Advertising for the introduction of an age‐sensitive product

Abstract

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

Arrow-type sufficient conditions for optimality of age-structured control problems

“…From this and from the conditions for local maximum and transversality, (16), (17), (19) and (20), it follows that ∆ ≥ 0.…”

“…Age-structured optimal control theory serves to study problems arising in different areas such as epidemiology [1], harvesting [2,3], investment in capital goods [4,12,13], investment in human capital [22], and marketing [11,16]. Solutions of these problems are often obtained by applying necessary optimality conditions of Pontryagin type.…”

Optimal double control problem for a PDE model of goodwill dynamics

“…We assume similarly to Grosset and Viscolani (2005) that the instantaneous costs of defensive and offensive marketing instruments are given by…”

“…In goodwill models with segmented market it is often assumed that the firm sells one product in infinitely many segments, indicated by the age of the customers a, and the demand in segment a and time t depends on the level G(t, a) of goodwill for this product. This assumption results in the representation of the goodwill dynamics by a first-order hyperbolic partial differential equation, see Grosset and Viscolani (2005) and Faggian and Grosset (2013). The same state equation but with a different interpretation is proposed by Barucci and Gozzi (1999).…”

The influence of consumer recommendations on advertising strategies in a non-linear optimal goodwill model with market segmentation

“…Buratto et al have considered a dynamic goodwill model with a finite number of market segments, which are distinguished by the age of the consumers [Buratto et al 2006]. Grosset and Viscolani have expanded the classical model to markets with infinitely many market segments [Grosset, Viscolani 2005]. They assumed that the level of goodwill in the initial segment is equal to 0.…”