Integrated Inventory Model for Deteriorating Items with Price-Dependent Demand under Quantity-Dependent Trade Credit

This paper explores an integrated inventory model when the deterioration rate follows exponential distribution under trade credit. Here, it is assumed that demand rate is a function of selling price and the permissible delay in payment depends on the order quantity. In the model shortages are completely backlogged. The maximization of the total profit per unit of time is taken as the objective function to study the retailer’s optimal ordering policy. This paper also presents a practical application example where the proposed inventory model is utilized to support business decision making. Particularly, the model developed in the paper could be useful in the area of supply chain management. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out. Our result illustrates that this model can be quite useful in determining the optimal ordering policy when the trade credit period is being analyzed. 1. Introduction Both in deterministic and probabilistic inventory models of classical type, it is observed that payments are made to the supplier immediately after receiving the items. In practice, the supplier will offer the retailer a delay period in payment for the amount of purchase to increase the demand known as trade credit period. Offering such a credit period to the retailer will encourage the supplier’s selling and reduce on-hand stock level. Simultaneously, without a primary payment the retailer can take the advantages of a credit period to reduce cost and increase profit. The customer does not have to pay any interest during the fixed period but if the payment gets delayed beyond the period interest will be charged by the supplier. This arrangement comes out to be very advantageous to the customer as he may delay the payment till the end of the permissible delay period. During this credit period the retailer can start to accumulate revenues on the sales and earn interest on that revenue. Thus, the delay in the payment offered by the supplier is a kind of price discount since paying later indirectly reduces the cost of holding and it encourages the retailers to increase their order quantity. Moreover, paying later indirectly reduces the cost of holding stock. Hence, trade credit can play an important role in inventory model for both the suppliers as well as the retailers in integrated inventory model. Goyal [1] first derived an EOQ model under the conditions of permissible delay in payments. Chung and Huang [2] extended Goyal’s [1] model to consider the case that the units are replenished at a finite rate