Coordinating Pricing, Ordering and Advertising for Perishable Products Over an Infinite Horizon

  • Ye Lu
  • Minghui Xu
  • Yimin Yu


Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions? To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infinite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies (advertising, pricing, inventory level) globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.


Pricing newsvendor problem advertising carryover effect perishable product 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to thank the associate editor for his patience and effort in handling this paper and the anonymous referees for their help to greatly improve the quality of the paper.

This research is supported by a grant from National Science Foundation of China (No. 71371146), and a research fund for Academic Team of Young Scholars at Wuhan University (No. Whu2016013).


  1. [1]
    Albright, S.C. & Winston, W. (1979). Markov models of advertising and pricing decisions. Operations Research, 27(4): 668–681.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Bakker, M., Riezebos, J. & Teunter, R.H. (2012). Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221(2): 275–284.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Balcer, Y. (1983). Optimal advertising and inventory control of perishable goods. Naval Research Logistics Quarterly, 30(4): 609–625.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Bertsekas, D.P. (2007). Dynamic programming and optimal control. Vol.2, Athena Scientific, Belmont, Massachusetts.MATHGoogle Scholar
  5. [5]
    Blackburn, J. & Scudder, G. (2009). Supply chain strategies for perishable products: the case of fresh produce. Production and Operations Management, 18(2): 129–137.CrossRefGoogle Scholar
  6. [6]
    Cai, X., Chen, J., Xiao, Y. & Xu, X. (2010). Optimization and coordination of fresh product supply chains with freshness- keeping effort. Production and Operations Management, 19(3): 261–278.CrossRefGoogle Scholar
  7. [7]
    Chen, X., Pang, Z. & Pan, L. (2014). Coordinating inventory control and pricing strategies for perishable products. Operations Research, 62(2): 284–300.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Clarke, G.D. (1976). Econometric measurement of the duration of advertising effect on sales. Journal of Marketing Research, 13(4): 345–357.CrossRefGoogle Scholar
  9. [9]
    Danaher, P.J. (2008). Advertising models. Handbook of Marketing Decision Models, International Series in Operations Research & Management Science, 2008, Vol.121, Part III, 81–106.CrossRefGoogle Scholar
  10. [10]
    Esmaeili, M. (2009). Optimal selling price, marketing expenditure and lot size under general demand function. The International Journal of Advanced Manufacturing Technology, 45(1–2): 191–198.CrossRefGoogle Scholar
  11. [11]
    Federgruen, A. & Heching, A. (1999). Combined pricing and inventory control under uncertainty. Operations Research, 47 (3): 454–475.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Fisher, M.L. (1997). What is the right supply chain for your product? Harvard Business Review, 75: 105–117.Google Scholar
  13. [13]
    Goyal, S.K. & Giri, B.C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134(1):1–16.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Hanssens, D., Parsons, L. & Schultz, R. (2001). Market Response Models: Econometric and Time Series Analysis, Second Edition, Kluwer Academic Publishers, Chapter 9.Google Scholar
  15. [15]
    Heien, D. (1980). Markup pricing in a dynamic model of the food industry. American Journal of Agricultural Economics, 62: 10–18.CrossRefGoogle Scholar
  16. [16]
    Johansson, J.K. (1979). Advertising and the S-curve: A new approach. Journal of Marketing Research, 16: 346–354.CrossRefGoogle Scholar
  17. [17]
    Jørgensen, S. & Zaccour, G. (2004). Differential Games in Marketing, Kluwer Academic Publishers, Chapter 6.CrossRefGoogle Scholar
  18. [18]
    Kazaz, B. (2004). Production planning under yield and demand uncertainty with yield- dependent cost and price. Manufacturing & Service Operations Management, 6(3): 209–224.CrossRefGoogle Scholar
  19. [19]
    Kazaz, B. & Webster, S. (2011). The impact of yield-dependent trading costs on pricing and production planning under supply uncertainty. Manufacturing & Service Operations Management, 13(3): 404–417.CrossRefGoogle Scholar
