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.

Mathematical tool to size rural digesters

Os biodigestores têm sido objetos de grande destaque devido a atual crise de energia e conseqüente busca de fontes alternativas. Outro fator que coloca os biodigestores em evidência é o intenso processo de modernização da agropecuária, que além da grande demanda de energia, produz um volume de resíduos animais e de culturas, que ocasiona muitas vezes problemas de ordem sanitária. O objetivo deste trabalho é fornecer uma ferramenta matemática para determinação de parâmetros para projetos de construção de biodigestores rurais, levando-se em consideração o atendimento de necessidades energéticas, obedecendo os dimensionamentos dos sistemas, fatores de rendimento e garantindo a funcionalidade. Para isto, foram formulados modelos de otimização não lineares, de fácil resolução, para os três principais tipos de biodigestores rurais. Com a resolução destes modelos são determinados a altura e o diâmetro que levem a um volume mínimo para cada tipo, com isto reduz-se a quantidade necessária de materiais de alvenaria e consequentemente o custo do biodigestor é diminuído.

Optimum design of microirrigation systems in sloping lands

When an area to be irrigated has a high slope gradient in the manifold line direction, an option is to use a tapered pipeline to economize on pipe costs and to keep pressure head variations within desired limits. The objective of this paper is to develop a linear optimization model to design a microirrigation system with tapered, downhill manifold lines, minimizing the equivalent annual cost of the hydraulic network and the annual pumping cost, and maximizing the emission uniformity previously established to the subunit. The input data are irrigation system layout, cost of all hydraulic network components, and electricity price. The output data are equivalent annual cost, pipeline diameter in each line of the system, pressure head in each node, and total operating pressure head. To illustrate its capability, the model is applied in a citrus orchard in Sao, Paulo State, Brazil, considering slopes of 3, 6, and 9%. The model proved to be efficient in the design of the irrigation system in terms of the emission uniformity desired.

Optimal charging of electric vehicles considering constraints of the medium voltage distribution network

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

Carregamento ótimo de veículos elétricos considerando as restrições das redes de distribuição de média tensão

Pós-graduação em Engenharia Elétrica - FEIS

Metaheurísticas em um problema de rotação de culturas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fluxo de potência ótimo em sistemas multimercados através de um algorítmo evolutivo multiobjetivo

Pós-graduação em Engenharia Elétrica - FEIS

Localização e preço de contrato ótimo da geração distribuída em sistemas de distribuição radiais de energia elétrica

Pós-graduação em Engenharia Elétrica - FEIS

Design and management optimization of trickle irrigation systems using non-linear programming

A non-linear model is presented which optimizes the lay-out, as well as the design and management of trickle irrigation systems, to achieve maximum net benefit. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. It can be applied to rectangular shaped fields, with uniform or zero slope. The software used is the Gams-Minos package. The basic inputs are the crop-water-production function, the cost function and cost of system components, and design variables. The main outputs are the annual net benefit and pipe diameters and lengths. To illustrate the capability of the model, a sensitivity analysis of the annual net benefit for a citrus field is evaluated with respect to irrigated area, ground slope, micro-sprinkler discharge and shape of the field. The sensitivity analysis suggests that the greatest benefit is obtained with the smallest microsprinkler discharge, the greatest area, a square field and zero ground slope. The costs of the investment and energy are the components of the objective function that had the greatest effect in the 120 situations evaluated. (C) 1996 Academic Press Limited

Distribuição da carga hidráulica em linhas de derivação otimizadas por programação linear

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Study of the potentiometric response of the doped spinel Li1.05Al0.02Mn1.98O4 for the optimization of a selective lithium ion sensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Design of a control system using linear matrix inequalities for the active vibration control of a plate

The study of algorithms for active vibration control in smart structures is an area of interest, mainly due to the demand for better performance of mechanical systems, such as aircraft and aerospace structures. Smart structures, formed using actuators and sensors, can improve the dynamic performance with the application of several kinds of controllers. This article describes the application of a technique based on linear matrix inequalities (LMI) to design an active control system. The positioning of the actuators, the design of a robust state feedback controller and the design of an observer are all achieved using LMI. The following are considered in the controller design: limited actuator input, bounded output (energy) and robustness to parametric uncertainties. Active vibration control of a flat plate is chosen as an application example. The model is identified using experimental data by an eigensystem realization algorithm (ERA) and the placement of the two piezoelectric actuators and single sensor is determined using a finite element model (FEM) and an optimization procedure. A robust controller for active damping is designed using an LMI framework, and a reduced model with observation and control spillover effects is implemented using a computer. The simulation results demonstrate the efficacy of the approach, and show that the control system increases the damping in some of the modes.

Game theory in sugarcane crop residue and available energy optimization

This work proposes a mathematical model to aid variety selection and planting quantity of sugarcane in order to reduce crop residues, maximize energy generated by this residue, and satisfy all the supply of the mill. We propose Linear Programming with two objective. The conflict between these objectives allows the use of the Nonzero-sum Game Theory. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

Heterogeneity correction in the construction of optimized planning in radiotherapy using linear programming

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