The m-Peripatetic Vehicle Routing Problem (m-PVRP) consists in finding a set of routes of minimum total cost over m periods so that two customers are never sequenced consecutively during two different periods. It models for example money transports or cash machines supply, and the aim is to minimize the total cost of the routes chosen. The m-PVRP can be considered as a generalization of two wellknown NP-hard problems: the Vehicle Routing Problem (VRP or 1-PVRP) and the m-Peripatetic Salesman Problem (m-PSP). In this paper we discuss some complexity results of the problem before presenting upper and lower bounding procedures. Good results are obtained not only on the m-PVRP in general, but also on the VRP and the m-PSP using classical VRP instances and TSPLIB instances.
This paper proposes an exact method for solving an optimization problem arising in several distribution networks, where customers can be served either directly, using vehicle routes from a central depot, or through transhipment facilities. The problem consists of optimizing the following interdependent decisions: selecting transhipment facilities, allocating customers to these facilities and designing vehicle routes emanating from a central depot to minimize the total distribution cost. This problem is called the Vehicle Routing Problem with Transhipment Facilities (vrptf). The paper describes two integer programming formulations for the vrptf, an edge-flow based formulation and a Set Partitioning (SP) based formulation. The LP-relaxation of the two formulations are further strengthened with the addition of different valid inequalities. Moreover, two new route relaxations that are used by dual ascent heuristics to find near-optimal dual solutions of the LP-relaxation of the SP model are described. The valid inequalities and the route relaxations are used in a branchand-cut-and-price approach to solve the problem to optimality. The proposed method is tested on a large family of instances, including real-world instances, and the computational results obtained indicate the effectiveness of the proposed method.
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