A mathematical model for supermarket order picking

Order picking consists in retrieving products from storage locations to satisfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best international practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature.

Acceleration of physics simulation engine through OpenCL

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Mathematical modelling of shallow flows: closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics

Canadian Journal of Civil Engineering 36(10) 1605–16

An approach to teach Calculus/Mathematical Analysis (for engineering students) using computers and active learning – its conception, development of materials and evaluation

Dissertação para obtenção do Grau de Doutor em Ciências da Educação

The national physics and chemistry exams and the learning of sciences

Dissertação apresentada para obtenção do Grau de Doutor em Ciências da Educação, pela Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa

Participatory Surveillance and Mathematical Models in Epidemiologic Research: Successes and Challenges

Theoretical epidemiology aims to understand the dynamics of diseases in populations and communities. Biological and behavioral processes are abstracted into mathematical formulations which aim to reproduce epidemiological observations. In this thesis a new system for the self-reporting of syndromic data — Influenzanet — is introduced and assessed. The system is currently being extended to address greater challenges of monitoring the health and well-being of tropical communities.(...)

Mathematical and numerical methods for inverse problems using fundamental solutions techniques

Fundação para a Ciência e a Tecnologia - SFRH/BD/27914/2006

José Anastácio da Cunha e o projeto MAT² : no trilho de uma história extraordinária

A ideia de que as Matemáticas de Portugal (e de Espanha) atravessaram, depois de um período áureo nos Descobrimentos, um longo deserto onde não foi possível florescerem Mestres, nem escolas, nem cultura científica, nem investigação de relevo foi, durante muito tempo, reiteradamente veiculada, inclusivé através de alguns dos nossos mais referenciados historiadores da Matemática, como é o caso de Gomes Teixeira ou de Rey Pastor. Mas a verdade é que o estudo da História das Matemáticas em Portugal tem, na última década, vivido um interesse crescente onde sobressaem, em particular, uma leitura menos enviesada sobre, por exemplo, o papel educativo dos Jesuítas ou a publicação das obras completas de Pedro Nunes. Está-se assim a contribuir para uma compreensão mais completa da História geral de Portugal, de que a História da Ciência e da Cultura faz parte. José Anastácio da Cunha (1744-1787) foi figura de proa no século XVIII português. Sabíamo-lo matemático que, sem nunca ter saído de Portugal, havia sido capaz de antecipar, em mais de 50 anos, os esforços de matemáticos franceses e alemães para fundar a Matemática com rigor. Sabíamo-lo também autor de uma vasta e diversificada obra de inegável importância matemática mas, igualmente, autor de textos poéticos. Agora, com o projecto que denominámos de MAT2, centramo-nos em José Anastácio da Cunha e pretendemos, se possível, ir ainda mais além. Partimos de uma descoberta, árdua mas com final feliz, em um Arquivo de família: o da Casa de Mateus. Sentimo-nos, com esta “sorte”, privilegiados e gratos por nos ter sido gentilmente concedido o acesso a um vasto conjunto de documentos únicos (diários de viagens, notas de aulas e correspondência) que incluem memórias autógrafas e inéditas de Anastácio da Cunha. Organizámo-nos, cientes do trabalho árduo que temos pela frente, multi e interdisciplinarmente englobando a Matemática (nas suas múltiplas especializações) e a História (incluindo a da Matemática) mas também contando com a Física, a Informática, os estudos militares ou a Arquivística e as Humanidades; reunimos académicos, mais e menos veteranos, com investigadores jovens e juntámos valências nacionais e estrangeiras. No presente artigo daremos conta do percurso trilhado, até agora, pelo projecto MAT2.

A multi–physics approach applied to masonry structures with non–hydraulic lime mortars

Tese de Doutoramento em Engenharia Civil (área de especialização em Engenharia de Estruturas).

Comprensión en resolución de problemas en Física: niveles de representación e inferencias basadas en el conocimiento. Comprehension in Physics Problem-Solving: levels of representation and knowledge-based inferences.

Se propone desarrollar e integrar estudios sobre Modelado y Resolución de Problemas en Física que asumen como factores explicativos: características de la situación planteada, conocimiento de la persona que resuelve y proceso puesto en juego durante la resolución. Interesa comprender cómo los estudiantes acceden al conocimiento previo, qué procedimientos usan para recuperar algunos conocimientos y desechar otros, cuáles son los criterios que dan coherencia a sus decisiones, cómo se relacionan estas decisiones con algunas características de la tarea, entre otras. Todo ello con miras a estudiar relaciones causales entre las dificultades encontradas y el retraso o abandono en las carreras.Se propone organizar el trabajo en tres ejes, los dos primeros de construcción teórica y un tercero de implementación y transferencia. Se pretende.1.-Estudiar los procesos de construcción de las representaciones mentales en resolución de problemas de física, tanto en expertos como en estudiantes de diferentes niveles académicos.2.-Analizar y clasificar las inferencias que se producen durante las tareas de comprensión en resolución de problemas de física. Asociar dichas inferencias con procesos de transición entre representaciones mentales de diferente naturaleza.3.-Desarrollar materiales y diseños instruccionales en la enseñanza de la Física, fundamentado en un conocimiento de los requerimientos psicológicos de los estudiantes en diversas tareas de aprendizaje.En términos generales se plantea un enfoque interpretativo a la luz de marcos de la psicología cognitiva y de los desarrollos propios del grupo. Se trabajará con muestras intencionales de alumnos y profesores de física. Se utilizarán protocolos verbales y registros escritos producidos durante la ejecución de las tareas con el fin de identificar indicadores de comprensión, inferencias, y diferentes niveles de representación. Se prevé analizar material escrito de circulación corriente sea comercial o preparado por los docentes de las carreras involucradas.Las características del objeto de estudio y el distinto nivel de desarrollo en que se encuentran los diferentes ojetivos específicos llevan a que el abordaje contemple -según consideracion de Juni y Urbano (2006)- tanto la lógica cualitativa como la cuantitativa.