A survey on benders decomposition applied to fixed-charge network design problems

Costa, Alysson M.

doi:10.1016/j.cor.2003.11.012

Cited by 245 publications

(153 citation statements)

References 49 publications

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“…Benders decomposition has been widely studied for xed charge network design problems (Costa, 2005). Indeed, these problems usually route multi-commodity ows on some network to be designed.…”

Section: General Schemementioning

confidence: 99%

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Models and algorithms for network design problems

Poss¹

2011

4OR-Q J Oper Res

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Section: General Schemementioning

confidence: 99%

“…Benders decomposition is one of the most common decomposition for (ND) (Gabrel et al, 1999;Costa, 2005), maybe because it is very easy to implement. However, it su ers from two drawbacks.…”

Section: Decompositionmentioning

confidence: 99%

Models and algorithms for network design problems

Poss¹

2011

4OR-Q J Oper Res

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“…Note that double-counting of demand satisfaction importance values is prevented by the maximum operator in (4). This operator is included in (4) to ensure that if demand point ∈ ℐ is covered by transmitters, then the importance value of §3.1 will not be accounted for times in ( ).…”

Section: Modelling Signal Strength Of a Single Transmittermentioning

confidence: 99%

Optimisation of Radio Transmitter Locations in Mobile Telecommunication Networks

Schmidt-Dumont

Vuuren

2016

SAJIE

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Multiple factors have to be taken into account when mobile telecommunication network providers make decisions about radio transmitter placement. Generally, area coverage and the average signal level provided are of prime importance in these decisions. These criteria give rise to a bi-objective problem of facility location, with the goal of achieving an acceptable trade-off between maximising the total area coverage and maximising the average signal level provided to the demand region by a network of radio transmitters. This paper establishes a mathematical modelling framework, based on these two placement criteria, for evaluating the effectiveness of a given set of radio transmitter locations. In the framework, coverage is measured according to the degree of obstruction of the so-called 'Fresnel zone' that is formed between handset and base station, while signal strength is modelled taking radio wave propagation loss into account. This framework is used to formulate a novel bi-objective facility location model that may form the basis for decision support aimed at identifying high-quality transmitter location trade-off solutions for mobile telecommunication network providers. But it may also find application in various other contexts (such as radar, watchtower, or surveillance camera placement optimisation). OPSOMMINGVerskeie faktore moet in ag geneem word wanneer radiosenderplasingsbesluite deur mobiele telekommunikasienetwerke gemaak word. In die algemeen word area-oordekking en gemiddelde seinsterkte in hierdie besluite as belangrike kriteria geag. Hierdie kriteria gee aanleiding tot 'n twee-doelige fasiliteitplasingsprobleem gemik op die soeke na aanvaarbare afruilings tussen die maksimering van totale area-oordekking en die maksimering van gemiddelde seinsterkte aan gebiede waarin aanvraag na oordekking bestaan. 'n Wiskundige modelleringsraamwerk, gebaseer op hierdie twee plasingskriteria, word in hierdie artikel vir die evaluering van 'n versameling radiosenderliggings daargestel. In die raamwerk word oordekking gemeet volgens die mate waartoe die Fresnel-sone tussen die handtoestel en die basisstasie belemmer is, terwyl seinsterkte aan die hand van radiogolf-voortsettingsverliese gemodelleer word. Hierdie raamwerk word gebruik om 'n nuwe, twee-doelige fasiliteitplasingsmodel te formuleer wat as basis kan dien vir besluitsteun in die soeke na hoë-kwaliteit senderliggingsafruilings deur mobiele telekommunikasie-netwerkverskaffers, maar vind ook toepassing in verskeie ander kontekste (soos die optimale plasing van radars, uitkyktorings, of waarnemingskameras).

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“…Cordeau et al (2001) applied Benders to simultaneously solve the aircraft routing and crew scheduling problems, while Binato et al (2001) used it to solve power transmission network design problems. Costa (2005) gives an extensive survey on applications to fixed-charge network design problems. In this section, we apply Benders decomposition to model (2).…”

Section: Benders Decompositionmentioning

confidence: 99%