An Elasticity Approach to the Newsvendor with Price-Sensitive Demand

Abstract

We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost-sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies, are characterized by monotonicity conditions, or bounds, on the elasticity of the lost-sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts.

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

“…An interesting extension that is even more related to this research is the price-setting newsvendor (see Petruzzi and Dada (1999) and Yao et al (2006)). More recently, Kocabıyıkoglu and Popescu (2011) identified a new measure of demand elasticity, the elasticity of the lost sales rate, to generalize and complement assumptions commonly made in the price-setting newsvendor. Kaya andÖzer (2012) provide a good survey of the literature on inventory risk sharing in a supply chain with a newsvendor-like retailer, which is closer to our framework.…”

Pricing and Revenue Management: The Value of Coordination

“…The first part of Proposition 2 extends the singleproduct newsvendor results in Kocabıyıkoglu and Popescu (2011) to the case of two products sharing a limited resource. A multiproduct extension of Proposition 2 follows along the same lines, generalizing the result obtained by Bertsimas and de Boer (2005) for additive-multiplicative demand models.…”

“…Examples include attraction models and additive-multiplicative specifications (e.g., with linear and isoelastic price dependence) with increasing failure rate (IFR). Our conditions on stochastic demand extend deterministic demand regularity conditions (Gallego andvan Ryzin 1994, Ziya et al 2004) as well as single-product newsvendor model assumptions (Kocabıyıkoglu and Popescu 2011), and they allow for sensitivity results characterizing the interaction of price and capacity decisions. For example, we show that in a hierarchical environment (i.e., one where pricing decisions precede allocation decisions), an increase in the high-end price should be met with a lower protection levelthat is, fewer reserved seats for this class-in contrast with implications of the standard revenue management model that does not capture price response.…”

“…Most of this literature characterizes price-sensitive demand uncertainty in terms of additive and/or multiplicative models. Our general demand model and approach are based on Kocabıyıkoglu and Popescu (2011), who use the concept of increasing LSR elasticity to provide general regularity conditions for the newsvendor pricing problem. Our analytical results in the first part of this paper show that similar demand regularity conditions are sufficient for several sequential pricing and revenue management problems.…”

“…Remark 2 (Kocabıyıkoglu and Popescu 2011). p x is increasing in x if and only if D p is stochastically decreasing in p with respect to the hazard rate order.…”