Stock-Dependent Inventory Model for Imperfect Items Under Permissible Delay in Payments

In the production process, the issue of quality is always ignored which results in defective production. These defective items can be removed from the lot through the inspection process which becomes essential for the system. Demand is considered as stock dependent. It is continuously declined to meet the customer’s demand which depends on the on-hand inventory up to the time t2. After that the inventory level declines by constant demand up to time t3. Thereafter, shortages occur and it accumulates at the rate \( \psi \left( {\tau - t} \right)\,till\,t = \tau \) when the next batch arrives. The whole cycle repeats itself after the cycle length τ. Further, it is assumed that payment will be made to the supplier for the goods immediately after receiving the consignment. Whereas, in practice, supplier does offer a certain fixed period to the retailer for settling the account. During this period, supplier charges no interest, but beyond this period interest is being charged. On the other hand, retailer can earn interest on the revenue generated during this period. Keeping this scenario in mind, an attempt has been made to formulate an inventory policy for the retailer dealing with imperfect quality items under permissible delay in payments. Results have been analyzed with the help of a numerical example and sensitivity analysis also carried out.