A multi-plant production planning problem in fuzzy environments

In this paper, a multi-plant production planning problem has been studied. The production of goods in multiple factories and the transportation of goods between the factories are involved while multi-product and multi-period are also taken into account. By considering the problem in the uncertain environments, which is more often to be come across in real world, some elements are supposed to be fuzzy. The problem then turns to be a multi-plant production planning problem in fuzzy environments. According to various comparison laws, expected value model, chance-constrained model and dependent-chance model are given. By solving these models in fuzzy environments, two efficient methods are introduced in the light of different circumstances. In the situation that the fuzzy variables are triangular variables and mutually independent, the model can be transformed into equivalent linear model which can be solved by simplex algorithm. Otherwise, when the fuzzy variables are not specific or mutually independent, fuzzy simulation and genetic algorithm are needed for solving these models.