Algoritmo tabu search especializado para o problema de planejamento da expansao de sistemas de transmissão

Pós-graduação em Engenharia Elétrica - FEIS

Reconfiguração de sistemas de distribuição operando em vários níveis de demanda através de uma meta-heurística de busca em vizinhança variável

Pós-graduação em Engenharia Elétrica - FEIS

Uma proposta de sequência didática para o ensino de Programação Linear no Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Reactive power planning under conditional-value-at-risk assessment using chance-constrained optimisation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelo de programação não-linear para otimização do padrão de cultivo e retorno financeiro em áreas irrigadas

Pós-graduação em Agronomia (Irrigação e Drenagem) - FCA

Integrated pulp and paper mill planning and scheduling

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.

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

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.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

A bayesian model for mixed responses and skew laten variable to measure HRQoL in children

The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Patient classification system: An integrated method for measuring nursing intensity and optimizing resource allocation

A patient classification system was developed integrating a patient acuity instrument with a computerized nursing distribution method based on a linear programming model. The system was designed for real-time measurement of patient acuity (workload) and allocation of nursing personnel to optimize the utilization of resources.^ The acuity instrument was a prototype tool with eight categories of patients defined by patient severity and nursing intensity parameters. From this tool, the demand for nursing care was defined in patient points with one point equal to one hour of RN time. Validity and reliability of the instrument was determined as follows: (1) Content validity by a panel of expert nurses; (2) predictive validity through a paired t-test analysis of preshift and postshift categorization of patients; (3) initial reliability by a one month pilot of the instrument in a practice setting; and (4) interrater reliability by the Kappa statistic.^ The nursing distribution system was a linear programming model using a branch and bound technique for obtaining integer solutions. The objective function was to minimize the total number of nursing personnel used by optimally assigning the staff to meet the acuity needs of the units. A penalty weight was used as a coefficient of the objective function variables to define priorities for allocation of staff.^ The demand constraints were requirements to meet the total acuity points needed for each unit and to have a minimum number of RNs on each unit. Supply constraints were: (1) total availability of each type of staff and the value of that staff member (value was determined relative to that type of staff's ability to perform the job function of an RN (i.e., value for eight hours RN = 8 points, LVN = 6 points); (2) number of personnel available for floating between units.^ The capability of the model to assign staff quantitatively and qualitatively equal to the manual method was established by a thirty day comparison. Sensitivity testing demonstrated appropriate adjustment of the optimal solution to changes in penalty coefficients in the objective function and to acuity totals in the demand constraints.^ Further investigation of the model documented: correct adjustment of assignments in response to staff value changes; and cost minimization by an addition of a dollar coefficient to the objective function. ^

An MBLP model for scheduling assessment centers

Firms aim at assigning qualified and motivated people to jobs. Human resources managers often conduct assessment centers before making such personnel decisions. By means of an assessment center, the potential and skills of job applicants can be assessed more objectively. For the scheduling of such assessment centers, we present a formulation as a mixed-binary linear program and report on computational results for four real-life examples.

An MILP-based heuristic for staff scheduling problems with acceptance levels

We present a real-world staff-assignment problem that was reported to us by a provider of an online workforce scheduling software. The problem consists of assigning employees to work shifts subject to a large variety of requirements related to work laws, work shift compatibility, workload balancing, and personal preferences of employees. A target value is given for each requirement, and all possible deviations from these values are associated with acceptance levels. The objective is to minimize the total number of deviations in ascending order of the acceptance levels. We present an exact lexicographic goal programming MILP formulation and an MILP-based heuristic. The heuristic consists of two phases: in the first phase a feasible schedule is built and in the second phase parts of the schedule are iteratively re-optimized by applying an exact MILP model. A major advantage of such MILP-based approaches is the flexibility to account for additional constraints or modified planning objectives, which is important as the requirements may vary depending on the company or planning period. The applicability of the heuristic is demonstrated for a test set derived from real-world data. Our computational results indicate that the heuristic is able to devise optimal solutions to non-trivial problem instances, and outperforms the exact lexicographic goal programming formulation on medium- and large-sized problem instances.