Dynamic Advertising-based Goodwill Incorporating Fuzzy Environment in Segment-Specific Market-Reference-Cited by-同舟云学术

Dynamic Advertising-based Goodwill Incorporating Fuzzy Environment in Segment-Specific Market

Published:2023-08-01 Issue:4 Volume:8 Page:688-709
ISSN:2455-7749
Container-title:International Journal of Mathematical, Engineering and Management Sciences
language:en
Short-container-title:Int. j. math. eng. manag. sci.

Author:

Kumar Pradeep¹,Chaudhary Kuldeep¹,Kumar Vijay¹,Singh V. B.²

Affiliation:

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

2. School of Computer and System Sciences, Jawaharlal Nehru University, Delhi, India.

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.

Publisher

Ram Arti Publishers

Subject

General Engineering,General Business, Management and Accounting,General Mathematics,General Computer Science

Reference49 articles.

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