Resumo Neste trabalho, é proposto um modelo matemático de programação linear inteira para auxiliar o setor de Planejamento, Programação e Controle da Produção de uma indústria gráfica. O modelo considera duas funções objetivos para tratar o problema, a primeira para minimizar os custos com o consumo de energia elétrica e, a segunda, para minimizar o tempo operacional das máquinas, ambas relativas à designação e utilização de conjuntos distintos de máquinas de impressão e de acabamento para a confecção dos itens demandados. São consideradas restrições operacionais da indústria, tais como, os limites de tempo de setup e de operação das máquinas, tipos de item impresso, capacidade de produção e atendimento de demanda. Além disso, uma heurística foi desenvolvida para auxiliar a programação da produção, permitindo ajustes nos respectivos turnos de produção da indústria, mas respeitando a designação obtida pela resolução do modelo matemático. Testes computacionais foram realizados com um conjunto de dados fornecidos por uma indústria gráfica situada no interior do estado de São Paulo. trabalho Planejamento problema segunda demandados como impresso demanda disso Paulo

Abstract In this study, an integer linear programming model is proposed to support the Production Planning, Scheduling and Control sector of a printing company. The model considers two objective functions to deal with the problem, the first is to minimize the costs with electric energy consumption and the second is to minimize the machine operating time. Both objectives are related to the assignment to different sets of printing and finishing machines for the manufacture of the ordered items. Operating constraints at the factory are considered, such as the setup time limits, how the machine is operated, the types of printed item, the production capacity and the demand. In addition, a heuristic was developed to support the production schedule, allowing adjustments in the different production shifts but respecting the assignments obtained using the mathematical model. Computational tests were performed with a set of data provided by a printing company located in the state of São Paulo. study Planning problem items considered limits operated item demand addition schedule Paulo

ABSTRACT: Brazil is the largest sugarcane producer in the world and the leader in the production of sugar and ethanol. Although sugarcane has become an important factor in the Brazilian economy, cultivation has presented many issues, for example, the problems due to burning before the manual harvest. The Brazilian authorities have approved a law that prohibits this practice and mechanized harvesting has thus become the most fitting approach. Given this development, areas for sugarcane plantation must be properly rebuilt to accommodate the new way of harvesting. The main characteristic demanded of sugarcane plots to use harvesting machines is that they must be rectangular. In the present paper, we propose a methodology for dividing the plantation area into plots and planning their allocation so as to accommodate mechanized harvesting. In view of the requirement for plots to be rectangular, we represented this problem as a two-dimensional cutting problem, and to find a solution we adopted the AND/OR graph approach. The computational experiments were conducted using real cases, and the proposed strategy was shown to perform well.

ABSTRACT This paper addresses the cutting stock/leftover problem (CSLP), which differs from the ordinary cutting stock problem (CSP) by retaining stock leftovers that can be cut in the future to meet new demands. Therefore, leftovers are not considered waste in the current period. A new mathematical model for the CSLP is presented to capture a well-used strategy in the practice of cutting, which consists of partially cutting the objects in stock, and keeping the leftovers to be cut in the next periods. Computational experiments were made for the one-dimensional case, although other dimensions can be considered straightforward.

Nesse trabalho, e estudado o problema de corte de estoque com sobras aproveitaveis (PCESA), que consiste em determinar uma política de aproveitamento das sobras de objetos cortados. Estas sobras, desde que não sejam demasiadamente pequenas, podem retornar ao estoque como retalhos para atender demandas futuras, não sendo, portanto, consideradas perdas. Para resolver o PCESA, podem ser utilizados varios procedimentos heurísticos propostos na literatura. Entretanto, e difícil identificar o melhor método de solução, pois cada um deles apresenta uma solução diferente em relação as características de interesse do problema, como quantidade de retalhos produzidos, perdas e distribuição de perdas e retalhos nos objetos. Para superar essa dificuldade, propoe-se utilizar técnicas da lógica fuzzy para considerar a contributo de cada característica de interesse na solução, classifica-la de acordo com critérios pré-estabelecidos e, finalmente, identificar o melhor método com base na respectiva solução. Com a metodologia fuzzy desenvolvida, facilitou-se a análise dos métodos de solução

In this paper, we study the cutting stock problem with usable leftovers (CSPUL), that consists in determining a policy of usable leftovers from cut objects. These leftovers, if large enough, can returned to the stock as retails in order to fulfill future demands and, therefore, they are not computed as waste. In order to solve the CSPUL, several heuristic procedures from the literature can be used. However, it is hard to point out which solution method performs better, since each one presents different solutions regarding some conflicting characteristics, such as quantity of new retails generated, wastes, and distribution of the wastes and retails in the cut objects. To overcome this difficulty, we propose some fuzzy techniques to consider the contribution of each characteristic in the solution, classify it according some criteria beforehand considered and, finally, identify the best solution method based on the respective solution. With the proposed fuzzy methodology, the solution methods analysis was simplified