An exact algorithm for the capacitated facility location problems with single sourcing

Holmberg, Kaj; Rönnqvist, Mikael; Yuan, Di

doi:10.1016/s0377-2217(98)00008-3

Cited by 163 publications

(113 citation statements)

References 17 publications

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“…Therefore for each single location problem considered here it may be possible ot obtain better results than those presented above, by incorporating specialized cutting, branching and heuristic procedures. Examples of specialized cutting planes devised for particular network location problems are those of [2] and [1]; specialized branching procedures are illustrated for instance in [14] and [36]; specialized heuristic procedures can be found in [20] and [13]. The performances of both branch-and-cut and branch-and-price genaral solvers can be strongly affected by such tailored additions.…”

Section: Discussionmentioning

confidence: 99%

“…Pirkul [36] obtained better results by dualizing the partitioning constraints (2): he could solve instances with 100 customers and 20 candidate facilities. Holmberg et al [20] proposed to couple a Lagrangean relaxation of the capacity constraints with a repeated matching heuristic, to solve problem instances involving up to 200 customers and 30 candidate facilities in some minutes. A column generation approach for the SS-CFLP was proposed by Neebe and Rao [34], who solved problem instances with more than 35 customers and 25 facilities.…”

Section: Fixed Set-up Costsmentioning

confidence: 99%

“…To this purpose we considered two SSCFLP datasets, both taken from the literature: the first one (indicated as HOLM) consists of 71 instances and it is described in [20]; the second (indicated as DIAZ) consists of 57 instances and it is described in [14]. The instances in these datasets have up to 200 users and 30 candidate sites, with non-uniform fixed costs and capacities.…”

Section: Cardinality Constraints and Fixed Costsmentioning

confidence: 99%

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A computational evaluation of a general branch-and-price framework for capacitated network location problems

2008

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The purpose of this paper is to illustrate a general framework for network location problems, based on column generation and branch-andprice. In particular we consider capacitated network location problems with single-source constraints. We consider several different network location models, by combining cardinality constraints, fixed set-up costs, concentrator restrictions and regional constraints. Our general branchand-price-based approach can be seen as a natural counterpart of the branch-and-cut-based commercial ILP solvers, with the advantage of exploiting the tightness of the lower bound provided by the set partitioning reformulation of network location problems. Branch-and-price and branch-and-cut are compared through an extensive set of experimental tests.

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Section: Discussionmentioning

confidence: 99%

Section: Fixed Set-up Costsmentioning

confidence: 99%

Section: Cardinality Constraints and Fixed Costsmentioning

confidence: 99%

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A computational evaluation of a general branch-and-price framework for capacitated network location problems

2008

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“…In 1970 and 1971, Held and Karp [72][73] applied a LR approach, based on the minimum spanning trees, in order to designing of a well-organized algorithm for the traveling salesman problem (TSP). This successful application caused to some motivations among several researchers.…”

Section: -1 General Pointsmentioning

confidence: 99%

A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem

2017

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Abstract:This study considers a multi-objective combined budget constrained facility location/network design problem (FL/NDP) in which the system uncertainty is considered. The most obvious practical examples of the problem are territorial designing and locating of academies, airline networks, and medical service centers. In order to assure the network reliability versus uncertainty, an efficient robust optimization approach is applied to model the proposed problem. The formulation is minimizing the total expected costs, including, transshipment costs, facility location (FL) costs, fixed cost of road/link utilization as well as minimizing the total penalties of uncovered demand nodes. Then, in order to consider of several system uncertainty, the proposed model is changed to a fuzzy robust model by suitable approaches. An efficient Sub-gradient based Lagrangian relaxation algorithm is applied. In addition, a practical example is studied. At the following, a series of experiments, including several test problems, is designed and solved to evaluate of the performance of the algorithm. The obtained results emphasize that considering of practical factors (e.g., several uncertainties, system disruptions, and customer satisfaction) in modelling of the problem can lead to significant improvement of the system yield and subsequently more efficient utilization of the established network.

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“…In structure the problem resembles the facility location problem with staircase costs (FLSC), see for example Holmberg (1984), Holmberg (1985), Holmberg (1994), Holmberg, Rönnqvist & Yuan (1999), or Harkness & ReVelle (2002, or the modular capacitated plant location problem (MCPL), see for example Correia & Captivo (2003) or Correia & Captivo (2004). Our problem diverges from these by having a continuous and differentiable objective function.…”

Section: Introductionmentioning

confidence: 99%

Location of slaughterhouses under economies of scale

Broek

Schütz

Stougie

et al. 2006

European Journal of Operational Research

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The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale.We present an approach based on linearisation of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.

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An exact algorithm for the capacitated facility location problems with single sourcing

Cited by 163 publications

References 17 publications

A computational evaluation of a general branch-and-price framework for capacitated network location problems

A computational evaluation of a general branch-and-price framework for capacitated network location problems

A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem

Location of slaughterhouses under economies of scale

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