A separation method for maximal covering location problems with fuzzy parameters

Our paper discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speciffic structure of the origi...

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Fecha de publicación:
2017
Institución:
Universidad de Medellín
Repositorio:
Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/4286
Acceso en línea:
http://hdl.handle.net/11407/4286
Palabra clave:
Integer optimization
MCLP
Numerical optimization
Integer programming
Multiobjective optimization
Numerical methods
Separation
Site selection
Supply chains
Computational algorithm
Integer optimization
Maximal covering location problems
Maximal covering location problems (MCLP)
MCLP
Multi-objective optimization problem
Numerical optimizations
Supply chain optimization
Optimization
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http://purl.org/coar/access_right/c_16ec
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network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.spa.fl_str_mv A separation method for maximal covering location problems with fuzzy parameters
title A separation method for maximal covering location problems with fuzzy parameters
spellingShingle A separation method for maximal covering location problems with fuzzy parameters
Integer optimization
MCLP
Numerical optimization
Integer programming
Multiobjective optimization
Numerical methods
Separation
Site selection
Supply chains
Computational algorithm
Integer optimization
Maximal covering location problems
Maximal covering location problems (MCLP)
MCLP
Multi-objective optimization problem
Numerical optimizations
Supply chain optimization
Optimization
title_short A separation method for maximal covering location problems with fuzzy parameters
title_full A separation method for maximal covering location problems with fuzzy parameters
title_fullStr A separation method for maximal covering location problems with fuzzy parameters
title_full_unstemmed A separation method for maximal covering location problems with fuzzy parameters
title_sort A separation method for maximal covering location problems with fuzzy parameters
dc.contributor.affiliation.spa.fl_str_mv Azhmyakov, V., Department of Basic Sciences, Universidad de Medellin, Medellin, Colombia
Fernandez-Gutierrez, J.P., Department of Basic Sciences, Universidad de Medellin, Medellin, Colombia
Pickl, S., Institut fur Theoretische Informatik, Mathematik und Operations Research, Fakultat fur Informatik, Universitat der Bundeswehr Munchen, Munchen, Germany
dc.subject.keyword.eng.fl_str_mv Integer optimization
MCLP
Numerical optimization
Integer programming
Multiobjective optimization
Numerical methods
Separation
Site selection
Supply chains
Computational algorithm
Integer optimization
Maximal covering location problems
Maximal covering location problems (MCLP)
MCLP
Multi-objective optimization problem
Numerical optimizations
Supply chain optimization
Optimization
topic Integer optimization
MCLP
Numerical optimization
Integer programming
Multiobjective optimization
Numerical methods
Separation
Site selection
Supply chains
Computational algorithm
Integer optimization
Maximal covering location problems
Maximal covering location problems (MCLP)
MCLP
Multi-objective optimization problem
Numerical optimizations
Supply chain optimization
Optimization
description Our paper discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speciffic structure of the originally given MCLP makes it possible to reduce it to two auxiliary Knapsack-type problems. The equivalent separation we propose reduces essentially the complexity of the resulting computational algorithms. This algorithm also incorporates a conventional relaxation technique and the scalarizing method applied to an auxiliary multiobjective optimization problem. The proposed solution methodology is next applied to Supply Chain optimization in the presence of incomplete information. We study two illustrative examples and give a rigorous analysis of the obtained results.
