883 resultados para Mixed integer models


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This work deals with a problem of mixed integer optimization model applied to production planning of a real world factory that aims for hydraulic hose production. To optimize production planning, a mathematic model of MILP Mixed Integer Linear Programming, so that, along with the Analytic Hierarchy process method, would be possible to create a hierarchical structure of the most import criteria for production planning, thus finding through a solving software the optimum hose attribution to its respective machine. The hybrid modeling of Analytic Hierarchy Process along with Linear Programming is the focus of this work. The results show that using this method we could unite factory reality and quantitative analysis and had success on improving performance of production planning efficiency regarding product delivery and optimization of the production flow

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Optical networks based on passive-star couplers and employing WDM have been proposed for deployment in local and metropolitan areas. These networks suffer from splitting, coupling, and attenuation losses. Since there is an upper bound on transmitter power and a lower bound on receiver sensitivity, optical amplifiers are usually required to compensate for the power losses mentioned above. Due to the high cost of amplifiers, it is desirable to minimize their total number in the network. However, an optical amplifier has constraints on the maximum gain and the maximum output power it can supply; thus, optical amplifier placement becomes a challenging problem. In fact, the general problem of minimizing the total amplifier count is a mixed-integer nonlinear problem. Previous studies have attacked the amplifier-placement problem by adding the “artificial” constraint that all wavelengths, which are present at a particular point in a fiber, be at the same power level. This constraint simplifies the problem into a solvable mixed integer linear program. Unfortunately, this artificial constraint can miss feasible solutions that have a lower amplifier count but do not have the equally powered wavelengths constraint. In this paper, we present a method to solve the minimum amplifier- placement problem, while avoiding the equally powered wavelength constraint. We demonstrate that, by allowing signals to operate at different power levels, our method can reduce the number of amplifiers required.

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Routing and wavelength assignment (RWA) is an important problem that arises in wavelength division multiplexed (WDM) optical networks. Previous studies have solved many variations of this problem under the assumption of perfect conditions regarding the power of a signal. In this paper, we investigate this problem while allowing for degradation of routed signals by components such as taps, multiplexers, and fiber links. We assume that optical amplifiers are preplaced. We investigate the problem of routing the maximum number of connections while maintaining proper power levels. The problem is formulated as a mixed-integer nonlinear program and two-phase hybrid solution approaches employing two different heuristics are developed

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Optical networks based on passive star couplers and employing wavelength-division multiplexing (WDhf) have been proposed for deployment in local and metropolitan areas. Amplifiers are required in such networks to compensate for the power losses due to splitting and attenuation. However, an optical amplifier has constraints on the maximum gain and the maximum output power it can supply; thus optical amplifier placement becomes a challenging problem. The general problem of minimizing the total amplifier count, subject to the device constraints, is a mixed-integer non-linear problem. Previous studies have attacked the amplifier placement problem by adding the “artificial” constraint that all wavelengths, which are present at a particular point in a fiber, be at the same power level. In this paper, we present a method to solve the minimum amplifier- placement problem while avoiding the equally powered- wavelength constraint. We demonstrate that, by allowing signals to operate at different power levels, our method can reduce the number of amplifiers required in several small to medium-sized networks.

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In this paper, we consider the problem of topology design for optical networks. We investigate the problem of selecting switching sites to minimize total cost of the optical network. The cost of an optical network can be expressed as a sum of three main factors: the site cost, the link cost, and the switch cost. To the best of our knowledge, this problem has not been studied in its general form as investigated in this paper. We present a mixed integer quadratic programming (MIQP) formulation of the problem to find the optimal value of the total network cost. We also present an efficient heuristic to approximate the solution in polynomial time. The experimental results show good performance of the heuristic. The value of the total network cost computed by the heuristic varies within 2% to 21% of its optimal value in the experiments with 10 nodes. The total network cost computed by the heuristic for 51% of the experiments with 10 node network topologies varies within 8% of its optimal value. We also discuss the insight gained from our experiments.

