Retailer’s optimal ordering policies with cash discount and progressive payment scheme derived algebraically

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 > 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.