Advertising andproduction of a seasonal good for a heterogeneous market

We bring some concepts from market segmentation, which is a fundamental topic of marketing theory and practice, into the statement of an advertising and production problem for a seasonal product with Nerlove- Arrow's linear goodwill dynamics. We consider two kinds of situations. In the rst one the advertising process can reach selectively each segment. In the second one one advertising medium is available which has a known eectiveness spectrum for a non-trivial set of segments. In both cases we solve, using the Pontryagin's Maximum Principle conditions, the optimal control problems in which goodwill productivity of advertising is concave and good production cost is convex. Two special cases are discussed in detail

Advertising policies for a museum temporary exhibition

Dipartimento di Matematica Applicata, Università Ca' Foscari di Venezi

Local search solution of a museum advertising problem via the analysis of linear optimal control problems

Dipartimento di Matematica Applicata, Università Ca' Foscari di Venezi

Advertising exposure for a seasonal good in a segmented market

ISSN: 2239-273

On an environmental sustainability problem

Beltratti et al proposed an environmental sustainability problem and stressed the importance of two related control problems, namely, the discounted utilitarian problem and the long-run utility problem. From the analysis of the latter, they obtained the definition of the Green Golden Rule (GGR). We discuss the optimal steady-state solutions of the first problem and provide new results, completing the known information on it. Then we tackle the second problem and its equivalent NLP problem of maximizing the steady-state utility. We obtain that the solutions to the NLP problem depend on the capital accumulation features, like those of the first problem. This corrects and completes the original analysis of the GGR

Determining optimal production and advertising policies for a seasonal product

OPTIMIZATIO

A single season production and advertising control problem with bounded final goodwill

JOURNAL OF INFORMATION AND OPTIMIZATION SCIENCE

A dynamic advertising model in a vaccination campaign

Vaccines save thousands of lives every year, but many people remain unvaccinated because serious adverse neurological disorders are wrongly attributed to vaccination. The \u201curban myth\u201d of a relevant vaccine-associated risk is sustained by anti-vaccination groups and it is spread by word-of-mouth communication. We face the problem of increasing the vaccination coverage using an approach which draws some elements from the theory of dynamic advertising models. We propose a dynamic model for the evolution of the number of unvaccinated people and assume that a policy-maker can control this dynamics through advertising. From a mathematical point of view, we state and analyze an optimal control problem with a pure state constraint. We find the unique optimal solution, which minimizes a cost functional, but may fail to be satisfactory from the different viewpoint of moving towards eradication of the disease. Our analysis suggests that we modify the problem statement in order to consider explicitly the goal of reducing the number of unvaccinated people, to a level which guarantees the herd immunity. Hence we introduce an upper bound to the final number of unvaccinated people. From the solutions to the two problems we obtain some prescriptions for the policy-maker