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An optimal dynamic advertising model with inverse inventory sensitive demand effect for deteriorating items

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Abstract

This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin’s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.

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Acknowledgements

The authors would like to express their appreciation to the referees for their careful reading of the original paper and valuable comments, and thank for their helpful suggestions that substantially improved the quality of this work.

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Authors and Affiliations

  1. School of Management, Jinan University, Guangzhou, 510632, China

    Minghui Xu & Xiaode Zuo

Authors
  1. Minghui Xu
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  2. Xiaode Zuo
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Correspondence to Xiaode Zuo.

Additional information

Minghui Xu is a Ph.D. candidate at Management School of Jinan University in China. He received his B.S. degree from Wuhan Polytechnic University in 2011 and M.S. degree from Guangxi University of Technology in 2014. His research interests include supply chain management, pricing and revenue management, and inventory control.

Xiaode Zuo is currently a professor at Management School of Jinan University in China. He received the B.S. degree, M.S. degree and Ph.D. degree, in 1989, 1992 and 1995, respectively, all from Tianjin University in China. His research interests lie in systems optimization and management decision, e.g., production planning optimization, logistics, inventory management and project management. He has published several research papers in the journals like Journal of Systems Engineering and Electronics, Journal of Systems Science and Information, Journal of Intelligent Information Management Systems and Technologies, Systems Engineering - Theory & Practice, Journal of Industrial Engineering and Engineering Management, etc.

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Xu, M., Zuo, X. An optimal dynamic advertising model with inverse inventory sensitive demand effect for deteriorating items. J. Syst. Sci. Syst. Eng. 26, 593–608 (2017). https://doi.org/10.1007/s11518-016-5316-2

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  • DOI: https://doi.org/10.1007/s11518-016-5316-2

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