A new approximation algorithm for the multilevel facility location problem

Gabor, Adriana F.; Ommeren, Jan-Kees van

doi:10.1016/j.dam.2009.11.007

Cited by 31 publications

(28 citation statements)

References 23 publications

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“…Erlenkotter [12] and Guignard [18] proposed dual-ascent algorithms for the uncapacitated facility location problem. A number of studies have applied dualascent approaches to adaptations of the uncapacitated facility location problem [7], including the multi-echelon variation [16,23,40], the location problem with a balancing requirement [3,9,36], and a multilevel version [6,14,37]. Furthermore, Guignard and Opaswongkarn [19] proposed a dual-ascent approach to the capacitated facility location problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Dual‐ascent and primal heuristics for production‐assembly‐distribution system design

Dong

Wilhelm

2012

Naval Research Logistics

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This article proposes two dual-ascent algorithms and uses each in combination with a primal drop heuristic embedded within a branch and bound framework to solve the uncapacitated production assembly distribution system (i.e., supply chain) design problem, which is formulated as a mixed integer program. Computational results indicate that one approach, which combines primal drop and dual-ascent heuristics, can solve instances within reasonable time and prescribes solutions with gaps between the primal and dual solution values that are less than 0.15%, an efficacy suiting it for actual large-scale applications. The fixed-charge network design problem is a generalization of the facility location problem [34]. Researchers have designed dual-ascent approaches to both uncapacitated [2] and capacitated [17,22] fixed-charge network design problems. In particular, Balakrishnan et al.[1] devised dual-ascent algorithms for networks with special topological structures (e.g., multilevel networks). The network design problem is a generalization of the fixed-charge network flow problem. The latter assumes that each arc provides a certain capacity, whereas the former allows arc capacity to be selected from several alternatives. The supply chain design problem is related to the productiondistribution network design problem [21,28], a special case of the network design problem in which the network is acyclic.

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Section: Literature Reviewmentioning

confidence: 99%

Dual‐ascent and primal heuristics for production‐assembly‐distribution system design

Dong

Wilhelm

2012

Naval Research Logistics

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“…[2], in which, however, it is shown that the reformulation applied to both levels yields to out-of-memory problems due to the large number of binary variables introduced and is, therefore, unsuitable for general purpose solvers. A comparison between the compact model IP strengthened by inequalities (8) and (9) and the discretized model DU-IP including (15) and (16) is reported in Section 4.…”

Section: Reformulation By Discretization Of the Upper Level Location mentioning

confidence: 99%

“…Each client must be assigned to a path of k facilities, and its demand must be routed through a facility of each level following a given order. Classical heuristics and exact approaches have been presented in [30]; recent approaches to the problem include approximation algorithms [15], metaheuristics [25], and polyhedral studies [24]. However, unlike the case we consider in this article, neither capacity nor single source restrictions are imposed: each facility can be fractionally assigned to many upper level facilities.…”

Section: Introductionmentioning

confidence: 99%

Exactly solving a two‐level location problem with modular node capacities

2011

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In many telecommunication networks, a given set of client nodes must be served by different sets of facilities—providing different services and having dif- ferent capabilities—which must be located and dimen- sioned in the design phase. Network topology must be designed as well, by assigning clients to facilities and facilities to higher level entities, when necessary. We tackle a particular location problem, where two sets of facilities have to be located, and in which different devices can be installed at each site, providing different capacities at different costs. We optimize location and dimensioning of these facilities simultaneously. We intro- duce a compact formulation of that problem, we use dis- cretization and Dantzig–Wolfe reformulation techniques to improve models, and we design an exact optimization algorithm. We test our approach on a set of instances derived from existing literature on facility location

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“…Aardal et al [2] propose some facet defining and valid inequalities for the polytope associated with the two level uncapacitated facility location problem. Approximation algorithms are studied by Aardal et al [1], Ageev [3], Ageev et al [4], Bumb [9], Bumb and Kern [10], Gabor and van Ommeren [14], Guha et al [16], Meyerson et al [22], Shmoys et al [26], Zhang [32], and Zhang and Ye [33]. Branch and bound algorithms are given by Kaufman et al [18], Ro and Tcha [25], Tcha and Lee [29], and Tragantalerngsak et al [31].…”

Section: Introductionmentioning

confidence: 99%

The vendor location problem

Çınar

Yaman

2011

Computers & Operations Research

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a b s t r a c tThe vendor location problem is the problem of locating a given number of vendors and determining the number of vehicles and the service zones necessary for each vendor to achieve at least a given profit. We consider two versions of the problem with different objectives: maximizing the total profit and maximizing the demand covered. The demand and profit generated by a demand point are functions of the distance to the vendor. We propose integer programming models for both versions of the vendor location problem. We then prove that both are strongly NP-hard and we derive several families of valid inequalities to strengthen our formulations. We report the outcomes of a computational study where we investigate the effect of valid inequalities in reducing the duality gaps and the solution times for the vendor location problem.

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A new approximation algorithm for the multilevel facility location problem

Cited by 31 publications

References 23 publications

Dual‐ascent and primal heuristics for production‐assembly‐distribution system design

Dual‐ascent and primal heuristics for production‐assembly‐distribution system design

Exactly solving a two‐level location problem with modular node capacities

The vendor location problem

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