A Lower Bound for the Split Delivery Vehicle Routing Problem

In this paper we consider the Split Delivery Vehicle Routing Problem (SDVRP), a relaxation of the known Capacitated Vehicle Routing Problem (CVRP) in which the demand of any client can be serviced by more than one vehicle. We define a feasible solution of this problem, and we show that the convex hu...

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Bibliographic Details
Published inOperations research Vol. 48; no. 5; pp. 801 - 810
Main Authors Belenguer, J. M, Martinez, M. C, Mota, E
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.09.2000
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Delivery vehicles
Heuristics
Integer programming
Integers
Logistics
Mathematical vectors
Optimal solutions
Optimization
Polyhedrons
Programming, integer, cutting plane: based on the polyhedral study, computational results are reported
Studies
Transportation, vehicle routing: a case with split demands, study of the polyhedron
Vehicle capacity
Vehicles
Vertices
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Summary:In this paper we consider the Split Delivery Vehicle Routing Problem (SDVRP), a relaxation of the known Capacitated Vehicle Routing Problem (CVRP) in which the demand of any client can be serviced by more than one vehicle. We define a feasible solution of this problem, and we show that the convex hull of the associated incidence vectors is a polyhedron ( P SDVRP ), whose dimension depends on whether a vehicle visiting a client must service, or not, at least one unit of the client demand. From a partial and linear description of P SDVRP and a new family of valid inequalities, we develop a lower bound whose quality is exhibited in the computational results provided, which include the optimal resolution of some known instances—one of them with 50 clients. This instance is, as far as we know, the biggest one solved so far.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.48.5.801.12407