presenting the mathematical model of fuzzy supply chain of integrated distribution system

A fuzzy supply chain is one of the modern attitudes that lead to reduce system costs, losses in shipping products, and reduce inventory levels. the queuing model which used in this study obeys from m/g/1 queue that the arrival rate has a poisson probability distribution, and the service rate has the general probability distribution. in this study, the fuzzy supply chain has been analysed in three levels. the suppliers are placed on the first level, the distribution centres are at the second level and the local warehouse (consumer) is on the third level. the objective function of the presented model is based on profit maximization which the resulted benefit from products sale obtained from the difference between total revenues and total costs. the presented model in the fuzzy set has been converted to the deterministic mathematical model. the appropriate results can be obtained from the analysis of the presented model. the model is solved by using maple 12 software. finally, this approach leads to the appropriate management of the market, increasing customer satisfaction, and ultimately, increasing the efficiency and effectiveness of the activities in the supply chain network.