Journal
APPLIED MATHEMATICAL MODELLING
Volume 36, Issue 1, Pages 97-107Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2011.05.037
Keywords
Network design; Vehicle routing problem; Generalized vehicle routing problem; Generalized traveling salesman problem; Integer programming
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The generalized vehicle routing problem (GVRP) is an extension of the vehicle routing problem (VRP) and was introduced by Ghiani and Improta [1]. The GVRP is the problem of designing optimal delivery or collection routes from a given depot to a number of predefined, mutually exclusive and exhaustive node-sets (clusters) which includes exactly one node from each cluster, subject to capacity restrictions. The aim of this paper is to provide two new models of the GVRP based on integer programming. The first model, called the node formulation is similar to the Kara-Bektas formulation [2], but produces a stronger lower bound. The second one, called the flow formulation, is completely new. We show as well that under specific circumstances the proposed models of the GVRP reduces to the well known routing problems. Finally, the GVRP is extended for the case in which the vertices of any cluster of each tour are contiguous. This case is defined as the clustered generalized vehicle routing problem and both of the proposed formulations of GVRP are adapted to clustered case. (C) 2011 Elsevier Inc. All rights reserved.
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