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Optimal control problems for a new product with word-of-mouth

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  • Yan, Xiaoming
  • Liu, Ke

Abstract

In this paper, we consider a firm to maximize its profit by choosing a production capacity and determining the production and sales policies for a new product during the lifetime of the product. We extend Bass demand process into more general case including the negative effectiveness of word-of-mouth. Under some mild conditions, we show that the optimal sales policy is myopic, then we obtain the closed forms of the optimal production and sales policies in three cases. Furthermore, we can determine the optimal production capacity by solving several equations.

Suggested Citation

  • Yan, Xiaoming & Liu, Ke, 2009. "Optimal control problems for a new product with word-of-mouth," International Journal of Production Economics, Elsevier, vol. 119(2), pages 402-414, June.
  • Handle: RePEc:eee:proeco:v:119:y:2009:i:2:p:402-414
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    1. Gaimon, Cheryl, 1988. "Simultaneous and dynamic price, production, inventory and capacity decisions," European Journal of Operational Research, Elsevier, vol. 35(3), pages 426-441, June.
    2. Thompson, Gerald L. & Sethi, Suresh P. & Teng, Jinn-Tsair, 1984. "Strong planning and forecast horizons for a model with simultaneous price and production decisions," European Journal of Operational Research, Elsevier, vol. 16(3), pages 378-388, June.
    3. Trichy V. Krishnan & Dipak C. Jain, 2006. "Optimal Dynamic Advertising Policy for New Products," Management Science, INFORMS, vol. 52(12), pages 1957-1969, December.
    4. Hermann Simon & Karl-Heinz Sebastian, 1987. "Diffusion and Advertising: The German Telephone Campaign," Management Science, INFORMS, vol. 33(4), pages 451-466, April.
    5. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    6. Sunil Kumar & Jayashankar M. Swaminathan, 2003. "Diffusion of Innovations Under Supply Constraints," Operations Research, INFORMS, vol. 51(6), pages 866-879, December.
    7. Vlachos, Dimitrios & Tagaras, George, 2001. "An inventory system with two supply modes and capacity constraints," International Journal of Production Economics, Elsevier, vol. 72(1), pages 41-58, June.
    8. Shlomo Kalish, 1983. "Monopolist Pricing with Dynamic Demand and Production Cost," Marketing Science, INFORMS, vol. 2(2), pages 135-159.
    9. Dipak Jain & Vijay Mahajan & Eitan Muller, 1991. "Innovation Diffusion in the Presence of Supply Restrictions," Marketing Science, INFORMS, vol. 10(1), pages 83-90.
    10. Cantamessa, Marco & Valentini, Carlo, 2000. "Planning and managing manufacturing capacity when demand is subject to diffusion effects," International Journal of Production Economics, Elsevier, vol. 66(3), pages 227-240, July.
    11. Joe A. Dodson, Jr. & Eitan Muller, 1978. "Models of New Product Diffusion Through Advertising and Word-of-Mouth," Management Science, INFORMS, vol. 24(15), pages 1568-1578, November.
    12. Teck-Hua Ho & Sergei Savin & Christian Terwiesch, 2002. "Managing Demand and Sales Dynamics in New Product Diffusion Under Supply Constraint," Management Science, INFORMS, vol. 48(2), pages 187-206, February.
    13. Brander, Par & Leven, Erik & Segerstedt, Anders, 2005. "Lot sizes in a capacity constrained facility--a simulation study of stationary stochastic demand," International Journal of Production Economics, Elsevier, vol. 93(1), pages 375-386, January.
    14. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.
    15. Ishii, Hiroaki & Nose, Toyokazu, 1996. "Perishable inventory control with two types of customers and different selling prices under the warehouse capacity constraint," International Journal of Production Economics, Elsevier, vol. 44(1-2), pages 167-176, June.
    16. Ananth V. Iyer & Apurva Jain, 2004. "Modeling the Impact of Merging Capacity in Production-Inventory Systems," Management Science, INFORMS, vol. 50(8), pages 1082-1094, August.
    17. Shlomo Kalish, 1985. "A New Product Adoption Model with Price, Advertising, and Uncertainty," Management Science, INFORMS, vol. 31(12), pages 1569-1585, December.
    18. Bruce Robinson & Chet Lakhani, 1975. "Dynamic Price Models for New-Product Planning," Management Science, INFORMS, vol. 21(10), pages 1113-1122, June.
    19. Afonso, Paulo & Nunes, Manuel & Paisana, António & Braga, Ana, 2008. "The influence of time-to-market and target costing in the new product development success," International Journal of Production Economics, Elsevier, vol. 115(2), pages 559-568, October.
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