Economies of Scale to Exploit Quantity Discounts

To investigate the impact of such quantity discounts on the supply chain, we must answer the following two basic questions  

Given a pricing schedule with quantity discounts, what is the optimal purchasing decision for a buyer seeking to maximize profits How does this decision affect the supply chain in terms of lot sizes, cycle inventories, and flow times  

Under what conditions should a suppher offer quantity discounts What are appropriate pricing schedules that a supplier seeking to maximize profits should offer  

We start by studying the optimal response of a retailer (the buyer) when faced with either of the two lot-size-based discount schemes offered by a manufacturer (the supplier). The retailer s objective is to select lot sizes to minimize the total annual material, order, and holding costs. Next, we evaluate the optimal lot size in the case of aU unit quantity discounts. 

In all unit quantity discounts, the pricing schednle contains specified break points qo,qi. Qr, where qo = 0. If an order placed is at least as large as qi bnt smaller than q j, each unit is obtained at a cost of C,. In general, the unit cost decreases as the quantity ordered increases that 

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