Alessandra Buratto

Advertising a new product in a segmented market

Abstract We bring some market segmentation concepts into the statement of the “new product introduction” problem with Nerlove-Arrow’s linear goodwill dynamics. In fact, only a few papers on dynamic quantitative advertising models deal with market segmentation, although this is a fundamental topic of marketing theory and practice. In this way we obtain some new deterministic optimal control problems solutions and show how such marketing concepts as “targeting” and “segmenting” may find a mathematical representation. We consider two kinds of situations. In the first one, we assume that the advertising process can reach selectively each target group. In the second one, we assume that one advertising channel is available and that it has an effectiveness segment-spectrum, which is distributed over a non-trivial set of segments. We obtain the explicit optimal solutions of the relevant problems.

New product introduction: goodwill, time and advertising cost

Abstract. The advertising activity has an important role in the introduction of a new product. We tackle the problem of determining the advertising plan for preparing the product introduction, having the objectives of maximizing the product image at the launch time, minimizing the campaign length and minimizing the total advertising expenditure, within a fixed time interval. After formulating the new product introduction optimal control problem, we study and solve two special cases of it, namely the minimum time and the advertising cost problems. From the former we derive the existence of an optimal solution of the original problem, whereas we obtain its structure from the latter. Finally we present two alternative formulations of the original problem in the non-linear programming framework and suggest using them to solve the bounded time problem.

Advertising channel selection in a segmented market

We consider a market with a finite number of segments and assume that several advertising channels are available, with different diffusion spectra and efficiencies. The problem of the choice of an advertising channel to direct the pre-launch campaign for a new product is analyzed in two steps. First, an optimal control problem is solved explicitly in order to determine the optimal advertising policy for each channel. Then a maximum profit channel is chosen. In a simulation example we consider the choice of a newspaper among six available and analyze the relations among the firm target market and the advertising channels environment which induce the optimal decision.

An optimal control student problem and a marketing counterpart

We tackle the problem of an economous and ambitious student with variable and bounded final time. We answer the questions of existence and uniqueness of the optimal solution positively and obtain that solution explicitly. Furthermore, we suggest a marketing interpretation of a slightly modified problem: determining an optimal advertising policy for a new product.

A communication mix for an event planning: a linear quadratic approach

The communication mix is a relevant decision issue for an organization that plans the advertising campaign for a fixed future event. It is assumed that the objectives of the organization are to minimize the cost of the advertising campaign and to drive the final demand as close as possible to a target value. Two different advertising channels are available: the first affects deterministically the consumers’ demand, whereas the second presents some stochastic aspects which are out of decision-maker’s control. Some recent mathematical developments on the stochastic linear quadratic control problem allow to formulate and solve some interesting instances of the problem. A comparative analysis of the efficiency of deterministic and stochastic controls is done and the optimal feedback policies are discussed. The trade-off between efficiency and risk of an advertising channel is essential to understand the features of the optimal solutions.

Advertising and Price to Sustain The Brand Value in a Licensing Contract

One of the reasons that induce a brand owner to issue a licensing contract is that of improving the value of his brand. In this paper, we look at a fashion licensing agreement where the licensee produces and sells a product in a complementary business. The value of a fashion brand is sustained by both the advertising efforts of the licensor and the licensee. We assume that demand is proportional to the brand value and decreases with the price. The licensor wants to maximize his revenue coming from the royalties and to minimize his advertising costs. Moreover, he does not want his brand to be devalued at the end of the selling season. On the other hand, the licensee plans her advertising campaign in order to invest in the brand value and maximize the sales revenue. The aim of this paper is to analyze the different strategies the licensor can adopt to sustain his brand. To this end, we determine the optimal advertising policies by solving a Stackelberg differential game, where the owner of the brand acts as the leader and the licensee as the follower. We determine the equilibrium policies of the two players assuming that advertising varies over time and price is constant. We also determine a minimum selling price which guarantees brand sustainability without advertising too much.

Optimal sustainable use of drinking water sources and interactions between multiple providers

The provision and conservation of drinking water are key issues worldwide. Optimal management involves conjunctive use of different sources by multiple providers, who share the same surface water source while using a personal stock source. In this paper we consider the interaction between two profit maximizer providers. We solve two optimal control problems where the optimal abstraction policy of the upstream provider influences the feasible controls of the downstream one. We determine the optimal sustainable policies at every catchment point.

ε -Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games

Open-loop Stackelberg equilibria in linear-state games are subgame perfect. This result holds under the hypothesis of unconstrained final state; whereas we need to take into account suitable final-state conditions in order to correctly formalize certain economic problems. A striking contribution of this paper is that it tackles the consistency problem for an open-loop Stackelberg equilibrium in linear-state games with a final-state constraint in the leader’s problem. In this paper, after proving that such a type of equilibrium is not subgame perfect, we introduce a weaker definition of subgame perfectness, which we call ε-subgame perfectness. This new definition can be applied to the open-loop Stackelberg equilibrium of a constrained linear-state game. Finally, we present some explanatory examples to show how the definition of ε-subgame perfectness can be meaningful.

Optimal study/advertising plan for a knowledge/goodwill evolution process with rank memory

Abstract We consider the problem of an economous and ambitious student with a variable and bounded time to take his examination. We assume that the first passage over a specified knowledge threshold affects the subsequent knowledge evolution process permanently. This first passage time is used to transform the original nondifferentiable optimal control problem into a nonlinear programming problem, whose decision variables are the first passage time and the final time. A marketing interpretation of the problem is also provided. Partially supported by MURST.