A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem

Klose, Andreas

doi:10.1016/s0377-2217(99)00300-8

Cited by 87 publications

(27 citation statements)

References 34 publications

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“…Network problems are appeared in [16], [9], [13] and [19]. For the resolution of the problem and its variants, several exact and approximate approaches are tested: the reference [3] applies a cutting plane algorithm based on the Fenchel cuts, references [18], [5] and [4] have chosen to www.ijacsa.thesai.org use the Branch & Price and branch & Bound methods based on Lagrangian relaxation, a resolution with column generation is applied by [4] and references [6], [15] and [12] used different approaches and techniques.…”

Section: Introductionmentioning

confidence: 99%

Multi-Stage Algorithms for Solving a Generalized Capacitated P-median Location Problem

Amrani¹,

Benadada²

2018

ijacsa

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Abstract-The capacitated p-median location problem is one of the famous problems widely discussed in the literature, but its generalization to a multi-capacity case has not. This generalization, called multi-capacitated location problem, is characterized by allowing facilities to use one of several capacity levels. For this purpose, a predefined list of capacity levels supported by all potential facilities is established. In this paper, we will detail the mathematical formulation and propose a new solving method. We try to construct, indeed, a multi-stage heuristic algorithm that will be called BDF (Biggest Demand First). This new method appears in two approaches: Integrated BDF (IBDF) and Hybridized BDF (HBDF) will be improved by using a local search optimization. A valid lower bound to the optimal solution value is obtained by solving a lagrangian relaxation dual of the exact formulation. Computational results are presented at the end using new instances with higher ratio between the number of customers, facilities and capacity levels or adapted from those of p-median drawn from the literature. The obtained results show that the IBDF is much faster with medium quality solution while HBDF is slower but provides very good solutions close to the optimality.

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Section: Introductionmentioning

confidence: 99%

Multi-Stage Algorithms for Solving a Generalized Capacitated P-median Location Problem

Amrani¹,

Benadada²

2018

ijacsa

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“…Tragantalerngsak et al (2000) use a similar hybrid that solves a two-echelon SSCFLP to optimality. Klose (2000) put forward a Lagrangian relax-and-cut approach for the two-stage CFLP for which the relaxation is strengthened by adding valid inequalities. Shen (2005) formulates a general multi-commodity supply chain design as a nonlinear integer programming and exploits the structure of the problem to apply LR problem.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem

Mohammad-Nezhad

Manzour

Salhi

2013

International Journal of Production Economics

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Facility location problem is one of the strategic logistical drivers within the supply chain which is a hard to solve optimization problem. In this study, we focus on the uncapacitated single-source multiproduct production/distribution facility location problem with the presence of set-up cost. To efficiently tackle this decision problem, two lagrangian-based heuristics are proposed one of which incorporates integer cuts to strengthen the formulation. Local search operators are also embedded within these methods to improve the upper bounds as the search progresses. Three set of instances with various characteristics are generated and used to evaluate the performance of the proposed algorithms. Encouraging results are obtained when assessed against an ILP formulation using CPLEX. The latter is used for generating optimal solutions for small size instances and also as a means for producing upper and lower bounds for larger ones when restricted by a limited amount of execution time.

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“…The goal of CFLP is to minimize both the fixed costs of opening facilities and the shipping costs. Recently, an extended model has attracted more and more researchers: the two-stage capacitated facility location problem (TSCFLP) (Klose 1999(Klose , 2000Martí and Pelegrín 1999;Keskin and Üster 2007a,b;Liu and Xu 2010). TSCFLP generalizes CFLP by considering flows of commodity shipped from capacitated origins (e.g.…”

Section: Introductionmentioning

confidence: 99%

A scatter search for a multi-type transshipment point location problem with multicommodity flow

Prins

2010

J Intell Manuf

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In this paper, we consider a multi-type transshipment point location problem with multicommodity flow which aims at locating transshipment points (TPs) and determining the type for each open TP. As an extension of the classical two-stage capacitated facility location problem, our problem allows flows of commodities to move among TPs and does not impose restrictions on the number of TPs traversed by flows going from plants to customers. In order to obtain high-quality feasible solutions, we propose a clustering-based scatter search in which the seed solution generation, the diversification technique and the local search are designed using the clusters generated by a data mining technique, the K-means method. The computational results show that the scatter search performs efficiently over different kinds of instances. Moreover, the solution quality is also good since the average gaps to lower bounds range between 1 and 3%.

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A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem

Cited by 87 publications

References 34 publications

Multi-Stage Algorithms for Solving a Generalized Capacitated P-median Location Problem

Multi-Stage Algorithms for Solving a Generalized Capacitated P-median Location Problem

Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem

A scatter search for a multi-type transshipment point location problem with multicommodity flow

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