The optimal production and sales policy for a new product with negative word-of-mouth

Xiaoming Yan; Ping Cao; Minghui Zhang; Ke Liu

doi:10.3934/jimo.2011.7.117

Article Contents

2011, Volume 7, Issue 1: 117-137. Doi: 10.3934/jimo.2011.7.117

This issue Previous Article Multistage hierarchical optimization problems with multi-criterion objectives Next Article Optimal consumption and investment under irrational beliefs

The optimal production and sales policy for a new product with negative word-of-mouth

1.
School of Software, Dongguan University of Technology, Dongguan 523808, Guangdong
2.
Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190

Received: November 30, 2009

Revised: September 30, 2010

Published: December 2010

Abstract Related Papers Cited by

Abstract

In this paper, we consider a firm which maximizes its profit by determining the production and sales policies for a new product during the lifetime of the product. Because of capacity constraint, we extend Bass demand process a more general case including the negative effectiveness of word-of-mouth. We analyze the production and sales policies in two cases: strong negative word-of-mouth and weak negative word-of-mouth. In the case of strong negative word-of-mouth, we show that myopic policy is optimal under some mild conditions. In the case of weak negative word-of-mouth, we show that build-up policy is optimal in a special case of negligible holding cost and discount rate. However, for positive holding cost and discount rate, we compare myopic policy with build-up policy by numerical examples, and show that the build-up policy is no longer a robust approximation to the optimal policy.

Keywords:

Mathematics Subject Classification: 90B30; 90B60.

Citation:

