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Mexico is the world’s third largest consumer of Polyethylene Terephthalate (PET), only preceded by the United States and China. PET is commonly used in plastic containers such as beverage bottles and food packaging. It can be argued that the main problem regarding pollution generated by PET waste lies in the lack of appropriate solid waste management. The decision regarding facility location is the central issue in solid waste management. A mixed integer linear programming model of the capacitated facility location problem is proposed and then a genetic algorithm is designed to optimize the model. The problem is described as follows: given the quantities of PET generated in the northern region of Veracruz, Mexico, by considering five cities and each as a single generation source, a collection center has to be selected among a set of pre-identified locations in the town of Tempoal, Veracruz; in order to serve a set of demand points in the re-use market; demands are assumed to be uncertain. The aim is to minimize the system’s overall cost.

This paper describes how the cut-and-solve framework and semi-Lagrangean based dual ascent algorithms can be integrated in two natural ways in order to solve the single source capacitated facility location problem. The first uses the cut-and-solve framework both as a heuristic and as an exact solver for the semi-Lagrangean subproblems. The other uses a semi-Lagrangean based dual ascent algorithm to solve the sparse problems arising in the cut-and-solve algorithm. Furthermore, we developed a simple way to separate a special type of cutting planes from what we denote the effective capacity polytope with generalized upper bounds. From our computational study, we show that the semi-Lagrangean relaxation approach has its merits when the instances are tightly constrained with regards to the capacity of the system, but that it is very hard to compete with a standalone implementation of the cut-and-solve algorithm. We were, however, able to increase the size of the instances solvable by almost 25 percent compared to methodologies proposed in the literature. This paper describes how the cut-and-solve framework and semi-Lagrangean based dual ascent algorithms can be integrated in two natural ways in order to solve the single source capacitated facility location problem. The first uses the cut-and-solve framework both as a heuristic and as an exact solver for the semi-Lagrangean subproblems. The other uses a semi-Lagrangean based dual ascent algorithm to solve the sparse problems arising in the cut-and-solve algorithm. Furthermore, we developed a simple way to separate a special type of cutting planes from what we denote the effective capacity polytope with generalized upper bounds. From our computational study, we show that the semi-Lagrangean relaxation approach has its merits when the instances are tightly constrained with regards to the capacity of the system, but that it is very hard to compete with a standalone implementation of the cut-and-solve algorithm. We were, however, able to increase the size of the instances solvable by almost 25 percent compared to methodologies proposed in the literature.

Mexico is the world's third largest consumer of Polyethylene Terephthalate (PET), only preceded by the United States and China. PET is commonly used in plastic containers such as beverage bottles and food packaging. It can be argued that the main problem regarding pollution generated by PET waste lies in the lack of appropriate solid waste management. The decision regarding facility location is the central issue in solid waste management. A mixed integer linear programming model of the capacitated facility location problem is proposed and then a genetic algorithm is designed to optimize the model. The problem is described as follows: given the quantities of PET generated in the northern region of Veracruz, Mexico, by considering five cities and each as a single generation source, a collection center has to be selected among a set of pre-identified locations in the town of Tempoal, Veracruz; in order to serve a set of demand points in the re-use market; demands are assumed to be uncertain. The aim is to minimize the system's overall cost. México es el tercer consumidor mundial de Tereftalato de Polietileno (PET), sólo después de Estados Unidos y China. El PET es utilizado comúnmente para fabricar recipientes de plástico tales como botellas para bebidas y empaques para alimentos. Se puede argumentar que el principal problema con respecto a la contaminación generada por los residuos de PET radica en una inadecuada gestión de residuos sólidos. Proponemos un modelo de programación entera mixta del problema de localización de instalaciones capacitado y luego un algoritmo genético es desarrollado para optimizar este modelo. El problema se describe de la siguiente manera: dada la cantidad de PET generado en la región norte de Veracruz, México, considerando cinco ciudades y cada una como una fuente de generación única, un centro de recolección tiene que ser seleccionado entre un conjunto de lugares previamente determinados en la ciudad de Tempoal, Veracruz; con el fin de servir a un conjunto de puntos de demanda en el mercado re-uso; se asume que las demandas como parámetros de incertidumbre. El objetivo es minimizar el costo total del sistema.

The cost optimal design of the majority of distribution and servicing systems consists of decisions on a number and on the locations of facilities from which customers’ demands are satisfied; however, there are severe difficulties in solving exact procedures because the underlying mathematical model is NP‐hard. These decisions should respect some additional conditions as a limited capacity of located facilities. The objective is to minimize the overall costs of the system and to satisfy all customers’ demands. In this paper, we enrich the set of constraints by a new requirement called sub‐pool compactness. This property of customer subset influences the quality of vehicle routes subsequently formed in a sub‐set of customers served by the same facility. This paper formulates the problem of the enriched capacitated facility location considering compactness condition, formalizes and studies the property of compactness and suggests the compound method solving this problem. First published online:27 Oct 2010