An economic production quantity model for items with time proportional deterioration under permissible delay in payments

In traditional economic order quantity (EOQ) models, the items are replenished instantaneously and payments for the purchased items are made whenever the items are received. But, sometimes, the supplier may offer the retailer a trade credit period for the purchased goods. The retailer can pay the amount of purchased goods within this stipulated credit period. Beyond this period, some interest may be charged for the purchased items. The supplier offers to the retailer this permissible delay in payments to attract the new customers. These new customers can increase their sells by reducing the price of the items or by increasing the amount of stock displayed to attract the customers. Therefore, within the trade credit period, the retailers can trade without using their capitals. The purpose of this paper is to investigate the optimal production time and optimal cycle time in an economic production quantity model for items with time-proportional deterioration. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of a numerical example. The model of Huang (2004) is deduced from this model as a special case.