Advertising and production of a seasonal good for a heterogeneous market: from total segment separability to real media

Market segmentation is a fundamental topic of marketing theory and practice. We bring some market segmentation concepts into the statement of an advertising and production problem for a seasonal product with Nerlove-Arrow's linear goodwill dynamics, along the lines of some analyses concerning the introduction of a new product. We consider two kinds of situations. In the first one, we assume that the advertising process can reach selectively each segment. In the second one, we assume that one advertising medium is available and that it has a known effectiveness segment-spectrum for a non-trivial set of segments. In both cases we study the optimal control problems in which goodwill productivity of advertising is either linear or concave, and good production costs are (convex and) quadratic. We obtain the explicit optimal solutions using the Pontryagin's Maximum Principle conditions.

Endogenous Royalty Factor in a Licensing Contract

The owner of a well known fashion brand grants a manufacturer the rights to produce and sell a second-line brand against a percentage of the sales called royalty. To this end, the brand owner and the manufacturer sign a licensing contract which assigns the owner, who has already determined his advertising campaign, the right of determining the royalty factor. The manufacturer will plan her advertising campaign for the licenced product in order to maximize her profit. The brand owner's objective is twofold: on one hand he wants to maximize the profit coming from the contract, on the other hand he wants to improve the value of the brand at the end of a given planning period. We model this interaction between the two agents using a Stackelberg game, where the brand owner is the leader and the manufacturer is the follower. We characterise the royalty percentage and the licensee's advertising effort which constitute the unique Stackelberg equilibrium of the game

Optimal advertising strategies in a sports licensing contract

We consider a licensing agreement that grants to a manufacturer (licensee) the rights to use the logo of a sports team (licensor) on the goods he produces. This contract stands over a royalty clause that re- quires that the licensee pays a financial reward to the licensor. A further payment can sometimes be required in terms of a sales percentage, in case the sales exceed a given amount. We take into account this partic- ular clause by considering a non-differentiable scrap value term in the objective functional of the licensee. We formulate and solve an optimal control problem, with non differentiable dependence on final state, in order to find the optimum advertising strategies for the licensee

Advertising exposures for a seasonal good in a segmented market

The optimal control problem of determining advertising efforts for a seasonal good in a heterogeneous market is considered. We characterize optimal advertising exposures under different conditions: the general situation in which several wide-spectrum media are available, under the assumption of additive advertising effects on goodwill evolution, the ideal situation in which the advertising process can reach selectively each segment and the more realistic one in which a single medium reaches several segments with different effectiveness.Marketing; advertising; optimal control

Advertising a social event in a heterogeneous market

We study the problem of advertising a social event in a segmented market using different media. The result of such advertising process is the evolution of a goodwill vector. We describe the problem as an optimal control one, assuming that the demand is a concave function of goodwill. We prove the existence of an optimal solution and characterize it using the Pontryagin Maximum Principle. This leads to the analysis of a family of linear programming problems. We provide a more explicit and detailed description of optimal solutions for the case of goodwill linear demand

Advertising in a segmented market: comparison of media choices

Segmentation is a core strategy in modern marketing but, to the best of our knowledge, it is not considered in most dynamic advertising models. In this paper, we aim to fill such a gap by presenting a dynamic advertising model which includes market segmentation. First, we model goodwill evolution in a segmented market under the assumption that the decision maker may independently choose the advertising intensity directed at each different segment. Then, we assume that the decision maker must use a single medium, which reaches several segments with different effectiveness. We obtain the explicit solutions of the relevant optimal control problems. These results permit us to compare the two different contexts and to obtain a preference index for advertising media

Inequalities concerning a random computational length of pattern recognizers

The computational length of an algorithm for pattern recognition by absolute comparison is a random variable, whose features depend on the probability distribution \u3c0 08Rk of the k classes to be discriminated. The Euclidean distance from the uniform probability distribution to any other distribution \u3c0 is proportional to the greatest lower bound of the total variation of the mean computational length of algorithms used to recognize classes with distribution \u3c0. This result is reached by first finding a suitable basis of Rk which allows simple representations of probability distributions and of the functions under study. Furthermore, by using the same basis, the Schwartz inequality easily gives an upper bound of the total variation of the mean computational length

Advertising decisions for a segmented market

We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments variably and we assume that the advertising effects on demand over time are mediated by a vector goodwill variable. A first general advertising decision problem is stated and solved in the non-linear programming framework. A preference index is then obtained for the medium selection problem when each segment demand function is linear in goodwill and each medium advertising cost function is quadratic in its level. Finally the theoretical case of disjoint advertising media is discussed

Computational length in pattern recognizers

The computational time of an absolute comparison recognizer is a random variable related to a measure of computational length. These variables depend on the choice of an algorithm which carries out the recognition. The expectation and the variance of the computational length are examined in detail with reference to the probability distribution of the classes to be discriminated. In particular, upper and lower bounds of the smallest mean computational length are found in easily evaluable forms