Heuristics for the one-dimensional cutting stock problem with limited multiple stock lengths

This paper deals with the classical one-dimensional integer cutting stock problem, which consists of cutting a set of available stock lengths in order to produce smaller ordered items. This process is carried out in order to optimize a given objective function (e.g., minimizing waste). Our study deals with a case in which there are several stock lengths available in limited quantities. Moreover, we have focused on problems of low demand. Some heuristic methods are proposed in order to obtain an integer solution and compared with others. The heuristic methods are empirically analyzed by solving a set of randomly generated instances and a set of instances from the literature. Concerning the latter. most of the optimal solutions of these instances are known, therefore it was possible to compare the solutions. The proposed methods presented very small objective function value gaps. (C) 2008 Elsevier Ltd. All rights reserved.

A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

Work disability remains a major problem in rheumatoid arthritis in the 2000s: data from 32 countries in the QUEST-RA Study

Introduction: Work disability is a major consequence of rheumatoid arthritis (RA), associated not only with traditional disease activity variables, but also more significantly with demographic, functional, occupational, and societal variables. Recent reports suggest that the use of biologic agents offers potential for reduced work disability rates, but the conclusions are based on surrogate disease activity measures derived from studies primarily from Western countries. Methods: The Quantitative Standard Monitoring of Patients with RA (QUEST-RA) multinational database of 8,039 patients in 86 sites in 32 countries, 16 with high gross domestic product (GDP) (>24K US dollars (USD) per capita) and 16 low-GDP countries (<11K USD), was analyzed for work and disability status at onset and over the course of RA and clinical status of patients who continued working or had stopped working in high-GDP versus low-GDP countries according to all RA Core Data Set measures. Associations of work disability status with RA Core Data Set variables and indices were analyzed using descriptive statistics and regression analyses. Results: At the time of first symptoms, 86% of men (range 57%-100% among countries) and 64% (19%-87%) of women <65 years were working. More than one third (37%) of these patients reported subsequent work disability because of RA. Among 1,756 patients whose symptoms had begun during the 2000s, the probabilities of continuing to work were 80% (95% confidence interval (CI) 78%-82%) at 2 years and 68% (95% CI 65%-71%) at 5 years, with similar patterns in high-GDP and low-GDP countries. Patients who continued working versus stopped working had significantly better clinical status for all clinical status measures and patient self-report scores, with similar patterns in high-GDP and low-GDP countries. However, patients who had stopped working in high-GDP countries had better clinical status than patients who continued working in low-GDP countries. The most significant identifier of work disability in all subgroups was Health Assessment Questionnaire (HAQ) functional disability score. Conclusions: Work disability rates remain high among people with RA during this millennium. In low-GDP countries, people remain working with high levels of disability and disease activity. Cultural and economic differences between societies affect work disability as an outcome measure for RA.

An analytical approach to the dwarf galaxies cusp problem

Aims. An analytical solution for the discrepancy between observed core-like profiles and predicted cusp profiles in dark matter halos is studied. Methods. We calculate the distribution function for Navarro-Frenk-White halos and extract energy from the distribution, taking into account the effects of baryonic physics processes. Results. We show with a simple argument that we can reproduce the evolution of a cusp to a flat density profile by a decrease of the initial potential energy.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Stress and coping in older people with Alzheimer`s disease

To investigate stress intensity and coping style in older people with mild Alzheimer`s disease. The potential risk assessment of a stress event and the devising of coping strategies are dependent on cognitive function. Although older individuals with Alzheimer`s disease present significant cognitive impairment, little is known about how these individuals experience stress events and select coping strategies in stress situations. Survey. A convenient sample of 30 cognitively healthy older people and 30 individuals with mild Alzheimer`s disease were given an assessment battery of stress indicators (Symptom Stress List, Cornell Scale for Depression in Dementia, State-Trait Anxiety Inventory), coping style (Jalowiec Coping Scale) and cognitive performance (mini-mental state exam) were applied in both groups. Statistical analysis of the data employed the Mann-Whitney test to compare medians of stress indicators and coping style, Fischer`s exact test to compare proportions when expected frequencies were lower than five, and Spearman`s correlation coefficient to verify correlation between coping style and cognitive performance. Both groups suffered from the same stress intensity (p = 0.254). Regarding coping styles, although differences were not statistically significant (p = 0.124), emotion-oriented coping was predominant in the patients with Alzheimer`s disease. However, those individuals displaying better cognitive performance in the Alzheimer`s disease group had selected coping strategies focused on problem solving (p = 0.0074). Despite a tendency for older people with Alzheimer`s disease to select escape strategies and emotional control, rather than attempting to resolve or lesser the consequences arising from a problem, coping ultimately depends on cognitive performance of the individual. The findings of this study provide information and data to assist planning of appropriate support care for individuals with Alzheimer`s disease who experience stress situations, based on their cognitive performance.

