Min‐Max <i>K</i>‐vehicles windy rural postman problem

Benavent, Enrique; Corberán, Ángel; Plana, Isaac; Sanchis, José M.

doi:10.1002/net.20334

Cited by 28 publications

(55 citation statements)

References 16 publications

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“…As in [7], we will assume that each vertex in V is incident with at least one required edge. Let us call G R = (V , E R ) the graph induced by the required edges.…”

Section: The Min-max K -Vehicles Windy Rppmentioning

confidence: 99%

“…In Section 2, we present some notation, the formulation of the problem and the inequalities studied in [7]. In Section 3 we describe several new facet-inducing inequalities obtained from the WRPP and, in Section 4, some inequalities that have to be satisfied by any optimal solution.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we deal with the min-max K-vehicles windy rural postman problem (Min-max K-WRPP), previously introduced in [7]. Given a windy graph, a distinguished vertex (the depot), a subset of required edges and a fixed number K of vehicles, the problem consists of finding a set of K routes for the vehicles in such a way that each route starts and ends at the depot and each required edge is serviced by exactly one vehicle.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem

et al. 2011

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The min-max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch-and-cut algorithm that produced some promising computational results was implemented. In this article, we present further results for this problem. We describe several new facet-inducing inequalities obtained from the WRPP, as well as some inequalities that have to be satisfied by any optimal solution. We present an enhanced branch-and-cut algorithm that takes advantage of both these new inequalities and high quality min-max K -WRPP feasible solutions obtained by a metaheuristic. Computational results on a large set of instances are also reported.

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“…As in [7], we will assume that each vertex in V is incident with at least one required edge. Let us call G R = (V , E R ) the graph induced by the required edges.…”

Section: The Min-max K -Vehicles Windy Rppmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem

et al. 2011

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“…In [23], new variants of the k-Chinese postman problem are presented, together with heuristics for the k-Chinese postman problem. In [3] the min-max k-vehicles windy rural postman is treated. General references for arc routing are [7,8].…”

Section: Surveymentioning

confidence: 99%

Heuristics for the weighted k-rural postman problem with applications to urban snow removal

Holmberg

2018

J Veh Routing Algorithms

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We describe a weighted version of the k-Chinese and k-rural postman problem that occurs in the context of snow removal. The problem concerns the questions of which vehicle shall take care of each link and how the vehicles shall travel between links. We also consider different numbers of vehicles, in view of a fixed cost for each vehicle. We describe and discuss heuristic solution approaches, based on usable substructures, such as heuristics for rural postman problems, meta-heuristics, k-means clustering and local search improvements by moving cycles. The methods have been implemented and tested on real life examples.

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“…The separation algorithms for disaggregate and Ω-aggregate K-C inequalities is similar to that described in [7] for the Min-Max K-vehicles Windy Rural Postman Problem. Figure 9: Construction of a PB in the separation algorithm.…”

Section: Separation Of K-c and 2-pb Inequalitiesmentioning

confidence: 99%

The Team Orienteering Arc Routing Problem

Archetti

Speranza

Corberán

et al. 2014

Transportation Science

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The Team Orienteering Arc Routing Problem (TOARP) is the extension to the arc routing setting of the Team Orienteering Problem (TOP). In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total profit collected while satisfying the given time limit for each vehicle.In this paper we propose a formulation for this problem and study its associated polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational experiments are run on a large set of benchmark instances.

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Min‐Max K‐vehicles windy rural postman problem

Cited by 28 publications

References 16 publications

New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem

New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem

Heuristics for the weighted k-rural postman problem with applications to urban snow removal

The Team Orienteering Arc Routing Problem

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