Discount pricing and ordering policy have been widely used in inventory management to reduce the total system cost. In a business dealing, the buyer controls when to replenish stock and how much stock to replenish to minimize total relevant cost. But the seller tries to influence the buyer's ordering behavior by offering a lower unit price to encourage larger orders. Large orders reduce the per-unit order processing and manufacturing setup costs for the seller. However, per-unit profit will be less due to lower unit cost. In this paper we assume this loss in profit

Both the buyer and the seller try to minimize their joint cost with the constraint that their resultant individual costs are no less desirable than their individual decisions without considering the other partner. The buyer tries to trade off buying price savings against higher total carrying costs, while the seller tries to trade off reduced order processing and manufacturing setup costs against loss of unit profit from sales. This buyer/seller bargaining process for the benefit of both parties is a common practice in the vegetables and fruits trade, though the parties do not actually apply any mathematical models. The model we developed allows more objective decision making in price and replenishment interval under the stated assumptions.

Quantity discount pricing is discussed in most books. See, for example, Hadley and Whitin [4], Naddor [9], Love [7] and Tersine [10]. All of these analyses have the following characteristics:

(1) They optimize the model solely from the buyer's perspective.

(2) They do not consider the effect of deterioration.

These traditional models assume that a pricing policy of the seller already exists, and they develop algorithms solely from the buyer's perspective. There is no analysis of how the seller can best develop a price structure to influence the buyer's ordering policy.

Monahan [8] was one of the early authors who studied the economic implications for the seller. His analytical approach to vendor-oriented optimal quantity discount policy maximized the supplier's resultant economic gain, but did so at no added cost to the buyer. Lal and Staelin [5] developed a fixed order quantity decision model with a discounting scheme aimed at the benefits of certain sellers and buyers. Their unified pricing policy motivated the buyer to increase the ordering quantity, thereby reducing the joint order and holding costs. The seller could reduce costs while leaving the buyer in a no worse, and often better, position. Lee and Rosenblatt [6] generalized Monahan's model somewhat on a more general order policy and added a constraint to the discount price. Their algorithm to solved the supplier's joint ordering and price discount policy. Chakravarty and Martin [1] developed a joint saving-sharing scheme between the seller and the buyer(s). Their algorithm determined both the discount price and the replenishment interval under a periodic review for any negotiation factor. Weng and Wong [11] developed general all-unit quantity discount models to simultaneously determine the optimal pricing and replenishment policies. Weng [12] later considered the supplier's quantity discount for reducing the supplier's operating costs and increasing the buyer's demand.