1,720,991 research outputs found
On an environmental sustainability problem
No full textBeltratti 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
Advertising and congestion management for a museum temporary exhibition
No full textWe propose a model for a museum institution which offers a special exhibition in a definite time period. Attention is given to the museum demand and the quality of the visitors experience, in particular in relation with the occurrence of congestion situations. The laws governing the behaviour of the system through time
are defined by three distinct dynamical systems, depending on the
position of the visitor attendance rate with respect to two critical
levels: the congestion threshold which is a fixed parameter of the
system and the extreme congestion threshold which depends on the congestion management policy. Because of the regime switching the optimal control problem is nondifferentiable and Clarke's generalized maximum principle necessary conditions are derived. We discuss the existence of an optimal solution and some special classes of control functions which are economically meaningful
Advertising andproduction of a seasonal good for a heterogeneous market
Full text linkWe 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
Decisions on production and quality
No full textQuality plays a central role in Operations Management as it is a relevant issue on which the customers of an organization focus their judgment. In a short-term production model, we can assume that quality is constant. Then, we treat the optimal choices of production rate and quality level as an optimal control problem with a parameter. Starting from a production planning model by Kamien and Schwartz, we introduce quality as a decision variable. In the solution, we observe that the optimal quality level and production rate are independent of each other. Next, we modify the model assuming that the ordered quantity is not exogenous, but is determined through optimization, when the market-clearing price depends on both quality and quantity. We get a more interesting solution in which optimal production and optimal quality are interdependent, in a way that is not straightforward. We characterize and discuss the optimal solutions to these problems using the necessary and sufficient conditions for optimal processes with parameters. This shows once again that the sufficient conditions for this kind of problem are too restrictive and introducing a more effective kind of sufficient conditions is still an open question
Dynamic modelling of a cultural event
No full textWe propose a family of dynamic models to represent the behaviour of
people participating in a cultural event and the objectives and management policies of the cultural institution involved. We focus on those cultural organizations which operate in the visual art sector, such as museums or art galleries, and which typically face cultural demand problems. The different visitors ow dynamics presented take into account the roles played by advertising, word of mouth communication and congestion inside the cultural communication process. Different objectives of the cultural institution and different congestion management possibilities lead to a variety of dynamic optimization problems
Allocazione dinamica delle risorse in un museo: il problema della gestione della congestione
No full text
A dynamic advertising model in a vaccination campaign
No full textVaccines save thousands of lives every year, but many people remain unvaccinated because serious adverse neurological disorders are wrongly attributed to vaccination. The “urban myth” 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
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