Heuristic and exact algorithms for a min–max selective vehicle routing problem

In this work, we investigate a vehicle routing problem where not all clients need to be visited and the goal is to minimize the longest vehicle route. We propose two exact solution approaches for solving the problem: a branch-and-cut (BC) algorithm and a local branching (LB) method that uses BC as i...

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Bibliographic Details
Published in:Computers & operations research Vol. 38; no. 7; pp. 1054 - 1065
Main Authors: Valle, Cristiano Arbex, Martinez, Leonardo Conegundes, da Cunha, Alexandre Salles, Mateus, Geraldo R.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.07.2011
Elsevier
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Branch & bound algorithms
Branch-and-cut
Exact sciences and technology
Exact solutions
Flows in networks. Combinatorial problems
Heuristic
Heuristics
Integer programming
Local branching
Logistics
Mathematical analysis
Mathematical programming
Operational research and scientific management
Operational research. Management science
Operations research
Optimization algorithms
Routing
Solvers
Studies
Upper bounds
Vehicle routing problem
Vehicles
Local branching
Branch-and-cut
Vehicle routing problem
Heuristics
Branching
Gripping
Covering problem
Routing
Coverage
Modeling
Exact solution
Integer programming
Upper bound
Branch and cut method
Heuristic method
Minimax method
Problem solving
Set covering
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:In this work, we investigate a vehicle routing problem where not all clients need to be visited and the goal is to minimize the longest vehicle route. We propose two exact solution approaches for solving the problem: a branch-and-cut (BC) algorithm and a local branching (LB) method that uses BC as its inner solver. Our computational experience indicates that, in practice, the problem is difficult to solve, mainly when the number of vehicles grows. In addition to the exact methods, we present a heuristic that relies on GRASP and on the resolution of a restricted integer program based on a set covering reformulation for the problem. The heuristic was capable of significantly improving the best solutions provided by BC and LB, in one tenth of the times taken by them to achieve their best upper bounds.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2010.10.010