Anaerobic digesters have been highlighted due to the current energy crisis and its consequent search for alternative energy sources, allied to the intense process of livestock farming and agriculture modernization, which besides demanding a lot of energy, produces a great amount of crop and animal residues, most of the times generating sanitary problems. The aim of this work is to provide a mathematical tool to establish parameters for projects of construction of rural digesters, considering the response to energy demand, the suitability of the dimensions of the systems, yield factors and the guarantee of functionality. Non-linear optimization models, of easy resolution, for the three main types of rural digesters were formulated in this way. With the resolution of these models one can determine the height and the diameter that lead to a minimum volume for each type, so reducing the necessary amount of masonry and, consequently, diminishing the cost. Key words: mathematical model, optimization, parameters for designing FERRAMENTA MATEMÁTICA PARA AUXÍLIO NO DIMENSIONAMENTO DE BIODIGESTORES RURAISRESUMO: Os biodigestores têm sido objetos de grande destaque devido a atual crise de energia e conseqüente busca de fontes alternativas. Outro fator que coloca os biodigestores em evidência é o intenso processo de modernização da agropecuária, que além da grande demanda de energia, produz um volume de resíduos animais e de culturas, que ocasiona muitas vezes problemas de ordem sanitária. O objetivo deste trabalho é fornecer uma ferramenta matemática para determinação de parâmetros para projetos de construção de biodigestores rurais, levando-se em consideração o atendimento de necessidades energéticas, obedecendo os dimensionamentos dos sistemas, fatores de rendimento e garantindo a funcionalidade. Para isto, foram formulados modelos de otimização não lineares, de fácil resolução, para os três principais tipos de biodigestores rurais. Com a resolução destes modelos são determinados a altura e o diâmetro que levem a um volume mínimo para cada tipo, com isto reduz-se a quantidade necessária de materiais de alvenaria e consequentemente o custo do biodigestor é diminuído. Palavras-chave: modelo matemático, otimização, parâmetros de projeto

This paper addresses the management of a sugarcane harvest over a multi-year planning period. A methodology to assist the harvest planning of the sugarcane is proposed in order to improve the production of POL (a measure of the amount of sucrose contained in a sugar solution) and the quality of the raw material, considering the constraints imposed by the mill such as the demand per period. An extended goal programming model is proposed for optimizing the harvest plan of the sugarcane so the harvesting point is as close as possible to the ideal, considering the constrained nature of the problem. A genetic algorithm (GA) is developed to tackle the problem in order to solve realistically large problems within an appropriate computational time. A comparative analysis between the GA and an exact method for small instances is also given in order to validate the performance of the developed model and methods. Computational results for medium and large farm instances using GA are also presented in order to demonstrate the capability of the developed method. The computational results illustrate the trade-off between satisfying the conflicting goals of harvesting as closely as possible to the ideal and making optimum use of harvesting equipment with a minimum of movement between farms. They also demonstrate that, whilst harvesting plans for small scale farms can be generated by the exact method, a meta-heuristic GA method is currently required in order to devise plans for medium and large farms.

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It is well known that Brazil is the largest producer of sugarcane in the world. Nevertheless, a great concern exists about the crop system used, because the most common practice is manual harvesting with prior straw burning. The Brazilian authorities have approved a law prohibiting the burning of sugarcane crop residue before harvesting. However, mechanized harvesting creates the new problem of having to deal with the residue. Many studies have indeed proposed the use of this residue as an energy source. A major difficulty in using this residue is how to economically transport sugarcane harvest biomass from a farm to a processing centre. Besides transport costs, another concern is knowing whether the energy generated by the straw offsets the energy used, in terms of fuel, in the process. This study proposes a multiobjective integer linear programming optimization model to choose sugarcane varieties so as to minimize costs in the use of crop residue and simultaneously maximize the energy balance in such a process. Computational results are presented and discussed.

The fact that Brazil is the world's largest sugarcane (Saccharum spp.) producer, leads to a great concern about the cropping systems used, since the most common practice involves manual harvesting prior to straw burning. Brazilian authorities approved a law prohibiting the burning practice of crop residues prior to harvest. However mechanized harvest creates the new problem of how to deal with the residues. Many studies have proposed the use of these residues as an energy source. The major difficulty in its use is how to economically transport sugarcane harvested biomass from the farm to a processing center. The aim of this work was to develop a model to optimize plant variety selection, minimize the cost of the residual biomass transfer process, to evaluate the economics of using this material, and to address sucrose production and planting area constraints, considering distances from plot to processing center. Mas, existe uma grande preocupação com o sistema de colheita utilizado nesta cultura, pois é prática comum a colheita manual com a pré-queima do palhiço. Autoridades brasileiras têm aprovado leis proibindo a queimada nos canaviais. Entretanto, a colheita mecanizada com cana crua cria novos problemas com a permanência do resíduo no solo. Assim, muitos estudos têm sido propostos para o uso deste resíduo para geração de energia. A maior dificuldade para o uso desta biomassa está no custo de coletar e transferir o resíduo do campo para o centro de processamento. Para análise da viabilidade deste sistema há a necessidade de um estudo do balanço econômico do processo. O objetivo deste trabalho é desenvolver um modelo matemático que auxilie na escolha das variedades de cana a serem plantadas, de forma a minimizar o custo do processo de transferência da biomassa residual de colheita e avaliar economicamente o uso deste material, colocando restrições sobre a produção de sacarose e limitações da área para plantio e considerando as distâncias entre os talhões e o centro de processamento. Para isto, técnicas de programação linear multiobjetivo 0-1 foram utilizadas. Os resultados da aplicação mostram a viabilidade do uso deste modelo para auxílio na seleção de variedades, otimizando o lucro do uso da biomassa residual de colheita para geração de energia. Palavras-chave: modelo matemático, biomassa residual, cana-de-açúcar, programação linear multiobjetivo 0-1

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