Nonlinear Pricing for Yield Management and Countering Strategic Consumer Behavior

Abstract

Many models in operations management assume that faced with excess inventory, retailers offer price discounts to increase sales. This discount is assumed to be a certain dollar amount per unit or a certain percent of the regular price. However, many retailers use nonlinear pricing, e.g. "Buy one, get one for 50% off" and "Buy two, get the third free", which we refer to as BOGO. We analyze BOGO promotions within the newsvendor model framework and identify the reasons for its popularity among retailers. We describe the type of products for which BOGO promotions are suitable, identify the optimal BOGO discount, and its effect on the retailer's profit. We compare the BOGO promotions to the straight price reduction promotions and analyze the newsvendor's optimal choice between them. We also examine the two promotions in the presence of strategic consumers. We find that for reasonable values of consumer marginal utility and a given order quantity, BOGO reduces strategic consumers' chances of obtaining a unit at a discount and their incentive to wait. Therefore, the newsvendor orders a larger quantity with BOGO than with a straight price reduction. Thus, BOGO promotions can be used by the newsvendor to counter strategic consumer behavior. Also, we find that in the presence of strategic consumers, there are some cases where it is optimal for the retailer to wait and discount the product at the end of the season. However, with BOGO it is always optimal to offer the BOGO promotion at the start of the season when realized demand is low.