On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Testing the gravity p-median model empirically

Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Organização e gerenciamento de frota e terminais em empresas de transporte de carga através de modelos de pesquisa operacional

Este trabalho discute a aplicação de modelos de Pesquisa Operacional como base para o gerenciamento de operações e análise de tecnologias em empresa de transporte de carga. Inicialmente, busca-se contextualizar o escopo deste trabalho dentro do ambiente competitivo atual a fim de que sejam percebidas as conexões entre os sistemas de operações vigentes e os modelos apresentados. Também é feita uma discussão preliminar do conceito de logística, visto que este enseja uma série de acepções para o termo. Em seguida é apresentada uma revisão de algumas ferramentas de modelagem que usualmente são aplicadas a problemas de suprimento, distribuição e transbordo de produtos. Com base nesta revisão é proposta uma abordagem hierarquizada para o tratamento de problemas de logística. Um estudo de caso realizado em uma empresa de transporte de carga busca então aplicar algumas ferramentas de Pesquisa Operacional nos diversos níveis de gerenciamento de operações. Por fim, o trabalho verifica as potencialidades do uso de uma abordagem hierarquizada e a importância da adoção de modelos em empresas de transporte de carga como forma de alavancagem da sua competividade frente as novas exigências do mercado.

Atenção à saúde mental na Estratégia Saúde da Família no Município de Parnamirim/RN: opinião dos profissionais, dos portadores de transtornos mentais e seus acompanhantes

This study aims to analyze and compare the opinion of professionals, managers and users about the mental health care in the Family Health Strategy (FHS). It is characterized as an Operations Research or Health System Research with a cross-sectional design and a descriptive quantitative nature. The study was developed from the application of the Opinion Measurement Scale allied to techniques of observation and structured interview in the city of Parnamirim / RN. The sample consists of 409 subjects, 209 professionals of the Family Health Strategy, 30 of the Oral Health Strategy, 19 of the Family Health Support Center, 24 directors of Basic Health Units, plus 68 users with mental disorders and 59 caregivers, respecting the ethical parameters of Resolution 196/96 of the National Health Council, trial registration number: CAAE 0003.0.051.000-11. Quantitative data were submitted to the Epi-info 3.5.2 for analysis. The network of mental health in Parnamirim involves the flow between the FHS, Psychosocial Care Centers, clinics and hospitals, having as main barriers the fragility of the referral and counter-referral system, of the municipal health conferences, of the FHS teams by the limitations in material and human resources as well as the population´s lack of acknowledge about the organization of the mental health network, issues that affect the integral attention. Even though the FHS professionals recognize the importance of their actions, they question their role in mental health care, experiencing difficulties in accessing psychiatric services (76.5%). Although most agree that the mentally ill is best treated in the family than in hospital (65.2%), the community health workers were the predominant category in the partial or total disagreement of this statement (40.8%), who is the professional in greater contact with the family. Nevertheless the caregivers miss the support of the FHS as the main focus of attention is on revenue control. The views of professionals, mental patients and caregivers converged in several statements, showing the main weaknesses to be focused by the mental health network of the city, as the perceptions that: (a) physical strength is needed to take care of mental patients for its tendency to aggression, requiring it to stay in the sanatorium for representing danger to society, (b) only a psychiatrist can help the person with emotional problems, (c) the user of alcohol and drugs does not necessarily develop mental illness, (d) the access barriers and doubts about the quality of psychiatric services, (e) caring of a mental health patient does not bring suffering to professionals. Therefore, the commitment to consensus building, monitoring and evaluation of the network are important mechanisms for an effective management system, reflecting in the importance of strengthening the health conferences and approximating different institutions. The results reinforce the importance of strengthening primary care through programs of continuing education focusing on the actions and functions of professionals in accordance with its competences and duties what contribute to the organization and response of mental health care, favoring user´s care and the promotion of family health

Contribuições da pesquisa operacional para gestão da produção e operações : uma análise exploratória da literatura

This research aims to investigate the evolution presented during three decades (1980, 1990 and 2000) of using the tools of Operations Research (OR) as a suport to decision making in Production Operation Management (POM). Hypothesis tests were made to verify the proportional growth of a given area over the decades to the detriment of the areas of facility layout, capacity planning, production scheduling and inventory management. Six journals were selected and from them more than 800 articles were used for classification and analysis in the grounds of review. It also discussed possible ways for future research and comparisons are made with other papers of literature review. As a result, it was found that areas of heuristics and simulation showed a greater quantity of contributions in all POM areas of this study

The open capacitated arc routing problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.

Programação linear por partes: revisão teórica e aplicações

Procura-se resgatar a importância de uma subárea da Programação Matemática conhecida como Programação Linear Por Partes - PLP. de fato a PLP tem inúmeras aplicações tanto na área teórica como em situações reais. Este trabalho apresenta os resultados de uma pesquisa bibliográfica, efetuada nas principais revistas técnicas e livros disponíveis relacionados com Pesquisa Operacional, que visou situar o estado da'arte da Programação Linear por Partes, bem como a abrangência de sua aplicabilidade. Particularmente, no contexto da PLP, este texto deslaca a Programação em Redes Lineares por Partes devido a sua relevância em muitas situações práticas.

Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.