Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem

Authors:
Tolga Bektaş;Güneş Erdoğan;Stefan Røpke
Affiliations:
School of Management and Centre for Operational Research, Management Science and Information Systems (CORMSIS), University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom;Industrial Engineering Department, Ozyegin University, Üsküdar, 34662 Istanbul, Turkey;Department of Transport, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
Venue:
Transportation Science
Year:
2011

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Abstract

The generalized vehicle routing problem (GVRP) consists of finding a set of routes for a number of capacitated vehicles on a graph where the vertices are partitioned into clusters with given demands, such that the total cost of travel is minimized and all demands are met. This paper describes and compares four new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential-size sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented.