The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect

In this paper, a two-dimensional cutting problem is considered in which a single plate (large object) has to be cut down into a set of small items of maximal value. As opposed to standard cutting problems, the large object contains a defect, which must not be covered by a small item. The problem is represented by means of an AND/OR-graph, and a Branch & Bound procedure (including heuristic modifications for speeding up the search process) is introduced for its exact solution. The proposed method is evaluated in a series of numerical experiments that are run on problem instances taken from the literature, as well as on randomly generated instances.Two-dimensional cutting, defect, AND/OR-graph, Branch & Bound

Qualidade de vida do doente após acidente vascular cerebral

Contextualização: Em Portugal, o AVC constitui a principal causa de incapacidade de longa duração e de diminuição da qualidade de vida. A reabilitação funcional do doente é um dos requisitos básicos no tratamento pós-AVC. Neste contexto, o objetivo do presente estudo pretendeu analisar o modo como determinadas variáveis de contexto sociodemográfico, familiar e clínico estão associadas à qualidade de vida destes doentes. Métodos: Realizou-se um estudo transversal, descritivo correlacional, de natureza quantitativa, no qual participaram 75 doentes, maioritariamente do sexo masculino (53,33%), com uma média de idades de 68 anos. Para a mensuração das variáveis utilizaram-se instrumentos de medida, de reconhecida fiabilidade, aferidos e validados para a população portuguesa: Escala de Apgar Familiar, Escala de Barthel e Questionário de avaliação da qualidade de vida (PSN). Foi também utilizada uma ficha sociodemográfica e clínica. Resultados: Analisando as dimensões da qualidade de vida constatamos que os doentes do sexo feminino apresentam scores superiores em todas as dimensões, existindo diferenças estatísticas significativas apenas para o Isolamento Social. Os participantes solteiros revelaram valores médios mais elevados, resultando em diferenças estatisticamente significativas para o Isolamento Social. Os participantes total e severamente dependentes foram os que revelaram médias mais elevadas na maioria das dimensões, com diferenças estatisticamente significativas em todas as dimensões, exceto na Dor. As variáveis idade, influência da residência, habilitações literárias, situação laboral, condições habitacionais, tipo de AVC, tempo de internamento, local da lesão, influência do programa de reabilitação e funcionalidade familiar não revelaram um efeito significativo sobre a qualidade de vida. Conclusão: As evidências encontradas neste estudo fornecem indicadores para uma melhor intervenção junto dos doentes com AVC, de forma a melhorar a sua adaptação e bem-estar, e da sua família, contribuindo para a sua qualidade de vida. Por outro lado, sensibilizou-nos para a importância em ajustar os cuidados específicos de reabilitação às expetativas e necessidades desses indivíduos. Palavras-chave: Acidente Vascular Cerebral, Qualidade de Vida, Reabilitação Funcional.Abstract Background: In Portugal, cerebrovascular accident (CVA) is the leading cause of long-term disability and diminished quality of life. The functional rehabilitation of the patient is one of the basic requirements in the treatment post-CVA. In this context, the objective of the present study is to examine how certain circumstantial, sociodemographic, familiar and clinical variables, the family functionality and functional independence are associated with the quality of life of these patients. Methods: it was made a cross-sectional, descriptive correlacional, quantitative study, in which participated 75 patients, mostly male (53,33%), with a mean age of 68 years old. For the measurement of the variables, were used measuring instruments of acknowledged reliability, measured and validated to the portuguese population: the Familiar Apgar Scale, the Barthel Scale and the Quality of Life Assessment Questionnaire. It was also used a sociodemographic and clinical data sheet. Results: Analyzing the dimensions of quality of life it was found that female patients have higher scores in all dimensions, and there are significant statistical differences only to Social Isolation. Unmarried participants showed higher average values, resulting in significant statistically differences to Social Isolation. The total and severely dependents participants were those who revealed higher average values in most dimensions, with differing slightly significant statistics, very significant and extremely significant in most dimensions, except in Pain. The variables age, influence of residence, qualifications, employment, housing conditions, type of cerebrovascular accident, time of hospitalization, location of the lesion, influence of rehabilitation programme and family functionality did not show a significant effect on the quality of life. Conclusion: The evidence found in this study provide indicators for a better assistance to patients with cerebrovascular accident, in order to improve their well-being and adjustment, and of his family, contributing to their quality of life. On the other hand, moved us to the importance in adjusting the specific rehabilitation cares of these patients’ expectations and needs. Keywords: Cerebrovascular Accident, Quality of Life, Functional Rehabilitation

The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect

In this paper, a two-dimensional cutting problem is considered in which a single plate (large object) has to be cut down into a set of small items of maximal value. As opposed to standard cutting problems, the large object contains a defect, which must not be covered by a small item. The problem is represented by means of an AND/OR-graph, and a Branch & Bound procedure (including heuristic modifications for speeding up the search process) is introduced for its exact solution. The proposed method is evaluated in a series of numerical experiments that are run on problem instances taken from the literature, as well as on randomly generated instances

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice. © 2006 Elsevier Ltd. All rights reserved

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort.Cutting Knapsack problem Column generation Heuristics

A NEW MATHEMATICAL MODEL FOR THE CUTTING STOCK/LEFTOVER PROBLEM

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