An Inventory Model for Deteriorating Items with Stock-Dependent Demand under Fuzzy Lead Time and Partial Backlogging

For inventory management purposes, lead time refers to the amount of time it takes for a purchase order to be completed. Its effect is an important phenomenon in inventory management system. It also plays a significant role when lead time unknown to the decision makers. This paper deals with an inventory model for deteriorating items under fuzzy lead time. The stock dependent demand with partially backlogged shortages are considered in the proposed model. The total inventory costs for both crisp model and fuzzy model are derived. The fuzzy lead time is assumed to be triangular and trapezoidal numbers. The signed distance methods (SD) is used for defuzzification purpose. The developed model is validated with the help of numerical illustration under both crisp and fuzzy scenario. A pictorial presentation is furnished to explain the behaviour of the total inventory costs towards lead-crisp, lead-triangular and lead-trapezoidal values. Lastly a sensitivity analysis is performed to judge the sensitive behaviour of the total cost towards changes of the cost parameters.