The Solution Of Facility Location Model With Fuzzy Demand

Facility location allocation problem has been widely studied by operational researchers.Many researchers have studied the facility location allocation problem in a deterministicenvironment. However, the models they proposed cannot accommodate satisfactorily variouscustomer demands in the real world. Thus, people consider the facility location allocationproblem in an uncertain environment. This paper mainly studies the facility locationallocation problem with fuzzy demands. In order to build a capacitated facility locationallocation problem with fuzzy demands, three types of fuzzy programming models-fuzzyexpected cost minimization model, fuzzy α-cost minimization model, and credibilitymaximization model-are proposed according to different decision criteria. In order to solvethese models, the simplex algorithm, fuzzy simulations and particle swarm optimization areintegrated to produce a hybrid intelligent algorithm, solving fuzzy α-cost minimization modelas an example to illustrate the effectiveness of the proposed algorithm. Based on Hurwiczcriterion to improve the fuzzy α-cost minimization model, obtained fuzzy α-costminimization model under Hurwicz criteria.The main contents are as follows:(1)This paper introduces the significance and the development of equipment selectionproblem, and particle swarm optimization algorithm is introduced in the domestic and foreignresearch situation.(2) We give some basic concept of credibility space, the credibility of the fuzzy variablesand expectations theory of knowledge. For the optimization problem under the fuzzy demandprovides a theoretical basis and method.(3)We give the problem description of the capacitated facility location with fuzzydemands, including the establishment of model and solution. According to different criteriawe set up three fuzzy programming models of the facility location problem, and prove thethree models are reasonable.(4)In order to calculate the uncertain function of the models, some fuzzy simulationmethods are designed for facility location allocation problem. And introduced the basicparticle swarm algorithm, through several numerical examples illustrate the convergence ofparticle swarm optimization algorithm. Compared with the genetic algorithm, the particleswarm algorithm in solving the problem is better than genetic algorithm.(5) The fuzzy simulations, simplex algorithm and particle swarm algorithm areintegrated to produce a hybrid intelligent algorithm, using the hybrid intelligent algorithm to solve the fuzzy programming model. With solving the fuzzy α-cost minimization model as anexample, illustrates the rationality and effectiveness of the hybrid particle swarm optimizationalgorithm.(6)Improving the fuzzy α-cost minimization model under the Hurwicz criterion, themodel is applied to the facility location allocation problem to verify the rationality of themodel.