A branch and cut algorithm for the hierarchical network design problem

Obreque, Carlos; Donoso, Macarena; Gutiérrez, Gabriel; Marianov, Vladimir

doi:10.1016/j.ejor.2008.12.022

Cited by 22 publications

(9 citation statements)

References 21 publications

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“…Volgenant (1989). A Lagrangian-relaxation based heuristic is developed in Pirkul et al (1991); in Sancho (1995) a dynamic programming procedure is proposed; and recently, a branch-and-cut algorithm is presented in Obreque et al (2010).…”

Section: The Two-level Network Design Problemmentioning

confidence: 99%

The Recoverable Robust Two-Level Network Design Problem

Álvarez-Miranda

Ljubić

Raghavan

et al. 2015

INFORMS Journal on Computing

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We consider a network design application which is modeled as the two level network design problem under uncertainty. In this problem, one of the two available technologies can be installed on each edge and all customers of the network need to be served by at least the lower level (secondary) technology. The decision maker is confronted with uncertainty regarding the set of primary customers, i.e., the set of nodes that need to be served by the higher level (primary) technology. A set of discrete scenarios associated to the possible realizations of primary customers is available. The network is built in two stages. In the first-stage the network topology must be determined. One may decide to install the primary technology on some of the edges in the first stage, or one can wait to see which scenario will be realized, in which case, edges with the installed secondary technology may be upgraded, if necessary to primary technology, but at higher recovery cost. The overall goal then is to build a spanning tree in the first stage that serves all customers by at least the lower level technology, and that minimizes the first stage installation cost plus the worst-case cost needed to upgrade the edges of the selected tree, so that the primary customers of each scenario can be served using the primary technology. Using the recently introduced concept of recoverable robustness, we address this problem of importance in the design of telecommunication and distribution networks, and provide mixed integer programming models and a branch-and-cut algorithm to solve it.

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Section: The Two-level Network Design Problemmentioning

confidence: 99%

The Recoverable Robust Two-Level Network Design Problem

Álvarez-Miranda

Ljubić

Raghavan

et al. 2015

INFORMS Journal on Computing

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“…Previous works examining a hierarchical system of networks have been based on discrete models, in which demand occurs only at nodes of a network (Current et al, 1986;Pirkul et al, 1991;Balakrishnan et al, 1994;Chopra and Tsai, 2002;Obreque et al, 2010). The focus of discrete models is on developing algorithms and obtaining numerical solutions.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical system of road networks with inward, outward, and through traffic

Miyagawa

2011

Journal of Transport Geography

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“…The hierarchical network design has been addressed in both discrete and continuous network models. The discrete models aim to develop efficient algorithms applicable to actual networks [4,7,17,18,20]. The discrete models usually use detailed traffic data and equilibrium traffic assignment.…”

Section: Introductionmentioning

confidence: 99%

Spacing of Intersections in Hierarchical Road Networks

Miyagawa

2018

JORSJ

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This paper presents an analytical model for examining the spacing of intersections that connect different levels of roads in a hierarchical network. An analytical expression for the average travel time is obtained for a grid road network with two road types: minor and major roads. The travel time is defined as the sum of the free travel time and the delay at intersections. The analytical expression gives basic properties of the tradeoff between the travel time on minor and major roads. The optimal pattern of intersections that minimizes the average travel time is then obtained. The result demonstrates how the road length, the intersection delay, the travel speed, and the size of the city affect the optimal pattern. The model is also applied to the road network of Tokyo. The proposed model explicitly considers the tradeoff between the accessibility to higher level roads and the delay at intersections, and is useful for hierarchical road network design.

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A branch and cut algorithm for the hierarchical network design problem

Cited by 22 publications

References 21 publications

The Recoverable Robust Two-Level Network Design Problem

The Recoverable Robust Two-Level Network Design Problem

Hierarchical system of road networks with inward, outward, and through traffic

Spacing of Intersections in Hierarchical Road Networks

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