An Analysis of Advance Booking Discount Programs Between Competing Retailers

  • Kevin F. McCardle
  • Kumar Rajaram
  • Christopher S. Tang
Part of the Applied Optimization book series (APOP, volume 98)


As product demand uncertainty increases and life cycles shorten, retailers respond by developing mechanisms for more accurate demand forecasting and supply planning to avoid over-stocking or under-stocking a product. We model the situation in which two retailers consider launching one such mechanism, known as the ‘Advance Booking Discount’ (ABD) program. In this program customers are enticed to pre-commit their orders at a discount price prior to the regular selling season. However, these pre-committed orders are filled during the selling season. While the ABD program enables the retailers to lock in a portion of the customer demand and use this demand information to develop more accurate forecasts and supply plans, the advance booking discount price reduces profit margin. We analyze the four possible scenarios wherein each of the two firms offer an ABD program or not, and establish conditions under which the unique equilibrium calls for launching the ABD program at both retailers. We also provide a detailed numerical example to illustrate how these conditions are affected by the level of demand uncertainty, demand correlation, market share, and fixed costs for instituting an ABD program.


Expected Profit Unique Equilibrium Discount Price Demand Uncertainty Optimal Order Quantity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Achabal, D.D., McIntyre, S.A. Smith, 1990. “Maximizing Profits from Periodic Department Store Promotions,” Journal of Retailing 66, 383–407.Google Scholar
  2. Bhardwaj, P., and Sismeiro, D., 2001. “Can Manufacturers and Retailers Agree on Store Brand Provision?” Working Paper, The Anderson School at UCLA.Google Scholar
  3. Bickel, P. and K. Doksum, 1977. Mathematical Statistics, Holden Day Publisher, San Francisco.zbMATHGoogle Scholar
  4. Choi, S.C., 1991. “Price Competition in a Channel Structure with a Common Retailer,” Marketing Science 10(Fall), 271–296.Google Scholar
  5. Eliashberg, J., and R. Steinberg, 1991. “Marketing-Production Joint Decision Making,” in J. Eliashberg and G. Lilien (Eds), Management Science in Marketing, Handbooks in Operations Research and Management Science, North Holland.Google Scholar
  6. Fisher, M., Rajaram, K. and Raman, A., 2001. “Optimizing Inventory Replenishment of Retail Fashion Products,” Manufacturing and Service Operations Management Summer 2001 3(3), 230–241.CrossRefGoogle Scholar
  7. Friedman, J., Game Theory with Applications to Economics, Oxford University Press, New York, 1986.Google Scholar
  8. Lal, R., 1990. “Price Promotions: Limiting Competitive Encroachment,” Marketing Science 9, 247–262.Google Scholar
  9. Lippman, S.A., J. Mamer, and K.F. McCardle, 1986. “Comparative Statics in Non-Cooperative Games via Transfinitely Iterated Play,” Journal of Economic Theory 41, 288–303.MathSciNetCrossRefGoogle Scholar
  10. Lollar, C, 1992. “Trade Secrets of the Travel Game,” Working Woman, 17, May, 94.Google Scholar
  11. McCardle, K.F., K. Rajaram, and C.S. Tang, 2004. “Advance Booking Discount Programs under Retail Competition,” Management Science 50, 701–708.CrossRefGoogle Scholar
  12. McVea, R., 1997. “Wild West Lives Again in Suburbs,” Chicago Tribune, August 3, 1997.Google Scholar
  13. Narasimhan, C, 1984. “A Price Discrimination Theory of Coupons,” Marketing Science 3, 128–147.MathSciNetCrossRefGoogle Scholar
  14. Raju, J.S., Sethuraman, R. and Dhar, S.K., 1995. “The Introduction and Performance of Store Brands,” Management Science 41, 957–978.CrossRefGoogle Scholar
  15. Shubik, M. and Levitan, R., 1980. Market Structure and Behavior, Harvard University Press, Cambridge, MA.Google Scholar
  16. Silver, E.A., D.F. Pyke, and R. Peterson, 1998. Inventory Management and Production Planning and Scheduling, Third Edition, John Wiley.Google Scholar
  17. Smith, S. A., and D.D. Achabal, 1998. “Clearance Pricing and Inventory Policies for Retail Chains,” Management Science 44, 285–300.zbMATHGoogle Scholar
  18. Tang, C.S., Rajaram K., Alptekinoglu, A., and Ou, J., 2004. “The Benefits of Advance Booking Discount Programs: Model and Analysis,” Management Science. 50, 465–478.CrossRefGoogle Scholar
  19. Weng, K., and Parlar, M., 1999. “Integrating Early Sales with Production Decisions: Analysis and Insights,” IIE Trans. Scheduling Logist. 31, 1051–1060.Google Scholar
  20. Xie, J., and Shugan, S., 2001. “Electronic Tickets, Smart Cards, and Online Prepayments: When and How to Advance Sell,” Marketing Science 20,3, 219–243.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Kevin F. McCardle
    • 1
  • Kumar Rajaram
    • 1
  • Christopher S. Tang
    • 1
  1. 1.Anderson Graduate School of ManagementUCLALos Angeles

Personalised recommendations