A Mathematical Analysis on Daily Inventory Clearance Pricing with Consumer's Reference Price

  • Koide, Takeshi ;
  • Sandoh, Hiroaki
  • Received : 2011.12.05
  • Accepted : 2012.02.18
  • Published : 2012.03.01


This paper discusses a clearance pricing on daily perishable products considering a reference price of consumers. The daily perishable products are sometimes sold at a discount price before closing time to stimulate demand when the number of unsold products is more than initially envisioned. The discount pricing results both in an increase of the revenue of the day and in a decrease of the disposal cost. The discounting, however, also declines a reference price of consumers which is a mental price and serves as an anchor price to judge if a current sales price is loss or gain for the consumers. An excess discounting decreases the demand for the products sold at a regular price in the future and diminishes long-term profit. This study conducts a mathematical analysis on the clearance pricing problem for a single period with stochastic variations both on demand and on the inventory level at clearance time. The expected profit function especially depends on the response of consumers to the clearing price against their reference prices. A procedure is proposed to derive an optimal clearance price when consumers are loss-neutral. A sufficient condition is shown to obtain an optimal price for loss-averse and loss-seeking consumers by an analogous procedure.


Optimal Pricing;Clearance;Inventory;Reference Price


  1. Arrow, K., Harris, T., and Marschak, J. (1951), Optimal inventory policy, Econometrika, 19, 250-272.
  2. Greenleaf, E. A. (1995), The Impact of Reference Price Effects on the Profitability of Price Promotions, Marketing Science, 14(1), 82-104.
  3. Kahneman, D. and Tversky, A. (1979), Prospect theory:An analysis of decision under risk, Econometrica, 47, 263-291.
  4. Kalyanaram, G. and Winer, R. S. (1995), Empirical Generalization from Reference Price Research, Marketing Science, 14(3), G161-169.
  5. Koide, T. and Sandoh, H. (2009), Reference Price Effect and Inventory Constraint on Optimal Pricing for Daily Perishable Products, Proceedings on the 2009 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Hong Kong, 370-374.
  6. Kopalle, P. K., Rao, A. G., and Assuncao, J. L. (1996), Asymmetric Reference Price Effects and Dynamic Pricing Policies, Marketing Science, 15(1), 60-85.
  7. Petruzzi, N. C. and Dada, M. (1999), Pricing and the Newsvendor Problem: A Review with Extensions, Operations Research, 47(2), 183-194.
  8. Popescu, I. and Wu, Y. (2007), Dynamic Pricing Strategies with Reference Effects, Operations Research, 55(3), 413-429.

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