Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 139030, 10 pages.

Product Demand Forecasting and Dynamic Pricing considering Consumers’ Mental Accounting and Peak-End Reference Effects

Wenjie Bi and Mengqi Liu

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We introduce a demand forecasting model for a monopolistic company selling products to consumers with double-entry mental accounting, which means consumers experience pleasure when consuming goods or service and feel pains when paying for them. Moreover, as the monopolist changes prices, consumers form a reference price that adjusts an anchoring standard based on the lowest price that they perceived, namely, the peak-end anchoring. We obtain the steady state prices under three different payment schemes for two- and infinite-period. We also analyze the relationship between these steady prices and maximal profit and compare the steady state prices of different payment schemes by changing the double-entry mental accounting’s parameters through numerical examples. The proposed model is computationally tractable for demand forecasting of realistic size.

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J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 139030, 10 pages.

First available in Project Euclid: 27 February 2015

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Bi, Wenjie; Liu, Mengqi. Product Demand Forecasting and Dynamic Pricing considering Consumers’ Mental Accounting and Peak-End Reference Effects. J. Appl. Math. 2014, Special Issue (2014), Article ID 139030, 10 pages. doi:10.1155/2014/139030.

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  • N. Mahbub, S. K. Paul, and A. Azeem, “A neural approach to product demand forecasting,” International Journal of Industrial and Systems Engineering, vol. 15, no. 1, pp. 1–18, 2013.
  • L. Wang, C. X. Dun, W. J. Bi, and Y. R. Zeng, “An effective and efficient differential evolution algorithm for the integrated stochastic joint replenishment and delivery model,” Knowledge-Based Systems, vol. 36, pp. 104–114, 2012.
  • J. Huang, M. Leng, and M. Parlar, “Demand functions in decision modeling: a comprehensive survey and research directions,” Decision Sciences, vol. 44, no. 3, pp. 557–609, 2013.
  • W. Bi, L. Tian, H. Liu, and X. Chen, “A stochastic dynamic programming approach based on bounded rationality and application to dynamic portfolio choice,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 840725, 11 pages, 2014.
  • W. Bi, Y. Sun, H. Liu, and X. Chen, “Dynamic nonlinear pricing model based on adaptive and sophisticated learning,” Mathematical Problems in Engineering, vol. 2014, Article ID 791656, 11 pages, 2014.
  • R. H. Thaler, “Mental accounting matters,” Journal of Behavioral Decision Making, vol. 12, no. 3, pp. 183–206, 1999.
  • M. Baucells and W. Hwang, “A Model of Mental Accounting and Reference Price Adaptation,” 2013,
  • R. H. Thaler, “Mental accounting and consumer choice,” Marketing Science, vol. 4, no. 3, pp. 199–214, 1985.
  • D. Prelec and G. Loewenstein, “The red and the black: mental accounting of savings and debt,” Marketing Science, vol. 17, no. 1, pp. 4–28, 1998.
  • N. Barberis and M. Huang, “Mental accounting, loss aversion, and individual stock returns,” The Journal of Finance, vol. 56, no. 4, pp. 1247–1292, 2001.
  • T. Langer and M. Weber, “Prospect theory, mental accounting, and differences in aggregated and segregated evaluation of lottery portfolios,” Management Science, vol. 47, no. 5, pp. 716–733, 2001.
  • S. Frederick, G. Loewenstein, and T. O'Donoghue, “Time discounting and time preference: a critical review,” Journal of Economic Literature, vol. 40, no. 2, pp. 351–401, 2002.
  • M. Grinblatt and B. Han, “Prospect theory, mental accounting, and momentum,” Journal of Financial Economics, vol. 78, no. 2, pp. 311–339, 2005.
  • Y. Liu, C. Ding, C. Fan, and X. Chen, “Pricing decision under DUAl-channel structure considering fairness and FREe-riding behavior,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 536576, 10 pages, 2014.
  • E. Shafir and R. H. Thaler, “Invest now, drink later, spend never: on the mental accounting of delayed consumption,” Journal of Economic Psychology, vol. 27, no. 5, pp. 694–712, 2006.
  • U. Simonsohn and F. Gino, “Daily horizons: evidence of narrow bracketing in judgment from 10 years of MBA admissions interviews,” Psychological Science, vol. 24, no. 2, pp. 219–224, 2013.
  • S. Erat and S. R. Bhaskaran, “Consumer mental accounts and implications to selling base products and add-ons,” Marketing Science, vol. 31, no. 5, pp. 801–818, 2012.
  • L. Chen, A. G. Kök, and J. D. Tong, “The effect of payment schemes on inventory decisions: the role of mental accounting,” Management Science, vol. 59, no. 2, pp. 436–451, 2013.
  • M. Liu, W. Bi, X. Chen, and G. Li, “Dynamic pricing of fashion-like multiproducts with customers' reference effect and limited memory,” Mathematical Problems in Engineering, vol. 2014, Article ID 157865, 10 pages, 2014.
  • I. Popescu and Y. Wu, “Dynamic pricing strategies with reference effects,” Operations Research, vol. 55, no. 3, pp. 413–429, 2007.
  • R. S. Winer, “A reference price model of brand choice for frequently purchased products,” Journal of Consumer Research, vol. 13, no. 2, pp. 250–256, 1986.
  • E. A. Greenleaf, “The impact of reference price effects on the profitability of price promotions,” Marketing Science, vol. 14, no. 1, pp. 82–104, 1995.
  • J. Nasiry and I. Popescu, “Dynamic pricing with loss-averse consumers and peak-end anchoring,” Operations Research, vol. 59, no. 6, pp. 1361–1368, 2011. \endinput