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Quantity Discounts Under Demand Uncertainty

Enterprise Valuation Group, Lehman Brothers, New York, New York 10019
Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
nihat.altintas{at}lehman.com
ferhun{at}stanford.edu
stayur{at}andrew.cmu.edu

To motivate buyers to increase their order quantity, suppliers often rely on a well-established and widely used approach—they offer quantity discounts. This practice is in large part driven to obtain improved economies in transportation through higher truckload utilization. Recently, transportation rates, which are increasing faster than other costs, have become a larger portion of total net landed cost, placing the traditional quantity-discount practices under scrutiny. Many suppliers are left perplexed as to why their approach is not effective anymore, and some are even concerned that their overall profits may have actually decreased due to their discount parameters. In this paper, we study a multiperiod model, with a buyer facing stochastic end-item demand and a supplier offering an all-units quantity discount to him, to understand better the dynamics of such systems. We provide guidelines and insights on how to set effective discount parameters, and when not to expect much from them. We derive the optimal policy of the buyer, develop insights as to why the policy is complex, study the supplier's profit as a function of her offered quantity-discount scheme (accommodating the buyer's optimal policy), and discover a new phenomenon that is distinct and structurally different from the well-known bullwhip effect.

Key Words: all-unit quantity discounts; inventory management; stochastic demand; periodic review policies; minimum-order quantity
History: Received: June 15, 2005;