publishDate 2017
dc.date.accessioned.none.fl_str_mv 2017-12-19T19:36:45Z
dc.date.available.none.fl_str_mv 2017-12-19T19:36:45Z
dc.date.created.none.fl_str_mv 2017
dc.type.eng.fl_str_mv Article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 11268042
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/4286
dc.identifier.reponame.spa.fl_str_mv reponame:Repositorio Institucional Universidad de Medellín
dc.identifier.instname.spa.fl_str_mv instname:Universidad de Medellín
identifier_str_mv 11268042
reponame:Repositorio Institucional Universidad de Medellín
instname:Universidad de Medellín
url http://hdl.handle.net/11407/4286
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-85029392455&partnerID=40&md5=6a4351f1e2812f81178c421a301bbbbb
dc.relation.ispartofes.spa.fl_str_mv Italian Journal of Pure and Applied Mathematics
Italian Journal of Pure and Applied Mathematics Issue 38, July 2017, Pages 653-670
dc.relation.references.spa.fl_str_mv Alexandris, G., & Giannikos, I. (2010). A new model for maximal coverage exploiting GIS capabilities. European Journal of Operational Research, 202(2), 328-338. doi:10.1016/j.ejor.2009.05.037
Atkinson, K., & Han, W. (2001). Theoretical Numerical Analysis.
Aytug, H., & Saydam, C. (2002). Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study. European Journal of Operational Research, 141(3), 480-494. doi:10.1016/S0377-2217(01)00260-0
Azhmyakov, V., Basin, M., & Reincke-Collon, C. (2014). Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs. Paper presented at the IFAC Proceedings Volumes (IFAC-PapersOnline), , 19 6976-6981.
Azhmyakov, V., & Fernandez-Gutierrez, J. P. (2016). St. pickl. A novel numerical ap-proach to the resilient MCLP based supply chain optimization. Proceed-Ings of the 12th IFAC Workshop on Intelligent Manufacturing Systems, , 145-150.
Azhmyakov, V., Martinez, J. C., & Poznyak, A. (2016). Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals. Optimal Control Applications and Methods, 37(5), 1035-1055. doi:10.1002/oca.2223
Azhmyakov, V., & Schmidt, W. (2006). Approximations of relaxed optimal control problems. Journal of Optimization Theory and Applications, 130(1), 61-77. doi:10.1007/s10957-006-9085-9
Batanović, V., Petrović, D., & Petrović, R. (2009). Fuzzy logic based algorithms for maximum covering location problems. Information Sciences, 179(1-2), 120-129. doi:10.1016/j.ins.2008.08.019
Berman, O., Kalcsics, J., Krass, D., & Nickel, S. (2009). The ordered gradual covering location problem on a network. Discrete Applied Mathematics, 157(18), 3689-3707. doi:10.1016/j.dam.2009.08.003
Berman, O., & Wang, J. (2011). The minmax regret gradual covering location problem on a network with incomplete information of demand weights. European Journal of Operational Research, 208(3), 233-238. doi:10.1016/j.ejor.2010.08.016
Bertsekas, D. P. (1995). Nonlinear Programming.
Canbolat, M. S., & Massow, M. v. (2009). Planar maximal covering with ellipses. Computers and Industrial Engineering, 57(1), 201-208. doi:10.1016/j.cie.2008.11.015
Church, R., & ReVelle, C. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32(1), 101-118. doi:10.1007/BF01942293
Galvão, R. D., Espejo, L. G. A., & Boffey, B. (2000). A comparison of lagrangean and surrogate relaxations for the maximal covering location problem. European Journal of Operational Research, 124(2), 377-389.
Ji, G., & Han, S. (2014). A strategy analysis in dual-channel supply chain based on effort levels. Proceedings of the 1th International Conference on Service Systems and Service Management.
Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack Problems.
Mitsos, A., Chachuat, B., & Barton, P. I. (2009). Mccormick-based relaxations of algorithms. SIAM Journal on Optimization, 20(2), 573-601. doi:10.1137/080717341
Moore, G. C., & ReVelle, C. (1982). The hierarchical service location problem. Management Science, 28(7), 775-780.
Polak, E. (1997). Optimization.
ReVelle, C., Scholssberg, M., & Williams, J. (2008). Solving the maximal covering location problem with heuristic concentration. Computers and Operations Research, 35(2), 427-435. doi:10.1016/j.cor.2006.03.007
Roubíček, T. (1997). Relaxation in Optimization Theory and Variational Calculus.
