Transforming arc routing into node routing problems
Computers and Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
The generalized assignment problem: valid inequalities and facets
Mathematical Programming: Series A and B
(1,k)-configuration facets for the generalized assignment problem
Mathematical Programming: Series A and B
Augment-insert algorithms for the capacitated arc routing problem
Computers and Operations Research
Polyhedral study of the capacitated vehicle routing problem
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A cutting plane algorithm for the capacitated arc routing problem
Computers and Operations Research
Computers and Operations Research
Solving capacitated arc routing problems using a transformation to the CVRP
Computers and Operations Research
Solving an urban waste collection problem using ants heuristics
Computers and Operations Research
Exploiting sparsity in pricing routines for the capacitated arc routing problem
Computers and Operations Research
The Clustered Prize-Collecting Arc Routing Problem
Transportation Science
Lower bounds for the mixed capacitated arc routing problem
Computers and Operations Research
Computers and Operations Research
Solving capacitated arc routing problems using a transformation to the CVRP
Computers and Operations Research
Robotics and Autonomous Systems
Split-Delivery Capacitated Arc-Routing Problem: Lower Bound and Metaheuristic
Transportation Science
An evolutionary approach to the multidepot capacitated arc routing problem
IEEE Transactions on Evolutionary Computation
The Windy Clustered Prize-Collecting Arc-Routing Problem
Transportation Science
An optimization-based heuristic for the Multi-objective Undirected Capacitated Arc Routing Problem
Computers and Operations Research
The capacitated arc routing problem with refill points
Operations Research Letters
Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem
Operations Research
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In this paper we study the polyhedron associated with the Capacitated Arc Routing Problem (CARP) where a maximum number K of vehicles is available. We show that a subset of the facets of the CARP polyhedron depends only on the demands of the required edges and they can be derived from the study of the Generalized Assignment Problem (GAP). The conditions for a larger class of valid inequalities to define facets of the CARP polyhedron still depend on the properties of the GAP polyhedron. We introduce the special case of the CARP where all the required edges have unit demand (CARPUD) to avoid the number problem represented by the GAP. This allows us to make a polyhedral study in which the conditions for the inequalities to be facet inducing are easily verifiable. We give necessary and sufficient conditions for a variety of inequalities, which are valid for CARP, to be facet inducing for CARPUD.The resulting partial description of the polyhedron has been used to develop a cutting plane algorithm for the Capacitated Arc Routing Problem. The lower bound provided by this algorithm outperformed all the existing lower bounds for the CARP on a set of 34 instances taken from the literature.