3 resultados para Production Inventory Model with Switching Time
em Repositório Institucional da Universidade de Aveiro - Portugal
Resumo:
We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.
Resumo:
O transporte marítimo e o principal meio de transporte de mercadorias em todo o mundo. Combustíveis e produtos petrolíferos representam grande parte das mercadorias transportadas por via marítima. Sendo Cabo Verde um arquipelago o transporte por mar desempenha um papel de grande relevância na economia do país. Consideramos o problema da distribuicao de combustíveis em Cabo Verde, onde uma companhia e responsavel por coordenar a distribuicao de produtos petrolíferos com a gestão dos respetivos níveis armazenados em cada porto, de modo a satisfazer a procura dos varios produtos. O objetivo consiste em determinar políticas de distribuicão de combustíveis que minimizam o custo total de distribuiçao (transporte e operacões) enquanto os n íveis de armazenamento sao mantidos nos n íveis desejados. Por conveniencia, de acordo com o planeamento temporal, o prob¬lema e divido em dois sub-problemas interligados. Um de curto prazo e outro de medio prazo. Para o problema de curto prazo sao discutidos modelos matemáticos de programacao inteira mista, que consideram simultaneamente uma medicao temporal cont ínua e uma discreta de modo a modelar multiplas janelas temporais e taxas de consumo que variam diariamente. Os modelos sao fortalecidos com a inclusão de desigualdades validas. O problema e então resolvido usando um "software" comercial. Para o problema de medio prazo sao inicialmente discutidos e comparados varios modelos de programacao inteira mista para um horizonte temporal curto assumindo agora uma taxa de consumo constante, e sao introduzidas novas desigualdades validas. Com base no modelo escolhido sao compara¬das estrategias heurísticas que combinam três heur ísticas bem conhecidas: "Rolling Horizon", "Feasibility Pump" e "Local Branching", de modo a gerar boas soluçoes admissíveis para planeamentos com horizontes temporais de varios meses. Finalmente, de modo a lidar com situaçoes imprevistas, mas impor¬tantes no transporte marítimo, como as mas condicões meteorológicas e congestionamento dos portos, apresentamos um modelo estocastico para um problema de curto prazo, onde os tempos de viagens e os tempos de espera nos portos sao aleatórios. O problema e formulado como um modelo em duas etapas, onde na primeira etapa sao tomadas as decisões relativas as rotas do navio e quantidades a carregar e descarregar e na segunda etapa (designada por sub-problema) sao consideradas as decisoes (com recurso) relativas ao escalonamento das operacões. O problema e resolvido por um metodo de decomposto que usa um algoritmo eficiente para separar as desigualdades violadas no sub-problema.
Resumo:
Although the genetic code is generally viewed as immutable, alterations to its standard form occur in the three domains of life. A remarkable alteration to the standard genetic code occurs in many fungi of the Saccharomycotina CTG clade where the Leucine CUG codon has been reassigned to Serine by a novel transfer RNA (Ser-tRNACAG). The host laboratory made a major breakthrough by reversing this atypical genetic code alteration in the human pathogen Candida albicans using a combination of tRNA engineering, gene recombination and forced evolution. These results raised the hypothesis that synthetic codon ambiguities combined with experimental evolution may release codons from their frozen state. In this thesis we tested this hypothesis using S. cerevisiae as a model system. We generated ambiguity at specific codons in a two-step approach, involving deletion of tRNA genes followed by expression of non-cognate tRNAs that are able to compensate the deleted tRNA. Driven by the notion that rare codons are more susceptible to reassignment than those that are frequently used, we used two deletion strains where there is no cognate tRNA to decode the rare CUC-Leu codon and AGG-Arg codon. We exploited the vulnerability of the latter by engineering mutant tRNAs that misincorporate Ser at these sites. These recombinant strains were evolved over time using experimental evolution. Although there was a strong negative impact on the growth rate of strains expressing mutant tRNAs at high level, such expression at low level had little effect on cell fitness. We found that not only codon ambiguity, but also destabilization of the endogenous tRNA pool has a strong negative impact in growth rate. After evolution, strains expressing the mutant tRNA at high level recovered significantly in several growth parameters, showing that these strains adapt and exhibit higher tolerance to codon ambiguity. A fluorescent reporter system allowing the monitoring of Ser misincorporation showed that serine was indeed incorporated and possibly codon reassignment was achieved. Beside the overall negative consequences of codon ambiguity, we demonstrated that codons that tolerate the loss of their cognate tRNA can also tolerate high Ser misincorporation. This raises the hypothesis that these codons can be reassigned to standard and eventually to new amino acids for the production of proteins with novel properties, contributing to the field of synthetic biology and biotechnology.