Research Snapshots

"Buy 3, Get 1 Free": Optimal pricing and inventory control policy

Retail outlets have long been trying to entice us with these sorts of quantity discounts to increase sales. But in the past decade or so, dynamic pricing has become increasingly accessible as a useful tool for retailers and manufacturers to better match supply with demand and increase profit. From the perspective of the retailer, the quantity-sales mode is an additional tool to dynamic pricing. Dr Ye Lu and Professor Youhua Chen of the Department of Management Sciences, along with colleagues Miao Song of the University of Hong Kong, and Xiaoming Yan of the Dongguan University of Technology show that substantial profit improvement can be gained as a result of shifting from uniform pricing to quantity-based pricing, especially when the product has a low unit ordering cost and high utility.

In "Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation" published in Operations Research, 2014, they propose an inventory-pricing model in which the optimal simultaneous decisions on inventory control and selling/pricing are based on a simple structure. One takeaway of managerial relevance: quantity-based price differentiation can produce a large profit improvement only if the firm shifts from the unit-sales mode to dynamic pricing. This benefit is significant when the ordering, holding, and shortage costs are relatively small, or when the marginal rate of utility is relatively large with respect to the purchased quantity. An equally important technical takeaway is the concept of the virtual value function, which has its roots in the auction and mechanism design literature and is applicable to inventory-pricing problems.

Read more:
Lu, Ye, Youhua (Frank) Chen, Miao Song, and Xiaoming Yan. "Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation." Operations Research 62.3 (2014): 512-523. INFORMS PubOnline. Web. 26 Jun. 2015.