An Elasticity Approach to the Newsvendor with Price-Sensitive Demand

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.

[1]  T. M. Whitin.  Inventory Control and Price Theory , 1955 .

[2]  E. Mills.  Uncertainty and Price Theory , 1959 .

[3]  Z. A. Lomnicki,et al.  Mathematical Theory of Reliability , 1966 .

[4]  A. J. Nevins,et al.  Some Effects of Uncertainty: Simulation of a Model of Price , 1966 .

[5]  E. Zabel.  Monopoly and Uncertainty , 1970 .

[6]  E. Zabel.  Multiperiod monopoly under uncertainty , 1972 .

[7]  Amy Hing-Ling Lau,et al.  The Newsboy Problem With Price-Dependent Demand Distribution , 1988 .

[8]  Dominique M. Hanssens,et al.  Market Response Models: Econometric and Time Series Analysis , 1989 .

[9]  Maqbool Dada,et al.  Pricing and the Newsvendor Problem: A Review with Extensions , 1999, Oper. Res..

[10]  Awi Federgruen,et al.  Combined Pricing and Inventory Control Under Uncertainty , 1999, Oper. Res..

[11]  Vipul Agrawal,et al.  Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem , 2000, Manuf. Serv. Oper. Manag..

[12]  Albert Y. Ha.  Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation , 2001 .

[13]  Evan L. Porteus,et al.  Selling to the Newsvendor: An Analysis of Price-Only Contracts , 2001, Manuf. Serv. Oper. Manag..

[14]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[15]  Nils Rudi,et al.  Centralized and Competitive Inventory Models with Demand Substitution , 2002, Oper. Res..

[16]  Mark A. McComb.  Comparison Methods for Stochastic Models and Risks , 2003, Technometrics.

[17]  Xin Chen,et al.  Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case , 2004, Oper. Res..

[18]  D. Simchi-Levi,et al.  Coordination of Pricing and Inventory Decisions: A Survey and Classification , 2004 .

[19]  Zuo-Jun Max Shen,et al.  Channel Performance Under Consignment Contract with Revenue Sharing , 2004, Manag. Sci..

[20]  Fernando Bernstein,et al.  A General Equilibrium Model for Industries with Price and Service Competition , 2004, Oper. Res..

[21]  David Simchi-Levi,et al.  Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science) , 2004 .

[22]  Wen Zhao,et al.  The Dynamic Pricing Problem from a Newsvendor's Perspective , 2004, Manuf. Serv. Oper. Manag..

[23]  Hayriye Ayhan,et al.  Relationships Among Three Assumptions in Revenue Management , 2004, Oper. Res..

[24]  M. Bagnoli,et al.  Log-concave probability and its applications , 2004 .

[25]  C. Yano,et al.  Coordinated Pricing and Production/Procurement Decisions: A Review , 2005 .

[26]  D. Atkins,et al.  On the effect of demand randomness on a price/quantity setting firm , 2005 .

[27]  Fernando Bernstein,et al.  Decentralized Supply Chains with Competing Retailers Under Demand Uncertainty , 2005, Manag. Sci..

[28]  R. Phillips,et al.  Pricing and Revenue Optimization , 2005 .

[29]  Evan L. Porteus,et al.  A Fractiles Perspective to the Joint Price/Quantity Newsvendor Model , 2006, Manag. Sci..

[30]  Martin A. Lariviere,et al.  A Note on Probability Distributions with Increasing Generalized Failure Rates , 2006, Oper. Res..

[31]  Hayriye Ayhan,et al.  Optimal prices for finite capacity queueing systems , 2006, Oper. Res. Lett..

[32]  Serguei Netessine,et al.  Dynamic pricing of inventory/capacity with infrequent price changes , 2006, Eur. J. Oper. Res..

[33]  Mark E. Ferguson,et al.  Bid-response models for customised pricing , 2007 .

[34]  Xuan Zhao,et al.  Newsvendors Under Simultaneous Price and Inventory Competition , 2008, Manuf. Serv. Oper. Manag..

[35]  Francis de Véricourt,et al.  Resource and Revenue Management in Nonprofit Operations , 2009, Oper. Res..

[36]  Craig Sorochuk.  The Newsvendor Problem with Pricing , 2011 .

[37]  E. Moradi,et al.  Quantitative Models in Supply Chain Management , 2012 .