Shavandi, H., & Mahlooji, H. (2006). A fuzzy queuing location model with a genetic algorithm for congested systems. Applied Mathematics and Computation, 181(1), 440-456. doi:10.1016/j.amc.2005.12.058
Sitek, P., & Wikarek, J. (2013). A hybrid approach to modeling and optimization for supply chain management with multimodal transport. Paper presented at the 2013 18th International Conference on Methods and Models in Automation and Robotics, MMAR 2013, 777-782.
Zarandi, M. H. F., Sisakht, A. H., & Davari, S. (2011). Design of a closed-loop supply chain (CLSC) model using an interactive fuzzy goal programming. International Journal of Advanced Manufacturing Technology, 56(5-8), 809-821. doi:10.1007/s00170-011-3212-y
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv Forum-Editrice Universitaria Udinese SRL
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
_version_ 1808481157138874368
spelling 2017-12-19T19:36:45Z2017-12-19T19:36:45Z201711268042http://hdl.handle.net/11407/4286reponame:Repositorio Institucional Universidad de Medellíninstname:Universidad de MedellínOur paper discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speciffic structure of the originally given MCLP makes it possible to reduce it to two auxiliary Knapsack-type problems. The equivalent separation we propose reduces essentially the complexity of the resulting computational algorithms. This algorithm also incorporates a conventional relaxation technique and the scalarizing method applied to an auxiliary multiobjective optimization problem. The proposed solution methodology is next applied to Supply Chain optimization in the presence of incomplete information. We study two illustrative examples and give a rigorous analysis of the obtained results.engForum-Editrice Universitaria Udinese SRLFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85029392455&partnerID=40&md5=6a4351f1e2812f81178c421a301bbbbbItalian Journal of Pure and Applied MathematicsItalian Journal of Pure and Applied Mathematics Issue 38, July 2017, Pages 653-670Alexandris, G., & Giannikos, I. (2010). A new model for maximal coverage exploiting GIS capabilities. European Journal of Operational Research, 202(2), 328-338. doi:10.1016/j.ejor.2009.05.037Atkinson, K., & Han, W. (2001). Theoretical Numerical Analysis.Aytug, H., & Saydam, C. (2002). Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study. European Journal of Operational Research, 141(3), 480-494. doi:10.1016/S0377-2217(01)00260-0Azhmyakov, V., Basin, M., & Reincke-Collon, C. (2014). Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs. Paper presented at the IFAC Proceedings Volumes (IFAC-PapersOnline), , 19 6976-6981.Azhmyakov, V., & Fernandez-Gutierrez, J. P. (2016). St. pickl. A novel numerical ap-proach to the resilient MCLP based supply chain optimization. Proceed-Ings of the 12th IFAC Workshop on Intelligent Manufacturing Systems, , 145-150.Azhmyakov, V., Martinez, J. C., & Poznyak, A. (2016). Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals. Optimal Control Applications and Methods, 37(5), 1035-1055. doi:10.1002/oca.2223Azhmyakov, V., & Schmidt, W. (2006). Approximations of relaxed optimal control problems. Journal of Optimization Theory and Applications, 130(1), 61-77. doi:10.1007/s10957-006-9085-9Batanović, V., Petrović, D., & Petrović, R. (2009). Fuzzy logic based algorithms for maximum covering location problems. Information Sciences, 179(1-2), 120-129. doi:10.1016/j.ins.2008.08.019Berman, O., Kalcsics, J., Krass, D., & Nickel, S. (2009). The ordered gradual covering location problem on a network. Discrete Applied Mathematics, 157(18), 3689-3707. doi:10.1016/j.dam.2009.08.003Berman, O., & Wang, J. (2011). The minmax regret gradual covering location problem on a network with incomplete information of demand weights. European Journal of Operational Research, 208(3), 233-238. doi:10.1016/j.ejor.2010.08.016Bertsekas, D. P. (1995). Nonlinear Programming.Canbolat, M. S., & Massow, M. v. (2009). Planar maximal covering with ellipses. Computers and Industrial Engineering, 57(1), 201-208. doi:10.1016/j.cie.2008.11.015Church, R., & ReVelle, C. