Elsevier

Discrete Applied Mathematics

Volume 116, Issue 3, 15 February 2002, Pages 193-229
Discrete Applied Mathematics

The vehicle routing problem with pickups and deliveries on some special graphs

Peter L. Hammer on the occasion of his 65th birthday
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Abstract

The vehicle routing with pickups and deliveries (VRPD) problem is defined over a graph G=(V,E). Some vertices in G represent delivery customers who expect deliveries from a depot, and other vertices in G represent pickup customers who have available supply to be picked up and transported to a depot. The objective is to find a minimum length tour for a capacitated vehicle, which starts at a depot and travels in G while satisfying all the requests by the delivery and pickup customers, without violating the vehicle capacity constraint, and returns to a depot. We study the VRPD problem on some special graphs, including trees, cycles and warehouse graphs when the depots are both exogenously and endogenously determined. Specifically, we develop linear time algorithms for the VRPD problem on tree graphs and polynomial algorithms on cycle and warehouse graphs.

MSC

68Q25
05C05
05C38
90B10

Keywords

Vehicle routing
Polynomial algorithm
Tree
Cycle graph
Warehouse graph

Cited by (0)

The authors gratefully acknowledge helpful comments by an anonymous referee on an earlier version of this paper. Research was partially supported by Natural Sciences and Engineering Research Council grants 3998 and 4181, by UBC HSS grants, and by a UBC Graduate Fellowship.

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Current address: Compugen Ltd., Tel-Aviv, Israel.