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This work deals with a problem of mixed integer optimization model applied to production planning of a real world factory that aims for hydraulic hose production. To optimize production planning, a mathematic model of MILP Mixed Integer Linear Programming, so that, along with the Analytic Hierarchy process method, would be possible to create a hierarchical structure of the most import criteria for production planning, thus finding through a solving software the optimum hose attribution to its respective machine. The hybrid modeling of Analytic Hierarchy Process along with Linear Programming is the focus of this work. The results show that using this method we could unite factory reality and quantitative analysis and had success on improving performance of production planning efficiency regarding product delivery and optimization of the production flow

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This article describes a real-world production planning and scheduling problem occurring at an integrated pulp and paper mill (P&P) which manufactures paper for cardboard out of produced pulp. During the cooking of wood chips in the digester, two by-products are produced: the pulp itself (virgin fibers) and the waste stream known as black liquor. The former is then mixed with recycled fibers and processed in a paper machine. Here, due to significant sequence-dependent setups in paper type changeovers, sizing and sequencing of lots have to be made simultaneously in order to efficiently use capacity. The latter is converted into electrical energy using a set of evaporators, recovery boilers and counter-pressure turbines. The planning challenge is then to synchronize the material flow as it moves through the pulp and paper mills, and energy plant, maximizing customer demand (as backlogging is allowed), and minimizing operation costs. Due to the intensive capital feature of P&P, the output of the digester must be maximized. As the production bottleneck is not fixed, to tackle this problem we propose a new model that integrates the critical production units associated to the pulp and paper mills, and energy plant for the first time. Simple stochastic mixed integer programming based local search heuristics are developed to obtain good feasible solutions for the problem. The benefits of integrating the three stages are discussed. The proposed approaches are tested on real-world data. Our work may help P&P companies to increase their competitiveness and reactiveness in dealing with demand pattern oscillations. (C) 2012 Elsevier Ltd. All rights reserved.

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The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.

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Validity of comparisons between expected breeding values obtained from best linear unbiased prediction procedures in genetic evaluations is dependent on genetic connectedness among herds. Different cattle breeding programmes have their own particular features that distinguish their database structure and can affect connectedness. Thus, the evolution of these programmes can also alter the connectedness measures. This study analysed the evolution of the genetic connectedness measures among Brazilian Nelore cattle herds from 1999 to 2008, using the French Criterion of Admission to the group of Connected Herds (CACO) method, based on coefficients of determination (CD) of contrasts. Genetic connectedness levels were analysed by using simple and multiple regression analyses on herd descriptors to understand their relationship and their temporal trends from the 19992003 to the 20042008 period. The results showed a high level of genetic connectedness, with CACO estimates higher than 0.4 for the majority of them. Evaluation of the last 5-year period showed only a small increase in average CACO measures compared with the first 5 years, from 0.77 to 0.80. The percentage of herds with CACO estimates lower than 0.7 decreased from 27.5% in the first period to 16.2% in the last one. The connectedness measures were correlated with percentage of progeny from connecting sires, and the artificial insemination spread among Brazilian herds in recent years. But changes in connectedness levels were shown to be more complex, and their complete explanation cannot consider only herd descriptors. They involve more comprehensive changes in the relationship matrix, which can be only fully expressed by the CD of contrasts.

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Background. The intrafamilial dynamics of endemic infection with human herpesvirus type 8 (HHV-8) in Amerindian populations is unknown. Methods. Serum samples were obtained from 517 Amerindians and tested for HHV-8 anti-latent nuclear antigen (anti-LANA) and antilytic antibodies by immunofluorescence assays. Logistic regression and mixed logistic models were used to estimate the odds of being HHV-8 seropositive among intrafamilial pairs. Results. HHV-8 seroprevalence by either assay was 75.4% (95% confidence interval [CI]: 71.5%-79.1%), and it was age-dependent (P-trend<.001). Familial dependence in HHV-8 seroprevalence by either assay was found between mother-offspring (odds ratio [OR], 5.44; 95% CI: 1.62-18.28) and siblings aged >= 10 years (OR 4.42, 95% CI: 1.70-11.45) or siblings in close age range (<5 years difference) (OR 3.37, 95% CI: 1.21-9.40), or in families with large (>4) number of siblings (OR, 3.20, 95% CI: 1.33-7.67). In separate analyses by serological assay, there was strong dependence in mother-offspring (OR 8.94, 95% CI: 2.94-27.23) and sibling pairs aged >= 10 years (OR, 11.91, 95% CI: 2.23-63.64) measured by LANA but not lytic antibodies. Conclusions. This pattern of familial dependence suggests that, in this endemic population, HHV-8 transmission mainly occurs from mother to offspring and between close siblings during early childhood, probably via saliva. The mother to offspring dependence was derived chiefly from anti-LANA antibodies.

