Path, Tree and Cycle Location

Labbé, Martine; Laporte, Gilbert; Rodríguez-Martín, Inmaculada

doi:10.1007/978-1-4615-5755-5_9

Cited by 26 publications

(17 citation statements)

References 26 publications

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“…Extensive facility location concerns locating a dimensional structure, for example a path or a cycle on a network. This falls outside the scope of this paper -we refer to Mesa and Boffey (1996), Labbé et al (1988) and Díaz-Báñez et al (2004) for reviews.…”

Section: Vehicle Routing-allocation Problemsmentioning

confidence: 42%

Location-routing: Issues, models and methods

Nagy

Salhi

2007

European Journal of Operational Research

795

366

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Section: Vehicle Routing-allocation Problemsmentioning

confidence: 42%

Location-routing: Issues, models and methods

Nagy

Salhi

2007

European Journal of Operational Research

795

366

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“…They can be classified according to the form of the facilities, so a distinction is made between point location problems, where the facilities are to be located either in nodes or in points of the network, and path-location problems, where the facilities are path-shaped. For a complete survey on path-location problems we refer the reader to Labbè et al [12].…”

Section: Introductionmentioning

confidence: 40%

A Branch-and-Cut Algorithm for the Median-Path Problem

Avella

Boccia

Sforza

et al. 2005

Comput Optim Applic

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The Median-Path problem consists of locating a st-path on a network, minimizing a function of two parameters: accessibility to the path and total cost of the path. Applications of this problem can be found in transportation planning, water resource management and fluid transportation.A problem formulation based on Subtour and Variable Upper Bound (VUB) inequalities was proposed in the seminal paper by (Current, Revelle and Cohon, 1989).In this paper we introduce a tighter formulation, based on a new family of valid inequalities, named Lifted Subtour inequalities, that are proved to be facet-defining. For the class of Lifted Subtour inequalities we propose a polynomial separation algorithm. Then we introduce more families of valid inequalities derived by investigating the relation to the Asymmetric Traveling Salesman Problem (ATSP) polytope and to the Stable Set polytope.These results are used to develop a Branch-and-Cut algorithm that enables us to solve to optimality small and medium size instances in less than 2 hours of CPU time on a workstation.

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“…Many similar problems, also consisting of locating a path on a network have been described in the literature (Labbé, Laporte, & Rodríguez, 1998;Mesa & Boffey, 1996). If the network represents a geographical region where there is population with certain needs, and it is assumed that the path serves these needs, it can be located so that it is within a threshold distance of part of the population (a ''covering path"); or it can be designed so to minimize its average distance to the customers -in this case, all the demand is assumed to be satisfied -(a ''median path").…”

Section: Introductionmentioning

confidence: 43%