Abstract
In this paper, we develop a vendor managed inventory system for a supply chain with two levels. First level is one manufacturer and second level is several non-competing retailers. The manufacturer produces a deteriorating product from a deteriorating raw material. All deteriorating rates assumed as fuzzy numbers. The demands in retailers are price sensitive based on predefined function with fuzzy parameters. The manufacturer can produce products at a variable production rate that is one of the decision variables of our model. Other decision variables are retail price, the replenishment frequency of raw material, the replenishment cycle of the product that obtained by maximising the total profit of the entire chain. Because of concavity of the profit functions, with a solution algorithm, the exact optimal solution was found. At the end, a numerical example is presented to illustrate the model performance with a sensitivity analysis. Finally, some conclusions and future research directions are proposed.
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