Advertising and Pricing Policies for a Diffusion Model Incorporating Price Sensitive Potential Market in Segment Specific Environment-Reference-Cited by-同舟云学术

Advertising and Pricing Policies for a Diffusion Model Incorporating Price Sensitive Potential Market in Segment Specific Environment

Published:2022-07-17 Issue:4 Volume:7 Page:547-557
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

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

Publisher

Ram Arti Publishers

Subject

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

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