Network flow problems with one side constraint: a comparison of three solution methods
Computers and Operations Research
A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On the Complexity of Finding a Minimum Cycle Cover of a Graph
SIAM Journal on Computing
Modeling and solving several classes of arc routing problems as traveling salesman problems
Computers and Operations Research
Computers and Operations Research
A hybrid algorithm for solving network flow problems with side constraints
Computers and Operations Research
Computers and Operations Research - Special issue on the traveling salesman problem
Optimization Based Algorithms for Finding Minimal Cost Ring Covers in Survivable Networks
Computational Optimization and Applications
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Drive: Dynamic Routing of Independent Vehicles
Operations Research
Solving the Two-Connected Network with Bounded Meshes Problem
Operations Research
The Bounded Cycle-Cover Problem
INFORMS Journal on Computing
The cardinality constrained covering traveling salesman problem
Computers and Operations Research
The Clustered Prize-Collecting Arc Routing Problem
Transportation Science
The undirected capacitated arc routing problem with profits
Computers and Operations Research
The Windy Clustered Prize-Collecting Arc-Routing Problem
Transportation Science
A Tabu Search Heuristic for the Prize-collecting Rural Postman Problem
Electronic Notes in Theoretical Computer Science (ENTCS)
The time-dependent prize-collecting arc routing problem
Computers and Operations Research
GRASP and Path Relinking for the Clustered Prize-collecting Arc Routing Problem
Journal of Heuristics
An ILP-refined tabu search for the Directed Profitable Rural Postman Problem
Discrete Applied Mathematics
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In this article, we introduce a new arc routing problem that we call the profitable arc tour problem. This problem is defined on a graph in which profits and travel costs are associated with the arcs. The objective is to find a set of cycles in the graph that maximizes the collection of profit minus travel costs, subject to constraints limiting the number of times that profit is available on arcs and the maximal length of cycles. The problem is related both to constrained flow problems and to vehicle-routing problems. We tackle it from this standpoint and propose a branch-and-price algorithm for its solution. In the column-generation phase, the issue of the collection decisions while traveling through the arcs is addressed. In the branching phase, the fact that viewing solutions in terms of flow variables regularly induces an integer flow matrix leads us to introduce a branching method called the flow-splitting method. Finally, the relationships of this problem with constrained flow optimization are taken into account in an initial phase of the algorithm.