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.

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

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The development of projects related to the yield of various crops has been greatly eiihaticcd with the incorporation of mathematical models as well as essential and more consistent equations which enable a prediction and greater approximation to their actual behavior, thus reducing error in estimate. Among the operations requiring further investigation are those related to crop growth, characterized by the ideal temperature for addition of dry matter. Due to the wide use of mathematical methods for representing, analyzing and attaining degree-day estimation as well as the great importance of sugarcane in the Brazilian economy, we carried out an evaluation of the mathematical models and numerical integration methods commonly used for estimating the availability of degrees-day for this crop in the region of Botucatu, in Sao Paulo State, Brazil. Integration models with discretization every 6 hours have shown satisfactory results in degree-day estimation. Conventional methodologies have shown satisfactory results when the estimation of degrees-day was based on the time-temperature curve for each day and for groups of 3, 7, 15 and 30 days. Through numerical integration method, the region of Botucatu showed a annual thermal availability average from 1,070.6 degrees-day for the sugarcane. Keywords: vegetative development, heat units, numerical integration methods, sugar cane.RESUMO. Cotnparaçâo de metodologias para estimativa de graus-dia usando métodos numéricos. O desenvolvimento de projetos relacionados ao desempenlio de diversas culturas tem recebido aperfeiçoamento cada vez maior, incorporado a modelos matemáticos sendo indispensável à utilizaçâo de equaçôes cada vez mais consistentes que possibilitem previsâo e maior aproximaçâo do coniportaniento real, diminuindo o erro na obtençâo das estimativas. Entre as operaçôes unitarias que demandam maior estudo estáo aquelas relacionadas com o crescimento da cultura, caracterizadas pela temperatura ideal para o acréscimo de materia seca. Pelo ampio uso dos métodos matemáticos na representaçâo, análise e obtençâo de estimativas de graus-dia, juntamente com a grande importancia que a cultura da cana-de-acúcar tem para a economia brasileira, foi realizada uma avaliaçâo dos modelos matemáticos comumente usados e dos métodos numéricos de integraçâo na estimativa da disponibilidade de graus-dia para essa cultura, na regiáo de Botucatu, Estado de Sao Paulo. Os modelos de integraçâo, com discretizaçâo de 6 em 6 h, apresentaram resultados satisfatórios na estimativa de graus-dia. As metodologias tradicionais apresentaram desempenhos satisfatórios quanto à estimativa de grausdia com base na curva de temperatura horaria para cada dia e para os agrupamentos de tres, sete, 15 e 30 dias. Pelo método numérico de integraçâo, a regiáo de Botucatu, Estado de Sao Paulo, apresentou disponibilidade térmica anual média de 1.070,6 GD para a cultura da cana-de-acúcar.Palavras-chave: desenvolvimento vegetativo, unidades térmicas, métodos de integraçâo numérica, cana-de-acúcar.

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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.