Solving the Prize-collecting Rural Postman Problem

Aráoz, Julián; Fernández, Elena; Meza, Oscar

doi:10.1016/j.ejor.2008.04.037

Cited by 52 publications

(33 citation statements)

References 17 publications

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“…Once T o is obtained, we evaluate all of its min cuts because the smallest value of the left-hand side of inequality (24) after making F odd is not necessarily associated with the smallest min-cut of T o . This exact separation procedure follows the same spirit as other exact separation procedures that have recently been proposed for separating blossom inequalities (Letchford, Reinelt, and Theis 2008) or cocircuit inequalities for PARPS Meza 2009, Aráoz, Fernández, andFranquesa 2009). …”

Section: D-odd Inequalitiesmentioning

confidence: 90%

“…Instances in sets S3 and S4 have not been considered thus far as CPARP instances so additional data is needed. Following Aráoz, Fernández, and Meza (2009), the profit for each demand edge e is generated from an integer uniform distribution in [c e , 3c e ]. Asymmetric instances in sets S2 and S4 are obtained by transforming each symmetric instance in sets S1 and S3 into an asymmetric instance on the same graph and with the same profit but with asymmetric costs.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…This is in contrast to the more general profitable arc-routing problems (Feillet, Dejax, and Gendreau 2005) where the profit of an edge is collected as many times as the edge is traversed. PARPs were introduced in Aráoz, Fernández, and Zoltan (2006) and an algorithm for solving the prize-collecting rural postman problem was presented in Aráoz, Fernández, and Meza (2009). A further PARP, which has recently been studied in Franquesa (2008) and Aráoz, Fernández, and Franquesa (2009), is the clustered prize-collecting arc-routing problem (CPARP).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Windy Clustered Prize-Collecting Arc-Routing Problem

Corberán

Fernández

Franquesa

et al. 2011

Transportation Science

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T his paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. A mathematical programming formulation is given and some polyhedral results including several facet-defining and valid inequalities are presented. The separation problem for the different families of inequalities is studied. Numerical results from computational experiments are analyzed.

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Section: D-odd Inequalitiesmentioning

confidence: 90%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Windy Clustered Prize-Collecting Arc-Routing Problem

Corberán

Fernández

Franquesa

et al. 2011

Transportation Science

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“…• References [2][3][4]14] propose models that maximize the total utility of the built routes, without violating the vehicle capacity or the time limit.…”

Section: Selecting Adequate Models For Our Proposalmentioning

confidence: 99%

Planning Ecotourism Routes in Nature Parks

Barrena

Laporte

Ortega

et al. 2016

SEMA SIMAI Springer Series

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The main objective of the Nature Parks is to preserve the diversity and integrity of biotic communities for present and future use. Additionally, the Nature Parks can contribute to the invigoration of the sustainable development and culture heritage of its neighboring regions, as well as to the strengthening of the environmental education for visitors by means of direct experiences. From this double point of view, ecotourism is gaining acceptance as a tool for sustainable development since the income of visitors to protected areas can contribute significantly to support the economy of these areas and of the rural communities. This article proposes different methodologies for determining efficient routes of ecotourism where the main objective is the maximization of the cultural transmission experienced by the visitors along the path traveled. The models are formulated by using integer linear programming and its potential applicability is illustrated in the context of the Doñana

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“…Several properties and integer formulations of the problem, as well as some families of valid inequalities are presented in this article. In a second piece of work [9], an LP-based algorithm for the PRPP resolution is developed. The algorithm solved optimally 94 of 118 instances with up to 100 vertices and 22 R-connected components.…”

Section: Other Rppmentioning

confidence: 99%

Recent results on Arc Routing Problems: An annotated bibliography

Corberán

Prins

2010

Networks

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Arc routing problems are vehicle routing problems in which the tasks to be performed are located on some arcs or edges of a network, e.g., spreading salt on a road or collecting municipal refuse in a street. They have been much less studied than node routing problems but impressive developments have been achieved in the last decade. The objective of this article is to survey these recent results and to provide an annotated bibliography. Except for a few references, the period surveyed starts from the publication of the book "Arc routing: theory, solutions and applications", edited by Dror in 2000. The article is made up of two main parts: one on uncapacitated (single vehicle) problems derived from the Chinese Postman Problem, the Rural Postman Problem, and the General Routing Problem; and one on multivehicle or capacitated problems such as the Capacitated Arc Routing Problem.

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Solving the Prize-collecting Rural Postman Problem

Cited by 52 publications

References 17 publications

The Windy Clustered Prize-Collecting Arc-Routing Problem

The Windy Clustered Prize-Collecting Arc-Routing Problem

Planning Ecotourism Routes in Nature Parks

Recent results on Arc Routing Problems: An annotated bibliography

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