Applications of the vehicle routing problem with trailers and transshipments

Abstract

The vehicle routing problem with trailers and transshipments (VRPTT) is a recent and challenging extension of the well-known vehicle routing problem. The VRPTT constitutes an archetypal representative of the class of vehicle routing problems with multiple synchronization constraints (VRPMSs). In addition to the usual task covering constraints, VRPMSs require further synchronization between vehicles, concerning spatial, temporal, and load aspects. VRPMSs possess considerable practical relevance, but limited coverage in the scientific literature. The purpose of the present paper is to describe how several important types of VRPMSs, such as multi-echelon location-routing problems and simultaneous vehicle and crew routing problems, can be modelled as VRPTTs.

Introduction

Vehicle routing problems (VRPs) are fundamental planning problems in logistics and transport, and they have been the subject of intensive study for more than half a century now [64], [24], [35]. A recent and challenging extension of the VRP is the vehicle routing problem with trailers and transshipments (VRPTT). The VRPTT constitutes an archetypal representative of the class of vehicle routing problems with multiple synchronization constraints (VRPMSs). VRPMSs are a broad class of VRPs which, despite their considerable practical relevance, have attracted comparatively little attention on the part of science so far. In classical VRPs, synchronization between vehicles is necessary only with respect to which vehicle visits which customer. VRPMSs are VRPs which exhibit additional synchronization requirements with regard to spacial, temporal, and load aspects. A recent survey of synchronization in vehicle routing [21] has shown that practical applications of VRPMSs abound and that the solution of several types of VRPMSs is still a research issue.

The fundamental difference between classical VRPs and VRPMSs is that the latter, contrary to the former, feature the so-called interdependence problem: In standard VRPs, vehicles are independent of one another in that a change in one route does not affect any other route. In VRPMSs, by contrast, a change in one route may have effects on other routes, due to the additional synchronization requirements. In the worst case, a change in one route may render all other routes infeasible. This has considerable implications on potential solution approaches. Actually, most exact and heuristic algorithms for classical VRPs rely on the fact that routes are mutually independent. Consequently, these algorithms cannot directly be applied to solve VRPMSs.

A first step toward solving problems is properly modelling them. Therefore, the contribution of the present paper, similar to the works of Noon and Bean [46], Crainic et al. [15], and Baldacci et al. [2] for other routing problems, is to propose the VRPTT as a unified modelling tool for VRPMSs in general. To this end, it is described how several important types of VRPMSs can be represented as VRPTTs. This demonstrates the versatility of the VRPTT as a representational framework for many types of rich VRPs and points out that the VRPTT needs and deserves further study. The development of exact or heuristic solution algorithms for the VRPTT is beyond the scope of the paper.

The next section describes the VRPTT and develops a graph-theoretic modelling framework which can serve as a basis for algorithmic solution approaches. Subsequent sections describe transformations of classical VRPs and of several types of VRPMSs that were identified as particularly relevant and challenging in the above-mentioned survey. The paper ends with a short conclusion.