A Multi-product and Multi-period Model for a Procurement-production-distribution in Supply Chain with Fuzzy Parameters

This paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (FMILP) type. Considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. To solve fuzzy mixed-integer linear programming model it is first converted into a crisp model using two ranking of fuzzy numbers, and then the crisp model is solved. To validate the proposed model, examples with different size are generated by random data and then solved by both crisp and fuzzy models. By comparing the related results, it is shown that fuzzy model has a smaller value for the objective function than for the crisp model and the fuzzy model does not increase the number of computations and run time significantly.