An MIP formulation for the open location-routing problem considering the topological characteristic of the solution-paths

Abstract

In the open location-routing problem (OLRP), one has a set of candidate depots to be installed and the vehicles start from the depot, visit all customers, and are not required to return to the depot after completing their service. Thus, the OLRP involves the problems of facility location and open vehicle routing. In this paper, a new mixed integer programming formulation for the OLRP is presented by proposing a set of constraints to obtain valid solutions formed by a graph consisting of a spanning tree in each connected component of the graph. This approach results in an alternative way of avoiding generating subtours, which significantly simplifies the set of constraints associated with the connectivity of the solution and the vehicle capacity requirements. The computational results show that the proposed formulation is competitive against state of-the-art methods for this type of problems.