  20. [20]
    Lee, W.J. & Kim, D. (1993). Optimal and heuristic decision strategies for integrated production and marketing planning. Decision Sciences, 24(6): 1203–1214.CrossRefGoogle Scholar
  21. [21]
    Li, C & Sexton, R.J. (2013). Grocery-retailer pricing behavior with implications for farmer welfare. Journal of Agricultural and Resource Economics, 38(2): 141–158.Google Scholar
  22. [22]
    Li, Y., Cheang, B. & Lim, A. (2012). Grocery perishables management. Production and Operations Management, 21(3): 504–517.CrossRefGoogle Scholar
  23. [23]
    Little, J.D.C. (1975). BRANDAID: A marketing-mix model, Part 1: Structure. Operations Research, 23(4): 628–655.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Little, J.D.C. (1979). Aggregate advertising models: the state of the art. Operations Research, 27(4): 629–667.CrossRefMATHGoogle Scholar
  25. [25]
    Milgrom, P. & Segal, I. (2002). Envelope theorems for arbitrary choice sets. Econometrica, 70(2): 583–601.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    Nerlove, M. & Arrow, K.J. (1962). Optimal advertising policy under dynamic conditions. Economica, 29(114): 129–142.CrossRefGoogle Scholar
  27. [27]
    Netessine, S. & Rudi, N. (2004). Supply chain structures on the internet and the role of marketing-operations interaction. Simchi-Levi, D., S. D. Wu & M. Shen (eds.), Handbook of Quantitative Supply Chain Analysis: Modeling in the E-business Era, Kluwer, 607–641.Google Scholar
  28. [28]
    Palda, K.S. (1965). The measurement of cumulative advertising effects. The Journal of Business, 38(2): 162–179.CrossRefGoogle Scholar
  29. [29]
    Pang, Z. (2011). Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operations Research Letters, 39(5): 375–379.MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    Petruzzi, N. C. & Dada, M. (1999). Pricing and the newsvendor problem: a review with extensions. Operations Research, 47(2): 183–194.CrossRefMATHGoogle Scholar
  31. [31]
    Popescu, I. & Wu, Y. (2007). Dynamic pricing strategies with reference effects. Operations Research, 55(3): 413–429.MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    Rao, A.R., & Monroe, K.B. (1989). The effect of price, brand name and store name on buyers’ perceptions of product quality: an integrative review. Journal of Marketing Research, 26(3): 351–357.CrossRefGoogle Scholar
  33. [33]
    Sainathan, A. (2013). Pricing and replenishment of competing perishable product variants under dynamic demand substitution. Production and Operations Management, 22(5): 1157–1181.Google Scholar
  34. [34]
    Topkis, D.M. (1998). Supermodularity and Complementarity. Princeton University Press, Princeton, NJ.Google Scholar
  35. [35]
    Tull, D.S., Wood, V.R., Duhan, D., Gillpatrick, T., Robertson, K.R. & Helgeson, J.G. (1986). “Leveraged” decision making in advertising: The flat maximum principle. Journal of Marketing Research, 23(1): 25–32.CrossRefGoogle Scholar
  36. [36]
    Urban, T.L. (1992). Deterministic inventory models incorporating marketing decisions. Computers & Industrial Engineering, 22(1): 85–93.CrossRefGoogle Scholar
  37. [37]
    Vidale, M.L. & Wolfe, H.B. (1957). An operations-research study of sales response to advertising. Operations Research, 5(3): 370–381.MathSciNetCrossRefGoogle Scholar
  38. [38]
    Wohlgenant, M.K. (2001). Marketing margins: Empirical analysis, Handbook of Agricultural Economics, Volume 1, Part B, Chapter 16: 933–970.Google Scholar
  39. [39]
    Wohlgenant, M.K. & Mullen, J.D. (1987). Modeling the farm-retail price spread for beef. Western Journal of Agricultural Economics, 12(2): 119–125.Google Scholar
  40. [40]
    Yano, C.A. & Gilbert, S.M. (2003). Coordinated pricing and production/procurement decisions: A review. Chakravarty, A., J. Eliashberg eds. ManagingBusiness Interfaces: Marketing, Engineering and Manufacturing Perspectives, Kluwer Academic Publishers, Boston.Google Scholar

Copyright information

© Systems Engineering Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Management SciencesCity University of Hong KongKowloon, Hong KongChina
  2. 2.School of Economics and ManagementWuhan UniversityWuhanChina

Personalised recommendations