A Decade of Capacitated Arc Routing

Wøhlk, Sanne

doi:10.1007/978-0-387-77778-8_2

Cited by 59 publications

(35 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other ARP applications include, for example, the routing of postmen, meter readers and power line inspectors. For a review of ARPs the reader is referred to Corberán and Prins (2010);Wøhlk (2008);Dror (2000);and Eiselt et al (1995a,b).…”

Section: Midfield-estatementioning

confidence: 99%

Applying min–maxkpostmen problems to the routing of security guards

Willemse¹,

Joubert

2012

Journal of the Operational Research Society

View full text Add to dashboard Cite

The most essential and alluring characteristic of a security estate is the estate's ability to provide 24-hour security to its residents, of which the continual patrolling of roads and paths is vital. The objective of this paper is to address the lack of sufficient patrol route design procedures by presenting a tabu search algorithm capable of generating multiple patrol routes for an estate's security guards. The paper shows that the problem of designing these routes can be modelled as an Arc Routing Problem, specifically as min-max k postmen problems. The algorithm is illustrated with a real problem instance from an estate in Gauteng, South Africa. The patrol routes generated by the algorithm provide a significant improvement in the even patrolling of the road network, and a more balanced work distribution among guards. The algorithm is also tested on several benchmark problems from literature.

show abstract

Section: Midfield-estatementioning

confidence: 99%

Applying min–maxkpostmen problems to the routing of security guards

Willemse¹,

Joubert

2012

Journal of the Operational Research Society

View full text Add to dashboard Cite

show abstract

“…A solution to the problem is a minimum weight tour consisting of a collection of subtours such that every edge of the graph is visited, the subtours originate at different depots, and each subtour starts and ends at the same depot. The MDCP can be seen as a special case of the multi-depot capacitated arc routing problem described in, e.g., Wøhlk (2008), and Kansou and Yassine (2010). Applications of the MDCP include for example snow plowing and winter gritting, Wøhlk (2008).…”

Section: Introductionmentioning

confidence: 99%

“…The MDCP can be seen as a special case of the multi-depot capacitated arc routing problem described in, e.g., Wøhlk (2008), and Kansou and Yassine (2010). Applications of the MDCP include for example snow plowing and winter gritting, Wøhlk (2008). The CPP arises as a special case if only one depot is available, i.e.…”

Section: Introductionmentioning

confidence: 99%

On games arising from multi-depot Chinese postman problems

Platz

Hamers

2015

Ann Oper Res

View full text Add to dashboard Cite

“…Recent exact algorithms using strong lower bounding procedures are found in [8,12]. See [4] for an overview of CARP lower bounds and [34] for a recent survey on CARP in general.…”

Section: Introductionmentioning

confidence: 99%

A lower bound for the Node, Edge, and Arc Routing Problem

Bach

Hasle

Wøhlk

2013

Computers & Operations Research

Self Cite

View full text Add to dashboard Cite

The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004. This problem 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 the 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. AbstractThe Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004. This problem 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 in-1 stances; 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 the main reason for the rather large gaps is the quality of the upper bound. This fact, and the high industrial relevance of...

show abstract

A Decade of Capacitated Arc Routing

Cited by 59 publications

References 76 publications

Applying min–maxkpostmen problems to the routing of security guards

Applying min–maxkpostmen problems to the routing of security guards

On games arising from multi-depot Chinese postman problems

A lower bound for the Node, Edge, and Arc Routing Problem

Contact Info

Product

Resources

About