Duality for constrained multifacility location problems with mixed norms and applications

Idrissi, H.; Lefebvre, O.; Michelot, Christian

doi:10.1007/bf02097796

Cited by 15 publications

(7 citation statements)

References 40 publications

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“…Ref. [6] develops a dual problem for the constrained multi-facility minimum location problems involving mixed norms. General optimality conditions were obtained providing new algorithms which are decomposition methods based on the concept of partial inverse of a multifunction.…”

Section: In the Area Of The Rectangular Distance Multi-facility Location Problemmentioning

confidence: 99%

Optimization of the Multi-Facility Location Problem Using Widely Available Office Software

Němec

Stodola

2021

Algorithms

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Multi-facility location problem is a type of task often solved (not only) in logistics. It consists in finding the optimal location of the required number of centers for a given number of points. One of the possible solutions is to use the principle of the genetic algorithm. The Solver add-in, which uses the evolutionary method, is available in the Excel office software. It was used to solve the benchmark in 4 levels of difficulty (from 5 centers for 25 points to 20 centers for 100 points), and one task from practice. The obtained results were compared with the results obtained by the metaheuristic simulated annealing method. It was found that the results obtained by the evolutionary method are sufficiently accurate. Their accuracy depends on the complexity of the task and the performance of the HW used. The advantage of the proposed solution is easy availability and minimal requirements for user knowledge.

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Section: In the Area Of The Rectangular Distance Multi-facility Location Problemmentioning

confidence: 99%

Optimization of the Multi-Facility Location Problem Using Widely Available Office Software

Němec

Stodola

2021

Algorithms

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“…Idrissi, Lefebvre, and Michelot [10] consider the dual of a multi-facility location problem with linear and rectangular distance constraints and provide a solution procedure using a decomposition method. Michelot [22], in a review of the mathematical properties of continuous location models, provides the conjugate dual formulation of a multi-facility location problem, and a linearly constrained single-facility location problem.…”

Section: M; D(u V)mentioning

confidence: 99%

Duality in constrained multi‐facility location models

Üster

Love

2002

Naval Research Logistics

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Abstract:We consider the p-norm multi-facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multifacility minisum location problem with the bp -norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation.

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“…A thorough set of necessary and sufficient optimality conditions were developed by Juel and Love (1976). Idrissi et al (1989) developed a dual problem for the constrained multifacility minisum location problems involving mixed norms. General optimality conditions were obtained providing new algorithms which are decomposition methods based on the concept of partial inverse of a multifunction.…”

Section: Rectangular Distance Minisum Location Problemmentioning

confidence: 99%