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In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented. These cuts are based on feasible and infeasible master problem solutions generated by means of a heuristic. This article includes general guidelines and a case study with a fixed charge network design problem. Computational tests with instances of this problem show the efficiency of the strategy. The most important aspect of the proposed ideas is their generality, which allows them to be used in virtually any Benders decomposition implementation.

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This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatorial optimization problems are widely spread in everyday life and the need of solving difficult problems is more and more urgent. Metaheuristic techniques have been developed in the last decades to effectively handle the approximate solution of combinatorial optimization problems; we will examine metaheuristics in detail, focusing on the common aspects of different techniques. Each metaheuristic approach possesses its own peculiarities in designing and guiding the solution process; our work aims at recognizing components which can be extracted from metaheuristic methods and re-used in different contexts. In particular we focus on the possibility of porting metaheuristic elements to constraint programming based environments, as constraint programming is able to deal with feasibility issues of optimization problems in a very effective manner. Moreover, CP offers a general paradigm which allows to easily model any type of problem and solve it with a problem-independent framework, differently from local search and metaheuristic methods which are highly problem specific. In this work we describe the implementation of the Local Branching framework, originally developed for Mixed Integer Programming, in a CP-based environment. Constraint programming specific features are used to ease the search process, still mantaining an absolute generality of the approach. We also propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing CP-based tree search and encloses concepts from metaheuristic techniques. SNS can be used as a stand alone search strategy, but it can alternatively be embedded in existing strategies as intensification and diversification mechanism. In particular we show its integration within the CP-based local branching. We provide an extensive experimental evaluation of the proposed approaches on instances of the Asymmetric Traveling Salesman Problem and of the Asymmetric Traveling Salesman Problem with Time Windows. The proposed approaches achieve good results on practical size problem, thus demonstrating the benefit of integrating metaheuristic concepts in CP-based frameworks.

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The research for exact solutions of mixed integer problems is an active topic in the scientific community. State-of-the-art MIP solvers exploit a floating- point numerical representation, therefore introducing small approximations. Although such MIP solvers yield reliable results for the majority of problems, there are cases in which a higher accuracy is required. Indeed, it is known that for some applications floating-point solvers provide falsely feasible solutions, i.e. solutions marked as feasible because of approximations that would not pass a check with exact arithmetic and cannot be practically implemented. The framework of the current dissertation is SCIP, a mixed integer programs solver mainly developed at Zuse Institute Berlin. In the same site we considered a new approach for exactly solving MIPs. Specifically, we developed a constraint handler to plug into SCIP, with the aim to analyze the accuracy of provided floating-point solutions and compute exact primal solutions starting from floating-point ones. We conducted a few computational experiments to test the exact primal constraint handler through the adoption of two main settings. Analysis mode allowed to collect statistics about current SCIP solutions' reliability. Our results confirm that floating-point solutions are accurate enough with respect to many instances. However, our analysis highlighted the presence of numerical errors of variable entity. By using the enforce mode, our constraint handler is able to suggest exact solutions starting from the integer part of a floating-point solution. With the latter setting, results show a general improvement of the quality of provided final solutions, without a significant loss of performances.

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Objective  Malnutrition is common in HIV-infected children in Africa and an indication for antiretroviral treatment (ART). We examined anthropometric status and response to ART in children treated at a large public-sector clinic in Malawi. Methods  All children aged <15 years who started ART between January 2001 and December 2006 were included and followed until March 2008. Weight and height were measured at regular intervals from 1 year before to 2 years after the start of ART. Sex- and age-standardized z-scores were calculated for weight-for-age (WAZ) and height-for-age (HAZ). Predictors of growth were identified in multivariable mixed-effect models. Results  A total of 497 children started ART and were followed for 972 person-years. Median age (interquartile range; IQR) was 8 years (4–11 years). Most children were underweight (52% of children), stunted (69%), in advanced clinical stages (94% in WHO stages 3 or 4) and had severe immunodeficiency (77%). After starting ART, median (IQR) WAZ and HAZ increased from −2.1 (−2.7 to −1.3) and −2.6 (−3.6 to −1.8) to −1.4 (−2.1 to −0.8) and −1.8 (−2.4 to −1.1) at 24 months, respectively (P < 0.001). In multivariable models, baseline WAZ and HAZ scores were the most important determinants of growth trajectories on ART. Conclusions  Despite a sustained growth response to ART among children remaining on therapy, normal values were not reached. Interventions leading to earlier HIV diagnosis and initiation of treatment could improve growth response.