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.2023.8.4.040

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Abstract

A new product's introduction to the market is greatly influenced by effective and enough advertising. In this paper, we have considered a problem in which the firm partitions the market into various segments to reduce costs associated with advertising and targets to maximize the total profit. By integrating single channel and differentiated advertising to segmented market, we extend Nerlove-goodwill Arrow's dynamic model in which advertising variables are control variables. It is assumed that the whole available budget is imprecise and fuzzy in nature in order to create a realistic model. Using necessity and possibility constraints, the optimal control model with fuzzy parameters is transformed into crisp form, and the Pontryagin Maximum principle is then used to solve the problem. Numerical examples are provided to support the theoretical analysis.

Keywords- Fuzzy parameter, Goodwill, Budget constraint, Maximum principle, Optimal control problem.

Citation

Kumar, P., Chaudhary, K., Kumar, V., & Singh, V. B. (2023). Dynamic Advertising-based Goodwill Incorporating Fuzzy Environment in Segment-Specific Market. International Journal of Mathematical, Engineering and Management Sciences, 8(4), 688-709. https://doi.org/10.33889/IJMEMS.2023.8.4.040.