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Advertising for the introduction of an age‐sensitive product
Author(s) -
Grosset Luca,
Viscolani Bruno
Publication year - 2005
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.758
Subject(s) - goodwill , product (mathematics) , computer science , order (exchange) , set (abstract data type) , channel (broadcasting) , mathematical optimization , process (computing) , advertising , mathematical economics , mathematics , economics , business , telecommunications , geometry , finance , programming language , operating system
An age‐dependent market segmentation is often observed for real life products. We introduce a simple age‐structured model for the advertising process of a firm and the consequent goodwill evolution. The model formal structure is characterized by a first order linear partial differential equation. We formulate the advertising problem for a new product introduction as a distributed parameter optimal control problem and solve it using the suitable maximum principle conditions. Then, we discuss and solve the same problem under the assumption that a finite set of boundedly age‐selective advertising channels are available, instead of one infinitely age‐selective channel. Copyright © 2005 John Wiley & Sons, Ltd.