Mathematical Production Inventory Model for Deteriorating Items with Stock and Time Dependent Demand, Time Varying Holding Cost and Shortages in a Fuzzy Environment

This study develops an EPQ model for deteriorating items assuming time and stock dependent demand and time varying holding cost under the effect of inflation in fuzzy environment. Shortages are allowed and partially backlogged. In finding the optimal production quantity, deterioration plays a crucial role in inventory management. Therefore handling of deterioration is in highlight and attracted many researchers. Deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. 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 triangular fuzzy numbers. To validate the optimal solution, numerical example is provided. Sensitivity analysis is carried out to explore the effect of changes in the values of different parameters.