Problemas de corte e empacotamento de itens irregulares são problemas que visam determinar um leiaute ótimo de objetos pequenos dentro de objetos maiores, a fim de atender a uma demanda. Estes problemas têm grande importância prática, já que surgem em vários tipos de indústria (como a têxtil, a de móveis e a de calçados). O problema estudado neste trabalho é o problema de corte de itens irregulares em recipientes. Os recipientes são delimitados e o objetivo é encontrar um leiaute dos objetos menores, sem sobreposição, dentro dos objetos maiores utilizando a menor quantidade de recipientes. Propomos um novo método de resolução para o problema. Nosso método é um algoritmo que gerencia um conjunto de heurísticas, de baixo nível, específicas para a resolução do problema com recipientes retangulares e irregulares. Recipientes irregulares são polígonos convexos e não convexos, que podem ser furados. As heurísticas desenvolvidas utilizam uma malha de pontos sobre a técnica de no-fit polygon para evitar a sobreposição dos itens e encontrar posições viáveis no recipiente retangular ou irregular. Os experimentos computacionais foram feitos para um grande conjunto de instâncias, de recipientes retangulares e irregulares. Os resultados demonstram a competitividade do método, que obtêm resultados bons e algumas soluções ótimas, em um tempo computacional aceitável. / Cutting and packing of irregular items are problems that aim to determine the optimum layout of small objects within larger objects (that we call bins), in order to meet a demand. These problems have great practical importance, since they emerge in various types of industry (such as textile, furniture and shoemaking). The problem studied in this work is the irregular bin packing problem. The bins are enclosed and the goal is to find a layout of items, without overlap, within the bins by using the minimum quantity of them. We propose a new method of resolution to this problem. Our method is an algorithm that manages a set of low-level heuristics, specific to solve the problem with rectangular bins and irregular bins. Irregular bins are convex and non-convex polygons, which may contain holes. The developed heuristics uses a mesh of points and the technique of no-fit polygon to avoid the overlapping of items and find feasible positions in rectangular or irregular bins. The computational experiments were performed for a large set of instances, using both rectangular and irregular bins. The results demonstrate the competitiveness of the method, which can get good results and some optimal solutions within an acceptable computational time.

Scheduling in the context of manufacturing systems has become increasingly impor- tant in order for organizations to achieve success in dynamic and competitive scenarios. Scheduling can be described as allocation of available jobs over resources to meet the performance criteria defined in a domain. Our research work fo cuses on scheduling a given set of three-dimensional cylindrical items, each characterized by width wj , height hj, and depth dj , onto parallel non-identical rectangular heat treatment kilns, such that the capacities of the kilns is optimally used. The problem is strongly NP-hard as it generalizes the (one-dimensional) Bin Packing Problem (1BP), in which a set of n positive values wj has to be partitioned into the minimum number of subsets so that the total value in each subset does not exceed the bin capacity W. The problem has been formulated as a variant of the 3D-BPP by following the MILP approach, and we propose a weight optimization heuristic that produces solutions comparable to that of the LP problem, in addition to reducing the computational complexity. Finally, we also propose a Decomposition Algorithm (DA) and validate the perfor- mance effectiveness of our heuristic. The numerical analyses provides useful insights that influence the shop-floor decision making process.