The Study On Fuzzy Single-Source Capacitated Facility Location Problems

Facility location problem is to study how to locate the facility and how toallocate the products for the customers. In realistic facility location problems, thetransportation cost of facility and the customers’ demands usually have fuzziness,so we could adopt a fuzzy theory to study facility location problem.This thesis takes credibility theory as the methematics foundation to study twoclasses of novel facility location problems: fuzzy single-source facility location modelwith service level requirements and fuzzy single-source facility location model withValue-at-Risk. Considering customers’ demands are charaterized by mutually inde-pendent fuzzy variables, we transform the first model into its equivalent form. whenthe fuzzy demands are mutivariate normal fuzzy vectors, we employ an approxima-tion approach to discretize normal fuzzy demand, and then turn the the originalproblem into a mixed-interger problem with logic constraints. We design geneticalgorithm and present some numerical examples to illustrate the efectiveness of thedesigned algorithm.The main contribution contains the following four aspects:(i) We present two new classes of facility location models: fuzzy single-sourcefacility location model with service level requirements and fuzzy single-source facilitylocation model with value-at-risk.(ii) For fuzzy single-source facility location model with service level require-ments, when the customers’ demands are mutually independent fuzzy variables,we turn the primary models into deterministic equivalent problems, which can beresolved by general purpose software.(iii) For fuzzy single-source facility location model with value-at-risk, when thecustomers’ demands are mutivariate normal fuzzy vectors, we designe approximationapproach and genetic algorithm to solve the model.(iv) We give some numerical examples to illustrate the modeling ideas and theefectiveness of the proposed genetic algorithm.