Street children and their relationship with the police

Background: This paper explores and analyses the experiences of school-age street children. It specifically addresses the relationship of the street children who live on the streets of Sao Paulo (a large Brazilian metropolis), in relation to their experiences, with the policemen. Methods: The paper is a secondary analysis of date previously collected in 1999. The data were collected through individual semi-structured interviews, with 14 school-age children frequenting two city public refuges, with their legal guardians` consent. The text from transcribed interviews was organized according to the validity norms of `thematic analysis`, a technique of contents analysis method. The decomposing and reconstructing process of that analysis gave rise to thematic categories (among which `the police category`) that represented the reconstruction of the difficulties faced by the children in their development. Results and discussion: The children portrayed the police as an enemy, a fearful figure and one of the most agonizing street experiences. Rarely did the police have a positive image to them. According to the children, police violence occurs in three forms: through systematic police persecution in an effort to remove the children from the streets against their will; actions that had the deliberate intent to humiliate them with verbal or physical aggression; and through alleged sexual abuse, revealed by the children in a veiled manner. The authority that is supposedly intended to protect them is portrayed as one of the most feared social agents. Conclusion: The reported hostile behaviour of the policemen shows the state of vulnerability of those children living on the street. This situation must be focused like a health problem because it causes injury to development of children. Nurses can help them through organizing assistance to children in situation of personal and social risk in the school nursing and health institution.

Ecodesign methods focused on remanufacturing

Understanding the product`s `end-of-life` is important to reduce the environmental impact of the products` final disposal. When the initial stages of product development consider end-of-life aspects, which can be established by ecodesign (a proactive approach of environmental management that aims to reduce the total environmental impact of products), it becomes easier to close the loop of materials. The `end-of-life` ecodesign methods generally include more than one `end-of-life` strategy. Since product complexity varies substantially, some components, systems or sub-systems are easier to be recycled, reused or remanufactured than others. Remanufacture is an effective way to maintain products in a closed-loop, reducing both environmental impacts and costs of the manufacturing processes. This paper presents some ecodesign methods focused on the integration of different `end-of-life` strategies, with special attention to remanufacturing, given its increasing importance in the international scenario to reduce the life cycle impacts of products. (C) 2009 Elsevier Ltd. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

A reference business process for ecological niche modelling

Ecological niche modelling combines species occurrence points with environmental raster layers in order to obtain models for describing the probabilistic distribution of species. The process to generate an ecological niche model is complex. It requires dealing with a large amount of data, use of different software packages for data conversion, for model generation and for different types of processing and analyses, among other functionalities. A software platform that integrates all requirements under a single and seamless interface would be very helpful for users. Furthermore, since biodiversity modelling is constantly evolving, new requirements are constantly being added in terms of functions, algorithms and data formats. This evolution must be accompanied by any software intended to be used in this area. In this scenario, a Service-Oriented Architecture (SOA) is an appropriate choice for designing such systems. According to SOA best practices and methodologies, the design of a reference business process must be performed prior to the architecture definition. The purpose is to understand the complexities of the process (business process in this context refers to the ecological niche modelling problem) and to design an architecture able to offer a comprehensive solution, called a reference architecture, that can be further detailed when implementing specific systems. This paper presents a reference business process for ecological niche modelling, as part of a major work focused on the definition of a reference architecture based on SOA concepts that will be used to evolve the openModeller software package for species modelling. The basic steps that are performed while developing a model are described, highlighting important aspects, based on the knowledge of modelling experts. In order to illustrate the steps defined for the process, an experiment was developed, modelling the distribution of Ouratea spectabilis (Mart.) Engl. (Ochnaceae) using openModeller. As a consequence of the knowledge gained with this work, many desirable improvements on the modelling software packages have been identified and are presented. Also, a discussion on the potential for large-scale experimentation in ecological niche modelling is provided, highlighting opportunities for research. The results obtained are very important for those involved in the development of modelling tools and systems, for requirement analysis and to provide insight on new features and trends for this category of systems. They can also be very helpful for beginners in modelling research, who can use the process and the experiment example as a guide to this complex activity. (c) 2008 Elsevier B.V. All rights reserved.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.