Lagrangean relaxation for the geographical partitioning problem

Among methodologies used in territory clustering, stand location-allocation and set partitioning models, to group small geographic areas, usually called “basic units” into a given number of larger groups called “territories”. The territory clustering problem is modeled as a p-median problem. A Lagra...

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Autores Principales: Díaz García, Juan Antonio, Bernabé Loranca, María Beatriz, Luna Reyes, Dolores Edwiges, Olivares Benítez, Elías, Martínez Flores, José Luis
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/1332
http://hdl.handle.net/10669/13016
Sumario: Among methodologies used in territory clustering, stand location-allocation and set partitioning models, to group small geographic areas, usually called “basic units” into a given number of larger groups called “territories”. The territory clustering problem is modeled as a p-median problem. A Lagrangean relaxation is used to obtain lower bounds to the optimal solution of the problem and a procedure is used to obtain upper bounds. In order to evaluate the performance of the proposed procedure, instances of two Mexico cities are used. The results obtained with the proposed method are compared to partitioning methods from the literature. According to the obtained results for the considered instances using different number of groups, optimal or near optimal solution are obtained with a reasonable amount of computer effort.Keywords: partitioning, Lagrangean relaxation, heuristics.Mathematics Subject Classification: 90C59, 62H30, 91C20.