Related Papers

Cited by

References

[1]	F. M. Bass, A new product growth for model consumer durables, Management Science, 15 (1969), 215-227.doi: 10.1287/mnsc.15.5.215.
[2]	F. M. Bass, T. V. Krishnan and D. C. Jain, Why the bass model fits without decision variables, Marketing Science, 13 (1984), 203-223.doi: 10.1287/mksc.13.3.203.
[3]	J. G. Blodgett, D. H. Granbois and R. G. Walters, The effects of perceived justice on complainants' negative word-of-mouth behavior and repatronage intentions, Journal of Retailing, 69 (1983), 399-428.doi: 10.1016/0022-4359(93)90015-B.
[4]	P. F. Bone, Word-of-Mouth effects on short-term and long-term product judgments, Journal of Business Research, 32 (1995), 213-223.doi: 10.1016/0148-2963(94)00047-I.
[5]	R. Cellini and L. Lambertini, Advertising in a differential oligopoly game, Journal of Optimization Theory and Applications, 116 (2003), 61-81.doi: 10.1023/A:1022158102252.
[6]	D. Charlett, R. Garland and N. Marr, How damaging is negative word of mouth? Marketing Bulletin, 6 (1995), 42-50.
[7]	G. Cheryl, Simultaneous and dynamic price, production, inventory and capacity decisions, European Journal of Operational Research, 35 (1988), 426-441.doi: 10.1016/0377-2217(88)90232-9.
[8]	C. Dellarocas, The digitization of word of mouth: promise and challenges of online feedback mechanisms, Management Science, 49 (2003), 1407-1424.doi: 10.1287/mnsc.49.10.1407.17308.
[9]	E. J. Dockner and G. E. Fruchter, Dynamic strategic pricing and speed of diffusion, Journal of Optimization Theory and Applications, 123 (2004), 331-348.doi: 10.1007/s10957-004-5152-2.
[10]	R. J. Dolan and A. P. Jeuland, Experience curves and dynamic demand models: implications for optimal pricing strategies, Journal of Marketing, 45 (1984), 52-63.doi: 10.2307/1251720.
[11]	J. A. Dodson and E. Muller, Models of new product diffusion through advertising and word-of-mouth, Management Science, 24 (1978), 1568-1578.doi: 10.1287/mnsc.24.15.1568.
[12]	R. Easta, K. Hammondb and W. Lomax, Measuring the impact of positive and negative word of mouth on brand purchase probability, International Journal of Research in Marketing, 25 (2008), 215-24.doi: 10.1016/j.ijresmar.2008.04.001.
[13]	R. Easta, K. Hammondb and M. Wright, The relative incidence of positive and negative word of mouth: A multi-category study, International Journal of Research in Marketing, 24 (2007), 175-184.doi: 10.1016/j.ijresmar.2006.12.004.
[14]	Z. Griliches, Hybrid corn: an exploration in the economics of technoligical change, Econometrica, 25 (1957), 501-522.doi: 10.2307/1905380.
[15]	R. F. Hartl, A. J. Novak and S. P. Sethi, Optimal pricing of a product diffusing in rich and poor populations, Journal of Optimization Theory and Applications, 117 (2003), 349-375.doi: 10.1023/A:1023635807884.
[16]	X. He and S. P. Sethi, Dynamic slotting and pricing decisions in a durable product supply chain, Journal of Optimization Theory and Applications, 137 (2008), 363-379.doi: 10.1007/s10957-007-9330-x.
[17]	D. Heyman and M. J. Sobel, "Stochastic Models in Operations Research Volume II: Stochastic Optimization," 1st edition, McGraw-Hill Book Company, New York, 1984.
[18]	T. Ho, S. Savin and C. Terwiesch, Managing demand and sale dynamics in new product diffusion under supply constraint, Management Science, 48 (2002), 187-206.doi: 10.1287/mnsc.48.2.187.257.
[19]	D. Jain, V. Mahajan and E. Muller, Innovation diffusion in the presence of supply restrictions, Marketing Science, 10 (1991), 83-90.doi: 10.1287/mksc.10.1.83.
[20]	S. JØrgensen, S. Taboubi and G. Zaccour, Cooperative advertising in a marketing channel, Journal of Optimization Theory and Applications, 110 (2001), 145-158.doi: 10.1023/A:1017547630113.
[21]	S. Kalish, Monopolist pricing with dynamic demand and production cost, Marketing Science, 2 (1983), 135-159.doi: 10.1287/mksc.2.2.135.
[22]	S. Kalish, A new product adoption model with price, advertising and uncertainty, Management Science, 31 (1985), 1569-1585.doi: 10.1287/mnsc.31.12.1569.
[23]	T. V. Krishnan, F. M. Bass and D. C. Jain, Optimal pricing strategy for new products, Management Science, 45 (1999), 1650-1663.doi: 10.1287/mnsc.45.12.1650.
[24]	T. V. Krishnan and D. C. Jain, Optimal dynamic advertising policy for new products, Management Science, 52 (2006), 1957-1969.doi: 10.1287/mnsc.1060.0585.
[25]	S. Kumar and J. M. Swaminathan, Diffusion of innovations under supply constraints, Operations Research, 51 (2003), 866-879.doi: 10.1287/opre.51.6.866.24918.
[26]	S. Kumar and S. P. Sethi, Dynamic pricing and advertising for web content providers, European Journal of Operational Research, 197 (2009), 924-944.doi: 10.1016/j.ejor.2007.12.038.
[27]	R. N. Laczniak, T. E. DeCarlo and S. N. Ramaswami, Consumers' responses to negative word-of-mouth communication: An attribution theory perspective, Journal of Consumer Psychology, 11 (2001), 57-73.doi: 10.1207/S15327663JCP1101_5.
[28]	G. T. Lau and S. Ng, Individual and situational factors influencing negative word-of-mouth behaviour, Canadian Journal of Administrative Sciences, 18 (2009), 163-178.doi: 10.1111/j.1936-4490.2001.tb00253.x.
[29]	X. Luo, Quantifying the long-term impact of negative word of mouth on cash flows and stock prices, Marketing Science, 28 (2009), 148-165.doi: 10.1287/mksc.1080.0389.
[30]	E. Mansfield, Technical change and the rate of imitation, Econometrica, 29 (1961), 741-766.doi: 10.2307/1911817.
[31]	V. Mahajan, E. Muller and F. M. Bass, New product diffusion models in marketing: A review and directions for research, Journal of Marketing Research, 54 (1990), 1-26.
[32]	V. Mahajan, E. Muller and R. A. Kerin, Introduction strategy for new products with positive and negative word-of-mouth, Management Science, 30 (1984), 1389-1404.doi: 10.1287/mnsc.30.12.1389.
[33]	V. Mahajan, E. Muller and Y. Wind, "New-Product Diffusion Models," 1st edition, Kluwer Academic Publisher, Boston, MA, 2000.
[34]	H. I. Mesak and J. W. Clark, Monopolist optimum pricing and advertising policies for diffusion models of new product innovations, Optimal Control Applications and Methods, 19 (1998), 111-136.doi: 10.1002/(SICI)1099-1514(199803/04)19:2<111::AID-OCA622>3.0.CO;2-M.
[35]	M. L. Richins, Negative word-of-mouth by dissatisfied consumers: a pilot study, Journal of Marketing, 47 (1983), 68-78.doi: 10.2307/3203428.
[36]	B. Robinson and C. Lakhani, Dynamic price models for new product planning, Management Science, 21 (1975), 1113-1122.doi: 10.1287/mnsc.21.10.1113.
[37]	S. P. Sethi and G. L. Thompson, "Optimal Control Theory," 2nd edition, Kluwer Academic Publisher, Boston, MA, 2000.
[38]	H. Simon and K. H. Sebastian, Diffusion and advertising: the german telephone campaign, Management Science, 33 (1987), 451-466.doi: 10.1287/mnsc.33.4.451.
[39]	J. Singh, Voice, exit, and negative word-of-mouth behaviors: An investigation across three service categories, Journal of the Academy of Marketing Science, 18 (1990), 1-15.doi: 10.1007/BF02729758.
[40]	G. L. Thomposon, S. P. Sethi and J-T. Teng, Strong planning and forecast horizons for a model with simultaneous price and production decisions, European Journal of Operational Research, 16 (1984), 378-388.doi: 10.1016/0377-2217(84)90292-3.
[41]	F. V. Wangenheim, Postswitching negative word of mouth, Journal of Service Research, 8 (2005), 67-78.doi: 10.1177/1094670505276684.
[42]	I. M. Wetzer, M. Zeelenberg and R. Pieters, Never eat in that restaurant, i did!: exploring why people engage in negative word-of-mouth communication, Psychology and Marketing, 24 (2007), 661-680.doi: 10.1002/mar.20178.
[43]	X. Yan and K. Liu, Optimal control problems for a new product with word-of-mouth, International Journal of Production Economics, 119 (2009), 402-414.doi: 10.1016/j.ijpe.2009.03.011.