Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity

Trade credit financing is increasingly recognized as an important strategy to increase profitability in Inventory Management. We revisit an economic order quantity model under conditionally permissible delay in payments, in which the supplier offers the retailer a fully permissible delay of M periods (i.e., there is no interest charge until M) if the retailer orders more than or equal to a predetermined quantity W. However, if the retailer’s order quantity is less than W, then the retailer must make a partial payment to the supplier, and enjoy a permissible delay of M periods for the remaining balance. In this paper, we extend the mentioned EOQ under conditionally permissible delay in payments to complement some shortcomings of the model. By contrast to the differential calculus method, we propose a simple arithmetic–geometric method to solve the problem. Furthermore, we establish some discrimination terms to identify the unique optimal solution among three alternatives, and explain those theoretical results by simply economical interpretations. Finally, we solve several numerical examples to illustrate the theoretical results and obtain some managerial implications.