Improving a supplier's quantity discount gain from many different buyers

We consider the pricing and inventory decisions of a vendor who supplies a single product to multiple heterogeneous buyers. The problem is analyzed as a Stackelberg game in which the vendor acts as the leader by announcing its pricing policy to all the buyers in advance and the buyers act as followers by choosing their order quantity and the associated purchasing price independently under the vendors' pricing scheme. We propose in this paper a pricing policy for the vendor that offers price discounts based on the percentage increase from a buyers' order quantity before discount. The proposed policy is defined as a discrete all-unit quantity discount schedule with many break points. We show that: (i) the proposed policy offers a higher price discount to a buyer ordering a larger quantity and hence complies with general fair trade laws; (ii) an explicit solution is obtained for the vendors' optimal decision; and (iii) although suppliers in reality normally offer price discounts based on a buyers' unit increase in order quantity, the proposed policy is superior for the vendor when there are many different buyers. Other benefits of the proposed pricing policy are demonstrated by numerical examples.