A new branch-and-cut algorithm for the capacitated vehicle routing problem

Authors:
Jens Lysgaard;Adam N. Letchford;Richard W. Eglese
Affiliations:
Aarhus School of Business, Department of Management Science and Logistics, Denmark;Lancaster University, Department of Management Science, England;Lancaster University, Department of Management Science, England
Venue:
Mathematical Programming: Series A and B
Year:
2004

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Abstract

We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts. For each of these classes of inequalities we describe our separation algorithms in detail. Also we describe the other important ingredients of our branch-and-cut algorithm, such as the branching rules, the node selection strategy, and the cut pool management. Computational results, for a large number of instances, show that the new algorithm is competitive. In particular, we solve three instances (B-n50-k8, B-n66-k9 and B-n78-k10) of Augerat to optimality for the first time.