Pradeep Kumar
Department of Mathematics, AIAS, Amity University, Noida, U.P., India.

Kuldeep Chaudhary
Department of Mathematics, AIAS, Amity University, Noida, U.P., India.

Vijay Kumar
Department of Mathematics, AIAS, Amity University, Noida, U.P., India.

V. B. Singh
School of Computer and System Sciences, Jawaharlal Nehru University, Delhi, India.

DOI https://doi.org/10.33889/IJMEMS.2022.7.4.035

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Abstract

This paper suggests an optimal control formulation of a diffusion model to determine the optimal advertising and pricing policy for a new product in segmented market involving price dependent market potential where total potential market is a decreasing function of price. We assume that sales rate is proportional to the number of adopters and evolved under the joint effect of a single advertising channel and segment specific advertising process that affect sales rate in unsaturated market. Single channel advertising with a fixed spectrum is available for each segment in whole market while segment specific advertising process can reach each target segment individually. The optimal dynamic price and advertising policies are obtained by applying Pontryagin’s maximum principle. Finally, numerical examples of two cases for a discrete version of the proposed control problem are provided to illustrate the efficacy of the proposed method

Keywords- Optimal control theory, Segmented market, Price-dependent potential market, Advertising and price policy.

Citation

Kumar, P., Chaudhary, K., Kumar, V., & Singh, V. B. (2022). Advertising and Pricing Policies for a Diffusion Model Incorporating Price Sensitive Potential Market in Segment Specific Environment. International Journal of Mathematical, Engineering and Management Sciences, 7(4), 547-557. https://doi.org/10.33889/IJMEMS.2022.7.4.035.