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

Pradeep Kumar, Kuldeep Chaudhary, Vijay Kumar, Vijay Singh
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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.
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细分市场中基于模糊环境的动态广告商誉
一种新产品推向市场在很大程度上受到有效和足够的广告的影响。在本文中,我们考虑了一个问题,即公司将市场划分为不同的细分市场,以降低与广告相关的成本,并实现总利润的最大化。通过将单一渠道和差异化广告整合到细分市场,我们扩展了Nerlove商誉Arrow的动态模型,其中广告变量是控制变量。为了创建一个现实的模型,假设整个可用预算在本质上是不精确和模糊的。利用必要性和可能性约束,将具有模糊参数的最优控制模型转化为清晰的形式,然后使用庞特里亚金最大值原理来求解该问题。数值算例支持了理论分析。
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来源期刊
CiteScore
3.80
自引率
6.20%
发文量
57
审稿时长
20 weeks
期刊介绍: IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.
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