An integrated inventory model with variable lead time, defective units and delay in payments

It is a common business strategy that suppliers offer credit period to motivate customers for buying more items. As a result, suppliers can increase their own profit by selling more and earning interest if customers are failed to credit the debited amount within the delay period. The model assumes this policy along with the production of defective items and the inspection policy where the order quantity and lead time are considered as decision variables. The lead time is stochastic in nature. The model is derived analytically and an algorithm is used to minimize the total cost of the system. Finally, a numerical example is given to illustrate the model.