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Journal Article

An Approximation Algorithm for the Traveling Salesman Problem with Backhauls

Michel Gendreau, Gilbert Laporte and Alain Hertz
Operations Research
Vol. 45, No. 4 (Jul. - Aug., 1997), pp. 639-641
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/172059
Page Count: 3
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An Approximation Algorithm for the Traveling Salesman Problem with Backhauls
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Abstract

The Traveling Salesman Problem with Backhauls (TSPB) is defined on a graph G = (V, E). The vertex set is partitioned into V=({v1},L,B), where v1 is a depot, L is a set of linehaul customers, and B is a set of backhaul customers. A cost matrix satisfying the triangle inequality is defined on the edge set E. The TSPB consists of determining a least-cost Hamiltonian cycle on G such that all vertices of L are visited contiguously after v1, followed by all vertices of B. Following a result by Christofides for the Traveling Salesman Problem, we propose an approximation algorithm with worst-case performance ratio of 3/2 for the TSPB.

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