Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous deli
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Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls J Dethloff * University of Hamburg, Hamburg, Germany Recently, an increasing number of papers on vehicle routing problems with backhauling has been published. Different types of backhauling problems are discussed. Two of them—the vehicle routing problem with backhauls and so-called ‘mixed loads’ (VRPBM) and the vehicle routing problem with simultaneous delivery and pick-up (VRPSDP)—are closely related. In this paper, we discuss that relationship. Our findings are that previously published results for VRPSDP instances obtained by using a heuristic suggested for the VRPBM do not take into account specific properties of the VRPSDP. As a result of the analysis of the relation between both problem types the possibility of solving the VRPBM by applying an insertion heuristic based on the concept of ‘residual capacities’ originally designed for the VRPSDP is investigated. Numerical results indicate that, for certain instances, this approach is more favourable than the application of a heuristic suggested for the VRPBM in the literature. Journal of the Operational Research Society (2002) 53, 115–118. DOI: 10.1057=palgrave=jors=2601263 Keywords: routing; heuristics; insertion; backhauling; vehicle routing
Introduction
Relation between VRPBM and VRPSDP
In the context of reverse logistics, an increasing focus of research efforts on vehicle routing problems with backhauling can be observed recently. All of these problems are generalizations of the classical vehicle routing problem (VRP). Several types of backhauling problems are discussed. The first is concerned with the situation where goods are to be brought back to the depot, but cannot be picked up before the last delivery of the respective vehicle has been performed. This type of vehicle routing problem with backhauls (VRPB) will not be discussed here. The reader is referred to Goetschalckx et al,1 Duhamel et al 2 and Toth et al 3,4 for more detailed information. The second type of vehicle routing problems with backhauls (VRPBM) deals with the case where pick-ups can be performed before the last delivery has been made, thus resulting in a ‘mixed load’ of deliveries and pick-ups in the vehicle (see Anily5 and Salhi et al 6). The third type is dedicated to the situation where customers simultaneously receive deliveries from the depot and send pick-ups back to the depot. This problem is referred to as the vehicle routing problem with simultaneous delivery and pick-up (VRPSDP, see Min7 and Dethloff 8).
The VRPBM (ie with mixed loads) and the VRPSDP are very closely related. It is sometimes stated that the VRPSDP can be modelled and solved as a VRPBM by dividing the customers into fictitious ‘pick-up only’ and ‘delivery only’ entities (see Salhi et al 6). However, customers of
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