In this paper we develop an inventory model for deteriorating items with price sensitive demand. Generally the vendor offers a cash discount or fix time period to the retailer to pay all the dues. According to the availability of money the retailer chooses his/her option. In this paper we discuss the possible cases of permissible delay and cash discount. The shortages are allowed in this model and are partially backlogged. Holding cost is considered as varying function of time, which reflects a more realistic concept. The purpose of this study is to optimize the overall cost of the system and to compute optimal ordering quantity. Numerical examples for different cases are also presented to illustrate the study. A sensitivity analysis with regard to distinct associated parameters is shown to make sure the constancy of the model.

This study presents optimal ordering policies for retailer when supplier offers cash discount and two progressive payment schemes for paying of purchasing cost. If the retailer pays the outstanding amount before or at first trade credit period M, the supplier provides r_1cash discount and does not charge any interest. If the retailer pays after M but before or at the second trade period N offered by the supplier, the supplier provides r_2 cash discount and charges interest on unpaid balance at the rate ?Ic?_1 . If retailer pays the balance after N, (N & GT; M) then the supplier does not provide any cash discount but charges interest on unpaid balance at the rate ?Ic?_2. The primary objective of this paper is to minimize the total cost of inventory system. This paper develops an algebraic approach to determine the optimal cycle time, optimal order quantity and optimal relevant cost. Numerical example are also presented to illustrate the result of propose model and solution procedure developed.