An EPQ model under cash discount and permissible delay in payments derived without derivatives

The main purpose of this paper is to investigate the case where the retailer’s unit selling price and the purchasing price per unit are not necessarily equal within the economic production quantity (EPQ) framework under cash discount and permissible delay in payments. We establish the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal inventory cycle time, optimal order quantity and optimal payment time. This paper provides an algebraic approach to determine the optimal cycle time, optimal order quantity and optimal payment time. This approach provides one theorem to efficiently determine the optimal solution. Some previously published results of other researchers are deduced as special cases. Finally, numerical examples are given to illustrate the result and the managerial insights are also obtained.