Optimal pricing and ordering policies for deteriorating items under a progressive trade credit scheme

In this paper, a mathematical model is developed to formulate optimal pricing and ordering policies when the units in inventory are subject to constant rate of deteriorating and the supplier offers progressive credit periods to settle the account. The concept of progressive credit periods is as follows: If the retailer settles the outstanding amount by M, the supplier does not charge any interest. If the retailer pays after M but before N (M < N), then the supplier charges the retailer on the un–paid balance at the rate Ic1. If the retailer settles the account after N, then he will have to pay an interest rate of Ic2 (Ic2 > Ic1) on the unpaid balance. The objective is to maximize the net profit. The decision variables are selling price and ordering quantity. An algorithm is given to find the flow of optimal selling price and ordering policy. A numerical illustration is given to study the effect of offered two credit periods and deterioration on decision variables and the net profit of the retailer.