A capacitated general routing problem on mixed networks
Computers and Operations Research
A cutting plane algorithm for the capacitated arc routing problem
Computers and Operations Research
A Hierarchical Relaxations Lower Bound for the Capacitated Arc Routing Problem
HICSS '02 Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS'02)-Volume 3 - Volume 3
A new branch-and-cut algorithm for the capacitated vehicle routing problem
Mathematical Programming: Series A and B
A comparison of two different formulations for arc routing problems on mixed graphs
Computers and Operations Research
New lower bound for the capacitated arc routing problem
Computers and Operations Research
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
Mathematical Programming: Series A and B
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Survey: matheuristics for rich vehicle routing problems
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
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The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004, although similar problems have been studied before. This problem, also called the Mixed Capacitated General Routing Problem (MCGRP), generalizes the classical Capacitated Vehicle Routing Problem (CVRP), the Capacitated Arc Routing Problem (CARP), and the General Routing Problem. It captures important aspects of real-life routing problems that were not adequately modeled in previous Vehicle Routing Problem (VRP) variants. The authors also proposed a memetic algorithm procedure and defined a set of test instances called the CBMix benchmark. The NEARP definition and investigation contribute to the development of rich VRPs. In this paper we present the first lower bound procedure for the NEARP. It is a further development of lower bounds for the CARP. We also define two novel sets of test instances to complement the CBMix benchmark. The first is based on well-known CARP instances; the second consists of real life cases of newspaper delivery routing. We provide numerical results in the form of lower and best known upper bounds for all instances of all three benchmarks. For three of the instances, the gap between the upper and lower bound is closed. The average gap is 25.1%. As the lower bound procedure is based on a high quality lower bound procedure for the CARP, and there has been limited work on approximate solution methods for the NEARP, we suspect that a main reason for the rather large gaps is the quality of the upper bound. This fact, and the high industrial relevance of the NEARP, should motivate more research on approximate and exact methods for this important problem.