In this paper, an inventory model is developed for deteriorating items for which the demand is dependent on the selling price as well as stock. The units in the inventory are subject to a constant rate of deterioration. Shortages are not allowed and the supplier provides a cash discount and a few permissible delays in payments. An optimal solution is characterized to optimize the net profit. An easy-to-use algorithm is given to find the optimal selling price, the optimal order quantity and a replenishment cycle time that maximizes the net profit. A numerical example is given to illustrate theoretical results and a sensitivity analysis of parameters on the optimal solutions is carried out at the end.

The second stringent assumption in the classical inventory model is that the payment will be made to the supplier for the goods immediately after receiving the consignment. However, practically it is observed that a supplier provides a credit period for a retailer to stimulate the demand or boost market share. Goyal (1985) first developed an EOQ model under the conditions of permissible delay in payments. Chung (1989) presented Discounted Cash Flow (DCF) approach for the analysis of the optimal inventory policy in the presence of trade credit. Shinn et al. (1996) extended Goyal’s (1985) model by considering quantity discounts for freight cost. Shah (1993), Aggarwal and Jaggi (1995), and Hwang and Shinn (1997) extended Goyal’s (1985) model to consider the deterministic inventory model with a constant rate of deterioration. Shah (1993), and Shah and Shah (1998) developed a probabilistic inventory model when delay in payments is permissible. They developed an EOQ model for constant rate of deteriorating items in which time is treated as a discrete variable. Deterioration of units is treated as a continuous variable and demand is a random variable. Jamal et al. (1997) extended Aggarwal and Jaggi’s (1995) model to allow for shortages.

On the other hand, in developed mathematical models, it is assumed that, the shortages are either completely backlogged or completely lost. Researchers derived models under the assumption that a fraction of the demand will be lost while the remaining fraction is backlogged. Wee (1995), and Yan and Cheng (1998).

Economic Order Quantity, EOQ Model, Stock-Dependent Demand, Discounted Cash Flow, DCF, Newton-Raphson’s method, Production Economics, Inventory Management, Production Planning, Probabilistic Inventory Model.