Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows

This paper presents a branch-and-cut-and-price algorithm for the vehicle-routing problem with time windows. The standard Dantzig-Wolfe decomposition of the arc flow formulation leads to a set-partitioning problem as the master problem and an elementary shortest-path problem with resource constraints...

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Vydané v:Operations research Ročník 56; číslo 2; s. 497 - 511
Hlavní autori: Jepsen, Mads, Petersen, Bjorn, Spoorendonk, Simon, Pisinger, David
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Linthicum, MD INFORMS 01.03.2008
Institute for Operations Research and the Management Sciences
Predmet:
Algorithms
Analysis
Applied sciences
Branch & bound algorithms
Exact sciences and technology
integer
Integer programming
Integers
Logistics
Operational research and scientific management
Operational research. Management science
Polynomials
Product labeling
programming
Routing
Studies
Time windows
Traffic congestion
Traffic flow
Transportation
Vehicle capacity
vehicle routing
Vehicles
Vertices
United States
Lower bound
Fleet
Vehicle routing problem
Shortest path
Dominance
Routing
Set partitioning
Cut generation
Integer programming
Time window
Branch and cut method
Resource constraint
Pricing
transportation: vehicle routing
Objective function
programming: integer
ISSN:0030-364X, 1526-5463
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Popis
Shrnutí:This paper presents a branch-and-cut-and-price algorithm for the vehicle-routing problem with time windows. The standard Dantzig-Wolfe decomposition of the arc flow formulation leads to a set-partitioning problem as the master problem and an elementary shortest-path problem with resource constraints as the pricing problem. We introduce the subset-row inequalities, which are Chvatal-Gomory rank-1 cuts based on a subset of the constraints in the master problem. Applying a subset-row inequality in the master problem increases the complexity of the label-setting algorithm used to solve the pricing problem because an additional resource is added for each inequality. We propose a modified dominance criterion that makes it possible to dominate more labels by exploiting the step-like structure of the objective function of the pricing problem. Computational experiments have been performed on the Solomon benchmarks where we were able to close several instances. The results show that applying subset-row inequalities in the master problem significantly improves the lower bound and, in many cases, makes it possible to prove optimality in the root node.
Bibliografia:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0449