P-Cable Trench Problem with Covering

30 Pages Posted: 13 Jul 2017

See all articles by Gabriel Gutiérrez-Jarpa

Gabriel Gutiérrez-Jarpa

Pontificia Universidad Católica de Valparaíso

Carlos Obreque

Universidad del Bío Bío

Vladimir Marianov

Pontificia Universidad Catolica de Chile

Alejandro Contreras

Pontificia Universidad Católica de Valparaíso

Date Written: December 18, 2015

Abstract

We introduce the p-Cable Trench Problem with Covering. Secondary servers are located to provide service within a coverage radius (e.g., Wi-Fi antennas). Each secondary server must be connected to a primary server (a router), through a dedicated cable (wire pair). Trenches need to be dug to bury ducts that contain all the cables. The service must be provided to a whole region, at the minimum cost, consisting of the trench and duct cost and the total cable length cost. The number of primary servers is preset, and they are located on nodes belonging to a set of candidate locations (nodes of an existing telephone network). We propose a linear integer optimization model based on multicommodity flow, which we solve using branch and bound, a linear relaxation and two different Lagrangian relaxation-based heuristics, for which we design ad-hoc procedures to improve the upper bounds. We solve instances of up to 200 nodes, and also an application consisting in locating Wi-Fi antennas in Viña del Mar, Chile.

Keywords: Location-routing; p-cable trench; covering; Lagrangian relaxation

Suggested Citation

Gutiérrez-Jarpa, Gabriel and Obreque, Carlos and Marianov, Vladimir and Contreras, Alejandro, P-Cable Trench Problem with Covering (December 18, 2015). Available at SSRN: https://ssrn.com/abstract=2814676 or http://dx.doi.org/10.2139/ssrn.2814676

Gabriel Gutiérrez-Jarpa

Pontificia Universidad Católica de Valparaíso ( email )

Avenida Brasil 2950
Escuela de Comercio - UCV
Valparaiso, Valparaiso 2362736
Chile

Carlos Obreque

Universidad del Bío Bío ( email )

Avda. Collao No. 1202 Casilla 5-C
Av. Collao 1202, Conception 4081112
Chile

Vladimir Marianov (Contact Author)

Pontificia Universidad Catolica de Chile ( email )

Av. Vicuna Mackenna 4860
Department of Electrical Engineering
Santiago
Chile
(562) 354 4974 (Phone)
(562) 552 2563 (Fax)

Alejandro Contreras

Pontificia Universidad Católica de Valparaíso ( email )

Avenida Brasil 2950
Escuela de Comercio - UCV
Valparaiso, Valparaiso 2362736
Chile

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