Mathematical modeling of integrated systems of production and distribution through approach of fuzzy supply chain management

Nowadays, the role of economics in different fields, such as automobile manufacturing industries, is developing. Fuzzy supply chain management is a new approach which leads to decrease in system costs, decrease in wastes, decrease in losses in transportation and decrease in stock supply. Management of fixed costs such as warehouse construction, and changing costs such as transportation, maintenance, shortage, human force, will lead to car manufacturing waste, etc. structure of queuing model used in this research follows M/G/1 queuing, which has Arrival rate of the Poisson probability distribution function and serving rate of general probability distribution function. In this research, fuzzy supply chain is analyzed in 3 levels. Suppliers are placed on the first level, ware houses and distribution centers are placed on the second level, and local warehouses (consumers) are placed on the third level. The structure of objective function of optimized model which is presented, is based on profit maximization, so that profit resulting from product sales is obtained from difference in total incomes and total costs. Determination of transfer rate from suppliers to middle warehouses (distribution centers), and also determination of transfer rate from middle warehouses tolocal warehouses, are two good results which can be obtained through model analysis. Model is processed by using Maple 12 software, and at the end suitable results of the model are expressed. This approach result in suitable market management, increase in customer satisfaction, and increase in efficiency of activities in supply chain, product distribution in car manufacturing industries.