Order-Sensitive Inventory Model with Trade Credit and All-Unit Discounts under Fuzzy Demand

This paper presents a fuzzy integrated inventory model under order-size-dependent trade credit with an all-unit discount linked to order purchasing costs. Our model allows for shortages and is fulfilled through partial back-ordering. The model addresses the complexities of retailer's capacity constraints. Here, the demand rate is fuzzy and expressed as a triangular and trapezoidal fuzzy number. We have formulated a total combined profit function for the retailer and the supplier and defuzzified it using graded mean integration and the signed distance method. We have also demonstrated the concavity of the total combined profit function. An algorithm is presented to determine the optimal production lot, positive inventory level period, and replenishment policies for the supplier and retailer. In this model, the unit production cost is considered as a function of the production rate. Numerical examples and sensitivity analysis are provided to analyze the graded mean integration and signed distance defuzzification techniques and to illustrate the theoretical findings. Our result highlights the advantages of a longer trade credit period, discounts on all units, and the expansion of warehouse capacity. We also found that by utilizing the graded mean integration and the signed distance method to defuzzify the total combined profit function, both the triangular and trapezoidal fuzzy demand deliver higher profit whose defuzzified demand is greater. Mathematics Subject Classification Code: 90B05, 90B35.