An inventory model with stock dependent demand, two parameter Weibull distribution deterioration in a fuzzy environment

An inventory model is considered for deteriorating items with a variable rate of deterioration, where deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. An EPQ model for Weibull deteriorating items with stock dependent demand rate is developed in this paper in fuzzy environment. Three different cases with complete, partial, no backlogging are considered. The optimal analytical model is derived. To retain the confidence of the buyers the machine reliability, flexibility and packaging cost are considered. Mathematical model has been presented to find the optimum total cost. The holding cost, setup cost, deterioration cost, labour cost for packing, material cost for packing, shortage cost, production cost involved in this model are taken as pentagonal fuzzy numbers. Graded mean representation method is used to defuzzify the model. To validate the optimal solution, suitable numerical example has been discussed. The effect of variations in the optimal solution with respect to the change in one parameter at a time is analyzed and sensitivity analysis is carried out.