On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

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 Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness. (C) 2009 Elsevier B.V. All rights reserved.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

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. (C) 2011 Elsevier BM. All rights reserved.

Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular two dimensional polygons inside a two dimensional container. This problem is approached with an heuristic based on simulated annealing. Traditional 14 external penalization"" techniques are avoided through the application of the no-fit polygon, that determinates the collision free area for each polygon before its placement. The simulated annealing controls: the rotation applied, the placement and the sequence of placement of the polygons. For each non placed polygon, a limited depth binary search is performed to find a scale factor that when applied to the polygon, would allow it to be fitted in the container. It is proposed a crystallization heuristic, in order to increase the number of accepted solutions. The bottom left and larger first deterministic heuristics were also studied. The proposed process is suited for non convex polygons and containers, the containers can have holes inside. (C) 2009 Elsevier Ltd. All rights reserved.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by 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.

Merluccius hubbsi (Teleostei: Merlucciidae): stock identification based on reproductive biology in the south-southeast brazilian region

The Argentine hake, Merluccius hubbsi, a demersal-pelagic species found from Rio de Janeiro, Brazil to the Tierra del Fuego, Argentina, has become an important target of the Brazilian bottom-trawler fleet since 2001. Earlier studies focusing on the species have suggested that more than one stock might occur off the Brazilian coast, in accordance with environmental features. In order to evaluate this hypothesis, fish were collected from four different areas in the Brazilian waters in which the hake is distributed, during the summers and winters of 1996-2001 and 2004, the females being used to analyze and compare spatial-temporal variations in ovarian maturation. Gonad indexes were also applied for the same purpose. Results indicate a north-south spawning gradient occurring as from summer at around 21°S to winter near 34°S, leading to the identification of two distinct stocks: one located between 21°S and 29°S (Southeastern stock) and the other between 29°S and 34°S (Southern stock), this latter shared with Uruguay and Argentina. Brazilian stocks present clear signs of overexploitation, the situation calling for an urgent solution.

Nutritional characteristics and in vitro digestibility of silages from different corn cultivars harvested at two cutting heights

The objective of this study was to evaluate the nutritional traits and in vitro digestibility of silages from different corn cultivars harvested at two cutting heights. It was evaluated 11 cultivars (Dina 766, Dina 657, Dina 1000, P 3021, P 3041, C 805, C 333, AG 5011, FO 01, Dina co 9621 and BR 205) harvest 5 cm above ground (low) and 5 cm below the intersection of the first ear (high). It was used a random block design (three blocks), arranged in a 11 × 2 factorial scheme. Silages from plants harvested at high cutting height presented average content of dry matter significantly superior to silages from plants harvested at low height. Cultivars FO 01, AG 5011, Dina co 9621 and Dina 766 presented greater content of crude protein than cultivars C 805, P 3041 and P 3021, which presented the lowest contents of this nutrient. The raise in the cut height increased in vitro dry matter true digestibility coefficients and in vitro dry matter digestibility of silage evaluated. The increase in cut height improved nutritive value of silages by decreasing concentrations of fibrous fractions and increasing in vitro dry matter digestibility.

Evaluation of corn cultivars harvested at two cutting heights for ensilage

The objective of this study was to evaluate the agronomic characteristics, bromatological-chemical composition and digestibility of 11 corn cultivars (Zea mays) harvested at two cutting heights. Cultivars D 766, D 657, D 1000, P 3021, P 3041, C 805, C 333, AG 5011, FO 01, CO 9621 and BR 205 were evaluated when they were harvested 5 cm above ground (low) and 5 cm below the insertion of the first ear (high). The experiment was designed as random blocks, with three replicates, arranged in an 11 x 2 factorial scheme. Cultivars presented similar productions of forage dry matter and grains. Percentages of stalk, leaf, straw, cob and kernel fractions were different among cultivars, as well as dry matter content of the whole plant at harvest. Considering the whole plant, only the contents of gross energy, nitrogen in neutral detergent fiber, and in vitro neutral and acid detergent fiber digestibility did not differ among cultivars. Increase on the cutting height improved forage quality due to the reduction of stalk and leaf fractions and contents of cell wall constituents.

A hepcidina como parâmetro bioquímico na avaliação da anemia por deficiência de ferro

A anemia por deficiência de ferro caracteriza-se como o mais prevalente problema nutricional em todo o mundo. Nesta revisão reuniu-se informações a respeito do metabolismo da hepcidina, avaliando-se seu valor como parâmetro bioquímico na anemia por deficiência de ferro. Realizou-se um levantamento bibliográfico nas bases de dados PUBMED e LILACS, período 2006-2010, referentes à hepcidina como um biomarcador para a regulação do metabolismo do ferro. Foram localizados 35 estudos publicados em revistas internacionais e um estudo sobre o assunto em revista nacional. A produção de hepcidina é regulada homeostaticamente pela anemia e hipóxia. Quando a oferta de oxigênio está inadequada ocorre diminuição do nível de hepcidina. Consequentemente, maior quantidade de ferro proveniente da dieta e dos estoques dos macrófagos e hepatócitos se tornam disponíveis. A hepcidina possui a função de se ligar à ferroportina, regulando a liberação do ferro para o plasma. Quando as concentrações de hepcidina estão baixas, as moléculas de ferroportina são expostas na membrana plasmática e liberam o ferro. Quando os níveis de hepcidina aumentam, a hepcidina liga-se às moléculas de ferroportina induzindo sua internalização e degradação, e o ferro liberado diminui progressivamente. Aparentemente o desenvolvimento do diagnóstico e terapia da anemia baseados no bioindicador hepcidina pode oferecer uma abordagem mais efetiva. Estudos epidemiológicos são necessários para comprovar o valor da hepcidina no diagnóstico diferencial das anemias, incluindo protocolos de amostragem para análise, com padronização similar às utilizadas em outras avaliações bioquímicas, e estabelecimento de pontos de corte para a expressão urinária e plasmática desse peptídeo

Herbage accumulation, growth and structural characteristics of Mombasa grass (Panicum maximum Jacq.) harvested at different cutting intervals

The objective of the present study was to evaluate herbage accumulation, morphological composition, growth rate and structural characteristics in Mombasa grass swards subject to different cutting intervals (3, 5 and 7 wk) during the rainy and dry seasons of the year. Treatments were assigned to experimental units (17.5 m(2)) according to a complete randomised block design, with four replicates. Herbage accumulation was greater in the rainy than in the dry season (83 and 17%, respectively). Herbage accumulation (24,300 kg DM ha(-1)), average growth rate (140 kg DM ha(-1) d(-1)) and sward height (111 cm) were highest in the 7 wk cutting interval, but leaf proportion (56%), leaf:stem (1.6) and leaf:non leaf (1.3) ratios decreased. Herbage accumulation, morphological composition and sward structure of Mombasa grass sward may be manipulated through defoliation frequency. The highest leaf proportion was recorded in the 3-wk cutting interval. Longer cutting intervals affected negatively sward structure, with potential negative effects on utilization efficiency, animal intake and performance.

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.