An Imperfect Inventory Model for Multi-Warehouses Under Different Discount Policies With Shortages

A multi-warehouse inventory model with shortage has been developed where demand is taken as deterministic. In reality, during production, if the machine works for a long time there may be a random breakdown and the system shifts from controlled to out of the controlled situation, in this time production system produces defective items. The retailer offers an all-unit quantity discount on the selling price of the item who in return gets a quantity-based discount on the purchase price of the item. The motive of this model is to study a multi-warehouse model for imperfect items under a quantity-based discount, where the defectives can be screened and then can be sold in a single batch where the decision variables are set as optimal ordering quantity and optimal shortage quantity, to maximize the total profit of the retailer. A solution procedure is given to find the optimal solution and a numerical example is given to illustrate this study. Sensitivity analysis is also performed to study the effect of the changes in parameter values on the optimal solution.