Optimal multiple-breakpoint quantity discount schedules for customers with heterogeneous demands: all-unit or incremental?

The supplier's problem of designing a quantity discount schedule is much more complicated when she faces customers who vary in size. This article considers both all-unit and incremental discount schedules with multiple breakpoints that maximize the supplier's net savings. Specifically, we assume that the distribution of customers’ demand belongs to the general family of Bender's Pareto curves, which generalizes the well-known “80-20” rule from A-B-C inventory analysis. For any number of breakpoints, we prove that the supplier is at least as well off under the optimal incremental discount schedule as she would be under the optimal all-unit discount schedule. Numerical study shows that most of the savings can be captured by a modest number (five) of breakpoints and that the advantage of incremental schedules over all-unit schedules goes to zero as the number of breakpoints grows large.

[1]  A. Banerjee.  Note-On A Quantity Discount Pricing Model to Increase Vendor Profits , 1986 .

[2]  Ming-Deh A. Huang,et al.  Proof of proposition 2 , 1992 .

[3]  Awi Federgruen,et al.  Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers , 2001, Manag. Sci..

[4]  Z. K. Weng,et al.  Channel coordination and quantity discounts , 1995 .

[5]  Qinan Wang,et al.  Improving a supplier's quantity discount gain from many different buyers , 2000 .

[6]  Leonard M. Adleman,et al.  Proof of proposition 3 , 1992 .

[7]  M. Dada,et al.  Pricing policies for quantity discounts , 1987 .

[8]  R. Staelin,et al.  An Approach for Developing an Optimal Discount Pricing Policy , 1984 .

[9]  Michael M Murphy.  Price Discrimination, Market Separation, and the Multi-Part Tariff , 1977 .

[10]  Raghuram Iyengar,et al.  Nonlinear pricing , 2022 .

[11]  Qinan Wang,et al.  Quantity discount pricing policies for heterogeneous retailers with price sensitive demand , 2005 .

[12]  Steven M. Shugan,et al.  Managing Channel Profits , 2008, Mark. Sci..

[13]  James P. Monahan.  A Quantity Discount Pricing Model to Increase Vendor Profits , 1984 .

[14]  Duangkamon Chotikapanich,et al.  A comparison of alternative functional forms for the Lorenz curve , 1993 .

[15]  C. Corbett,et al.  A Supplier's Optimal Quantity Discount Policy Under Asymmetric Information , 2000 .

[16]  N. Kakwani.  On a Class of Poverty Measures , 1980 .

[17]  Amy Hing-Ling Lau,et al.  Quantity discount and handling-charge reduction schemes for a manufacturer supplying numerous heterogeneous retailers , 2008 .

[18]  Prafulla Joglekar.  Note-Comments on A Quantity Discount Pricing Model to Increase Vendor Profits , 1988 .

[19]  Qinan Wang.  Determination of suppliers' optimal quantity discount schedules with heterogeneous buyers , 2002 .

[20]  K. Moorthy.  Market Segmentation, Self-Selection, and Product Line Design , 1984 .

[21]  Stephen M. Gilbert,et al.  Quantity Discounts in Single Period Supply Contracts with Asymmetric Demand Information , 2005 .

[22]  Amiya K. Chakravarty,et al.  Managing business interfaces : marketing, engineering, and manufacturing perspectives , 2004 .

[23]  M. Parry,et al.  Channel Coordination When Retailers Compete , 1995 .

[24]  M. J. Rosenblatt,et al.  THEORIES AND REALITIES OF QUANTITY DISCOUNTS: AN EXPLORATORY STUDY * , 2009 .

[25]  M. J. Rosenblatt,et al.  A generalized quantity discount pricing model to increase supplier's profits , 1986 .

[26]  R. Dolan.  Quantity Discounts: Managerial Issues and Research Opportunities , 1987 .

[27]  R. Rasche,et al.  Functional Forms for Estimating the Lorenz Curve: Comment , 1980 .

[28]  Manash Ranjan Gupta,et al.  Functional Form for Estimating the Lorenz Curve , 1984 .

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