Problemas de localización de instalaciones no fiables
The aim of facility location problems consists on deciding where to optimally locate several plants or facilities (like industries, warehouses, schools, hospitals, distribution centers, datawarehouse, etc.) as well as how to optimally assign the clients to these facilities satisfying their demand. T...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad Miguel Hernández de Elche |
| Repositorio: | REDIUMH. Depósito Digital de la UMH |
| OAI Identifier: | oai:dspace.umh.es:11000/5129 |
| Acceso en línea: | http://hdl.handle.net/11000/5129 |
| Access Level: | acceso abierto |
| Palabra clave: | Programación entera Programación lineal Distribución y transporte Fiabilidad de sistemas CDU::5 - Ciencias puras y naturales::51 - Matemáticas CDU::5 - Ciencias puras y naturales::51 - Matemáticas::519.1 - Teoría general del análisis combinatorio. Teoría de grafos |
| Sumario: | The aim of facility location problems consists on deciding where to optimally locate several plants or facilities (like industries, warehouses, schools, hospitals, distribution centers, datawarehouse, etc.) as well as how to optimally assign the clients to these facilities satisfying their demand. These decisions are usually determined considering the opening costs, and the costs of serving the clients. In the literature, it is frequently assumed that the open facilities are always availaible. Nevertheles, in practice some facilities can interrupt their service and become unavailaible. A lot of location problems of the most recent literature include the failing distribution of the plants in their models, and this type of problems are known like reliability facility location problems. The three contributions collected in the present dissertation are referred to reliability facility location problems. The objective of this dissertation is to analyze the properties of the so called Reliability Fixed-Charge Location Problem. Paper 1.- In this first paper, we discuss the previously known formulation of the Reliability Fixed-Charge Location Problem, in which the number of open facilities has to be decided and depends on the opening costs and it is assumed that some of the facilities, called failable, may fail with a given probability, which is identical for all of them. We reformulate the original mathematical programming model as a set packing problem and we study some polyhedral properties of this type of problems. Then, conditions for optimal solutions are introduced. We propose an improved compact formulation for the problem and we check the performance through an extensive computational study. Paper 2.- In this paper, we analyze which allocation variables in the Reliability Fixed-Charge Location Problem formulation can be linearized so that the optimal value match the optimal value of the binary problem.We prove that we can relax the integrality of all the allocation variables associated to non-failable facilities or all the allocation variables associated to failable facilities, but not both simultaneously. We also demonstrate that we can relax the integrality of all the allocation variables whenever a family of valid inequalities is added to the set of constraints or whenever the parameters of the problem satisfy certain conditions. Finally, on solving the instances in a data set, we discuss which integrality relaxation or which modification of the problem performs better in terms of resolution time, and we illustrate that to inappropriately relax the integrality of the allocation variables can incur in a high difference at the objective value. Paper 3.- In the last paper we propose and discuss different models to include capacity constraints into the Reliability Fixed-Charge Location Problem. In all cases, the proposed models represent a trade off between the extreme models that can be found in the literature, where a priori assignments are either fixed, or can be fully modified at each scenario. By several computational experiments, we analyze the obtained solutions of introducing capacity constraints according to the different proposed models, in terms of computational burden and in terms of solution cost. |
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