Quantity Discounts Under Demand Uncertainty

Abstract

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.all-unit quantity discounts, inventory management, stochastic demand, periodic review policies, minimum-order quantity

Estimation of Economic Order Quantity with Variable Parameters (Ukraine Case Study)

“…Multi-decision choice on orders was presented by [1]. This approach allows optimizing buyers and sellers goals according different ordering strategy.…”

“…75% of supply chain participants working on its operations optimization to decrease costs of order scope [1]. To asses optimal inventory levels with variable demand used newsvendor models [9], when demand varies over time -the dynamic lot-size model [10].…”

“…Stochastic demand and constant variability of buyer behaviour [1] have multiple complicatedness decisions of supply-production-distribution process. The system effect can be explored while examining the logistic chain interrelation on vehicle's and storage parameters for optimal order quantity (EOQ) example.…”

The newsvendor problem: Review and directions for future research

“…Altintas, Erhun and Tayur [3] addressed the problem of designing the optimal all-units quantity discount with a single price break from the perspective of a supplier that faces a newsvendor-type buyer in a multiple-period setting. It is assumed that, for every period in the planning horizon except the last one, leftover units at the end of one period will be carried over to the next period and unfilled demand will be backlogged at a cost.…”

Editorial: How to Monetize the Value of OR

“…Some of my past and current papers on discrete-time inventory models were motivated by such interactions. For example, working with grocery retailers and their suppliers, such as Heinz, helped us to create a Management Science paper on quantity discounts (Altintas et al 2008) and an OR Practice paper (Erhun and Tayur 2003). I would guess that for every one practice paper, three to four theoretical papers are possible.…”