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32(1), 101-118. doi:10.1007/BF01942293Galvão, R. D., Espejo, L. G. A., & Boffey, B. (2000). A comparison of lagrangean and surrogate relaxations for the maximal covering location problem. European Journal of Operational Research, 124(2), 377-389.Ji, G., & Han, S. (2014). A strategy analysis in dual-channel supply chain based on effort levels. Proceedings of the 1th International Conference on Service Systems and Service Management.Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack Problems.Mitsos, A., Chachuat, B., & Barton, P. I. (2009). Mccormick-based relaxations of algorithms. SIAM Journal on Optimization, 20(2), 573-601. doi:10.1137/080717341Moore, G. C., & ReVelle, C. (1982). The hierarchical service location problem. Management Science, 28(7), 775-780.Polak, E. (1997). Optimization.ReVelle, C., Scholssberg, M., & Williams, J. (2008). Solving the maximal covering location problem with heuristic concentration. Computers and Operations Research, 35(2), 427-435. doi:10.1016/j.cor.2006.03.007Roubíček, T. (1997). Relaxation in Optimization Theory and Variational Calculus.Shavandi, H., & Mahlooji, H. (2006). A fuzzy queuing location model with a genetic algorithm for congested systems. Applied Mathematics and Computation, 181(1), 440-456. doi:10.1016/j.amc.2005.12.058Sitek, P., & Wikarek, J. (2013). A hybrid approach to modeling and optimization for supply chain management with multimodal transport. Paper presented at the 2013 18th International Conference on Methods and Models in Automation and Robotics, MMAR 2013, 777-782.Zarandi, M. H. F., Sisakht, A. H., & Davari, S. (2011). Design of a closed-loop supply chain (CLSC) model using an interactive fuzzy goal programming. International Journal of Advanced Manufacturing Technology, 56(5-8), 809-821. doi:10.1007/s00170-011-3212-yScopusA separation method for maximal covering location problems with fuzzy parametersArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Azhmyakov, V., Department of Basic Sciences, Universidad de Medellin, Medellin, ColombiaFernandez-Gutierrez, J.P., Department of Basic Sciences, Universidad de Medellin, Medellin, ColombiaPickl, S., Institut fur Theoretische Informatik, Mathematik und Operations Research, Fakultat fur Informatik, Universitat der Bundeswehr Munchen, Munchen, GermanyAzhmyakov V.Fernandez-Gutierrez J.P.Pickl S.Department of Basic Sciences, Universidad de Medellin, Medellin, ColombiaInstitut fur Theoretische Informatik, Mathematik und Operations Research, Fakultat fur Informatik, Universitat der Bundeswehr Munchen, Munchen, GermanyInteger optimizationMCLPNumerical optimizationInteger programmingMultiobjective optimizationNumerical methodsSeparationSite selectionSupply chainsComputational algorithmInteger optimizationMaximal covering location problemsMaximal covering location problems (MCLP)MCLPMulti-objective optimization problemNumerical optimizationsSupply chain optimizationOptimizationOur paper discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speciffic structure of the originally given MCLP makes it possible to reduce it to two auxiliary Knapsack-type problems. The equivalent separation we propose reduces essentially the complexity of the resulting computational algorithms. This algorithm also incorporates a conventional relaxation technique and the scalarizing method applied to an auxiliary multiobjective optimization problem. The proposed solution methodology is next applied to Supply Chain optimization in the presence of incomplete information. We study two illustrative examples and give a rigorous analysis of the obtained results.http://purl.org/coar/access_right/c_16ec11407/4286oai:repository.udem.edu.co:11407/42862020-05-27 15:44:54.527Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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