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

Abstract

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.

Keywords

Pricing / newsvendor problem / advertising carryover effect / perishable product

References

[1] Albright S.C., Winston W.. Markov models of advertising and pricing decisions. Operations Research, 1979, 27(4): 668-681.

[2] Bakker M., Riezebos J., Teunter R.H.. Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 2012, 221(2): 275-284.

[3] Balcer Y.. Optimal advertising and inventory control of perishable goods. Naval Research Logistics Quarterly, 1983, 30(4): 609-625.

[4] Bertsekas D.P.. Dynamic programming and optimal control, 2007.

[5] Blackburn J., Scudder G.. Supply chain strategies for perishable products: the case of fresh produce. Production and Operations Management, 2009, 18(2): 129-137.

[6] Cai X., Chen J., Xiao Y., Xu X.. Optimization and coordination of fresh product supply chains with freshness- keeping effort. Production and Operations Management, 2010, 19(3): 261-278.

[7] Chen X., Pang Z., Pan L.. Coordinating inventory control and pricing strategies for perishable products. Operations Research, 2014, 62(2): 284-300.

[8] Clarke G.D.. Econometric measurement of the duration of advertising effect on sales. Journal of Marketing Research, 1976, 13(4): 345-357.

[9] Danaher P.J.. Advertising models. Handbook of Marketing Decision Models, International Series in Operations Research & Management Science, 2008, 121: 81-106.

[10] Esmaeili M.. Optimal selling price, marketing expenditure and lot size under general demand function. The International Journal of Advanced Manufacturing Technology, 2009, 45(1–2): 191-198.

[11] Federgruen A., Heching A.. Combined pricing and inventory control under uncertainty. Operations Research, 1999, 47(3): 454-475.

[12] Fisher M.L.. What is the right supply chain for your product. Harvard Business Review, 1997, 75: 105-117.

[13] Goyal S.K., Giri B.C.. Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 2001, 134(1): 1-16.

[14] Hanssens D., Parsons L., Schultz R.. Market Response Models: Econometric and Time Series Analysis, Second Edition, Kluwer Academic Publishers, Chapter 9, 2001

[15] Heien D.. Markup pricing in a dynamic model of the food industry. American Journal of Agricultural Economics, 1980, 62: 10-18.

[16] Johansson J.K.. Advertising and the S-curve: A new approach. Journal of Marketing Research, 1979, 16: 346-354.

[17] Jørgensen S., Zaccour G.. Differential Games in Marketing, Kluwer Academic Publishers, Chapter 6, 2004.

[18] Kazaz B.. Production planning under yield and demand uncertainty with yield- dependent cost and price. Manufacturing & Service Operations Management, 2004, 6(3): 209-224.

[19] Kazaz B., Webster S.. The impact of yield-dependent trading costs on pricing and production planning under supply uncertainty. Manufacturing & Service Operations Management, 2011, 13(3): 404-417.

[20] Lee W.J., Kim D.. Optimal and heuristic decision strategies for integrated production and marketing planning. Decision Sciences, 1993, 24(6): 1203-1214.

[21] Li C., Sexton R.J.. Grocery-retailer pricing behavior with implications for farmer welfare. Journal of Agricultural and Resource Economics, 2013, 38(2): 141-158.

[22] Li Y., Cheang B., Lim A.. Grocery perishables management. Production and Operations Management, 2012, 21(3): 504-517.

[23] Little J.D.C.. BRANDAID: A marketing-mix model, Part 1: Structure. Operations Research, 1975, 23(4): 628-655.

[24] Little J.D.C.. Aggregate advertising models: the state of the art. Operations Research, 1979, 27(4): 629-667.

[25] Milgrom P., Segal I.. Envelope theorems for arbitrary choice sets. Econometrica, 2002, 70(2): 583-601.

[26] Nerlove M., Arrow K.J.. Optimal advertising policy under dynamic conditions. Economica, 1962, 29(114): 129-142.

[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.

[28] Palda K.S.. The measurement of cumulative advertising effects. The Journal of Business, 1965, 38(2): 162-179.

[29] Pang Z.. Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operations Research Letters, 2011, 39(5): 375-379.

[30] Petruzzi N. C., Dada M.. Pricing and the newsvendor problem: a review with extensions. Operations Research, 1999, 47(2): 183-194.

[31] Popescu I., Wu Y.. Dynamic pricing strategies with reference effects. Operations Research, 2007, 55(3): 413-429.

[32] Rao A.R., Monroe K.B.. The effect of price, brand name and store name on buyers’ perceptions of product quality: an integrative review. Journal of Marketing Research, 1989, 26(3): 351-357.

[33] Sainathan A.. Pricing and replenishment of competing perishable product variants under dynamic demand substitution. Production and Operations Management, 2013, 22(5): 1157-1181.

[34] Topkis D.M.. Supermodularity and Complementarity, 1998

[35] Tull D.S., Wood V.R., Duhan D., Gillpatrick T., Robertson K.R., Helgeson J.G.. “Leveraged” decision making in advertising: The flat maximum principle. Journal of Marketing Research, 1986, 23(1): 25-32.

[36] Urban T.L.. Deterministic inventory models incorporating marketing decisions. Computers & Industrial Engineering, 1992, 22(1): 85-93.

[37] Vidale M.L., Wolfe H.B.. An operations-research study of sales response to advertising. Operations Research, 1957, 5(3): 370-381.

[38] Wohlgenant M.K.. Marketing margins: Empirical analysis, Handbook of Agricultural Economics, 2001, 16: 933-970.

[39] Wohlgenant M.K., Mullen J.D.. Modeling the farm-retail price spread for beef. Western Journal of Agricultural Economics, 1987, 12(2): 119-125.

[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.