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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Towards an intelligent graphical interface for linear programming modelling

The increase of computing power of the microcomputers has stimulated the building of direct manipulation interfaces that allow graphical representation of Linear Programming (LP) models. This work discusses the components of such a graphical interface as the basis for a system to assist users in the process of formulating LP problems. In essence, this work proposes a methodology which considers the modelling task as divided into three stages which are specification of the Data Model, the Conceptual Model and the LP Model. The necessity for using Artificial Intelligence techniques in the problem conceptualisation and to help the model formulation task is illustrated.

Optimality conditions for pareto nonsmooth nonconvex programming in banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush-Kuhn-Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

A new solution to the optimal power flow problem

A new approach to solving the Optimal Power Flow problem is described, making use of some recent findings, especially in the area of primal-dual methods for complex programming. In this approach, equality constraints are handled by Newton's method inequality constraints for voltage and transformer taps by the logarithmic barrier method and the other inequality constraints by the augmented Lagrangian method. Numerical test results are presented, showing the effective performance of this algorithm. © 2001 IEEE.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Modified barrier method for optimal power flow problem

In this paper is presented a new approach for optimal power flow problem. This approach is based on the modified barrier function and the primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first-order necessary conditions for optimality are fulfilled by Newton's method, and by updating the barrier terms. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus, IEEE118-bus and IEEE162-bus systems.

A nonlinear model for the long-term hydro-thermal generation scheduling problem over multiple areas with transmission constraints

This paper presents a nonlinear model with individual representation of plants for the centralized long-term hydrothermal scheduling problem over multiple areas. In addition to common aspects of long-term scheduling, this model takes transmission constraints into account. The ability to optimize hydropower exchange among multiple areas is important because it enables further minimization of complementary thermal generation costs. Also, by considering transmission constraints for long-term scheduling, a more precise coupling with shorter horizon schedules can be expected. This is an important characteristic from both operational and economic viewpoints. The proposed model is solved by a sequential quadratic programming approach in the form of a prototype system for different case studies. An analysis of the benefits provided by the model is also presented. ©2009 IEEE.

Optimal reactive power dispatch using stochastic chance-constrained programming

Deterministic Optimal Reactive Power Dispatch problem has been extensively studied, such that the demand power and the availability of shunt reactive power compensators are known and fixed. Give this background, a two-stage stochastic optimization model is first formulated under the presumption that the load demand can be modeled as specified random parameters. A second stochastic chance-constrained model is presented considering uncertainty on the demand and the equivalent availability of shunt reactive power compensators. Simulations on six-bus and 30-bus test systems are used to illustrate the validity and essential features of the proposed models. This simulations shows that the proposed models can prevent to the power system operator about of the deficit of reactive power in the power system and suggest that shunt reactive sourses must be dispatched against the unavailability of any reactive source. © 2012 IEEE.

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

The usable leftover one-dimensional cutting stock problem-a priority-in-use heuristic

We consider a one-dimensional cutting stock problem in which the material not used in the cutting patterns, if large enough, is kept for use in the future. Moreover, it is assumed that leftovers should not remain in stock for a long time, hence, such leftovers have priority-in-use compared to standard objects (objects bought by the industry) in stock. A heuristic procedure is proposed for this problem, and its performance is analyzed by solving randomly generated dynamic instances where successive problems are solved in a time horizon. For each period, new demands arise and a new problem is solved on the basis of the information about the stock of the previous periods (remaining standard objects in the stock) and usable leftovers generated during those previous periods. The computational experiments show that the solutions presented by the proposed heuristic are better than the solutions obtained by other heuristics from the literature. © 2012 The Authors. International Transactions in Operational Research © 2012 International Federation of Operational Research Societies.

A hybrid multi-population genetic algorithm applied to solve the multi-level capacitated lot sizing problem with backlogging

The present paper proposes a new hybrid multi-population genetic algorithm (HMPGA) as an approach to solve the multi-level capacitated lot sizing problem with backlogging. This method combines a multi-population based metaheuristic using fix-and-optimize heuristic and mathematical programming techniques. A total of four test sets from the MULTILSB (Multi-Item Lot-Sizing with Backlogging) library are solved and the results are compared with those reached by two other methods recently published. The results have shown that HMPGA had a better performance for most of the test sets solved, specially when longer computing time is given. © 2012 Elsevier Ltd.

Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Goal Programming (GP) is an important analytical approach devised to solve many realworld problems. The first GP model is known as Weighted Goal Programming (WGP). However, Multi-Choice Aspirations Level (MCAL) problems cannot be solved by current GP techniques. In this paper, we propose a Multi-Choice Mixed Integer Goal Programming model (MCMI-GP) for the aggregate production planning of a Brazilian sugar and ethanol milling company. The MC-MIGP model was based on traditional selection and process methods for the design of lots, representing the production system of sugar, alcohol, molasses and derivatives. The research covers decisions on the agricultural and cutting stages, sugarcane loading and transportation by suppliers and, especially, energy cogeneration decisions; that is, the choice of production process, including storage stages and distribution. The MCMIGP allows decision-makers to set multiple aspiration levels for their problems in which the more/higher, the better and the less/lower, the better in the aspiration levels are addressed. An application of the proposed model for real problems in a Brazilian sugar and ethanol mill was conducted; producing interesting results that are herein reported and commented upon. Also, it was made a comparison between MCMI GP and WGP models using these real cases. © 2013 Elsevier Inc.

The integrated lot sizing and cutting stock problem in a furniture factory

This work studies the integrated lot sizing and cutting stock problem, where the goal is to capture the dependency that exists between two important decisions in the production process, in order to economize raw materials and also reduce production and inventory costs. The integrated lot sizing and cutting stock problem is studied in a small furniture factory that produces wardrobes, dressing tables and cupboards and the lot sizing and cutting stock decisions are taken by the production manager. A column-generation technique is used to solve a linear relaxation of the proposed model. The computational results, using real data from the factory, show that it is possible to reduce total inventory and raw material costs when integrated planning is used. © 2013 IFAC.

A Fuzzy Goal Programming model for solving aggregate production-planning problems under uncertainty: A case study in a Brazilian sugar mill

This paper proposes a Fuzzy Goal Programming model (FGP) for a real aggregate production-planning problem. To do so, an application was made in a Brazilian Sugar and Ethanol Milling Company. The FGP Model depicts the comprehensive production process of sugar, ethanol, molasses and derivatives, and considers the uncertainties involved in ethanol and sugar production. Decision-makings, related to the agricultural and logistics phases, were considered on a weekly-basis planning horizon to include the whole harvesting season and the periods between harvests. The research has provided interesting results about decisions in the agricultural stages of cutting, loading and transportation to sugarcane suppliers and, especially, in milling decisions, whose choice of production process includes storage and logistics distribution. (C)2014 Elsevier B.V. All rights reserved.