# American Institute of Mathematical Sciences

January  2011, 7(1): 117-137. doi: 10.3934/jimo.2011.7.117

## 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, China 2 Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China, China, China

Received  December 2009 Revised  October 2010 Published  January 2011

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.
Citation: Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial & Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117
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