Multi echelon fuzzy inventory model for perishable items in a supply chain with imperfect production and exponential demand rate

In this paper, an integrated inventory model for perishable item is developed from the supplier, manufacturer and buyer's point of view. Generally, the value of perishable items is determined by its quality. Demand is a major factor in supply chain system and it may increase due to consumer's preference. In reality, it is seen that demand and production of perishable item is almost uncertain because at the time of production, there are possibilities of being imperfect production. So the parameters that are affecting the quantity of demand and production rate are taken as triangular fuzzy numbers. Three different methods are used to defuzzify the total profit function. This model has been accomplished with the different rate of deterioration for raw material and finished goods. The change in deterioration rate of finished goods leads to continuous increase in total profit and cycle time, and the change in deterioration rate for raw material leads to gradual decrease in total profit as well as cycle time. The setup has been detected numerically to obtain an optimal solution and also the sensitivity analysis is performed.