ABSTRACT Irregular strip packing problems are present in a wide variety of industrial sectors, such as the garment, footwear, furniture and metal industry. The goal is to find a layout in which an object will be cut into small pieces with minimum raw-material waste. Once a layout is obtained, it is necessary to determine the path that the cutting tool has to follow to cut the pieces from the layout. In the latter, the goal is to minimize the cutting distance (or time). Although industries frequently use this solution sequence, the trade-off between the packing and the cutting path problems can significantly impact the production cost and productivity. A layout with minimum raw-material waste, obtained through the packing problem resolution, can imply a longer cutting path compared to another layout with more material waste but a shorter cutting path, obtained through an integrated strategy. Layouts with shorter cutting path are worthy of consideration because they may improve the cutting process productivity. In this paper, both problems are solved together using a biobjective matheuristic based on the Biased Random-Key Genetic Algorithm. Our approach uses this algorithm to select a subset of the no-fit polygons edges to feed the mathematical model, which will compute the layout waste and cutting path length. Solving both strip packing and cutting path problems simultaneously allows the decision-maker to analyze the compromise between the material waste and the cutting path distance. As expected, the computational results showed the trade-off’s relevance between these problems and presented a set of solutions for each instance solved.

ABSTRACT Two integer linear programming models are developed for the unrestricted vehicle routing problem with two-dimensional loading constraints. The first one is a complete model, and the other uses valid inequalities to guarantee that routes are connected and respect the two-dimensional loading constraints. The models are solved with a branch-and-cut algorithm. Computational experiments on benchmark instances showed the complete model has allowed optimal solutions for 5% of the instances, while the second model optimally solved 64% of the instances. Given the superior performance of the second model, we adapted it to handle the sequential variant of the problem, which is harder, and then optimal solutions were obtained for 46% of the instances within the given time limit. The second model compared with a branch-and-cut algorithm from the literature found identical or better solutions for all the instances.

ABSTRACT The irregular strip packing problem is a common variant of cutting and packing problems. Only a few exact methods have been proposed to solve this problem in the literature. However, several heuristics have been proposed to solve it. Despite the number of proposed heuristics, only a few methods that combine exact and heuristic approaches to solve the problem can be found in the literature. In this paper, a matheuristic is proposed to solve the irregular strip packing problem. The method has three phases in which exact mixed integer programming models from the literature are used to solve the sub-problems. The results show that the matheuristic is less dependent on the instance size and finds equal or better solutions in 87,5% of the cases in shorter computational times compared with the results of other models in the literature. Furthermore, the matheuristic is faster than other heuristics from the literature.

Resumo O problema abordado neste trabalho consiste na redução dos custos de energia elétrica necessária para o funcionamento de bombas hidráulicas, que são utilizadas para captar água de poços artesianos ou estações de tratamento de água para abastecer reservatórios distribuídos por bairros de uma cidade. A população é então atendida por força gravitacional. Como o custo da energia elétrica varia ao longo do dia, é necessário um planejamento do funcionamento das bombas. O problema consiste em decidir quando as bombas devem permanecer ligadas e quando deve haver transferência de água entre os reservatórios para que a demanda de cada reservatório seja atendida, minimizando os custos com energia elétrica. Este problema é modelado como um problema de programação linear inteira, e uma solução heurística é proposta. Experimentos computacionais mostram a eficiência da heurística e como a abordagem pode ser utilizada para analisar o impacto de alterações na infraestrutura do sistema de abastecimento.

Abstract The problem considered in this paper consists of the reduction of electrical energy costs necessary for the operation of hydraulic pumps, which are used to collect water from artesian wells or from a Water Treatment Station to fill water tanks located in many districts of a city. The water is then supplied by gravitational force. Because the cost of electrical energy varies throughout the day, a pump running schedule is necessary. The problem consists of determining when the pumps must be on and when there must be water transfer among tanks to ensure that the demand of each water tank be supplied, thereby minimizing the costs of electrical energy. This problem was modeled as an integer linear optimization problem, and a heuristic solution to the problem is proposed. Computational experiments show the efficiency of the heuristic and highlight how the approach can be used to analyze the impact of changes in the infrastructure of the water supply system.

Neste trabalho, estudamos um caso particular do problema de dimensionamento de lotes, envolvendo o planejamento da produção de um único item em vários centros produtivos que não apresentam restrições de capacidade. A demanda pode ser atendida com ou sem atraso. Este problema surge da decomposição de problemas práticos, como o sistema de requerimento de materiais (MRP), e também de problemas de dimensionamento de lotes com múltiplos itens e capacidade de produção limitada. Primeiramente, apresentamos uma implementação eficiente de um algoritmo de programação dinâmica progressiva proposto para a solução do problema com um único centro produtivo. Embora, essa implementação não reduza a complexidade do algoritmo, experimentos computacionais mostraram que ela é significativamente mais rápida. Em seguida, estudamos o problema com vários centros, para o qual são implementados dois algoritmos, o primeiro é uma extensão do algoritmo original e o segundo incorpora as idéias que tornam essa implementação mais eficiente. O desempenho computacional dos algoritmos é analisado e propostas para futuras pesquisas são apresentadas.

In this paper, a case study is carried out concerning the lot-sizing problem involving a single item production planning in several production centers that do not present capacity constraints. Demand can be met with backlogging or not. This problem results from simplifying practical problems, such as the material requirement planning (MRP) system and also lot-sizing problems with multiple items and limited production capacity. First we propose an efficient implementation of a forward dynamic programming algorithm for problems with one single production center. Although this does not reduce its complexity, it has shown to be rather effective, according to computational tests. Next, we studied the problem with a production environment composed of several production centers. For this problem two algorithms are implemented, the first one is an extension of the dynamic programming algorithm for one production center and the second one is an efficient implementation of the first algorithm. Their efficiency are shown by computational testing of the algorithms and proposals for future research are presented.