility to the demand point, then from the demand point to one of the collection depots (which provides the shortest route back to the facility), and back to the facility. The problem is analyzed and properties of the solution point are formulated and proved. Computational results on randomly generated problems are reported.