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.

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

Percepção do estado de saúde da pessoa idosa institucionalizada

RESUMO: O envelhecimento da população portuguesa é um facto. Esta alteração da estrutura demográfica exige o investimento no conhecimento científico para que se conheçam as consequências a nível, económico, social, cultural, biológico, físico e, principalmente, a nível da saúde. Isto porque, é emergente que a sociedade tenha capacidade para responder às necessidades específicas das pessoas neste estádio de vida, tendo sempre por base o conceito de qualidade de vida. Este estudo teve como objectivo avaliar a percepção do estado de saúde da pessoa idosa institucionalizada. Foram nove as instituições participantes, denominadas por lares de idosos de residência permanente, onde se contou com uma amostra de 75 indivíduos entre os 66 e 100 anos, de ambos os sexos. Foram recolhidos dados através de uma caracterização sócio-demográfica, através do Mini Mental State e através do Questionário de auto-avaliação da saúde e do bem-estar físico (de Fonseca e Paúl, 1999). Os dados obtidos foram trabalhados numa perspectiva de estatística descritiva e estatística inferencial, nomeadamente com a análise do coeficiente de Spearman. A partir desta análise determinou-se que: a grande maioria da amostra designa como “aceitável” ou “fraca” a sua percepção da saúde, em geral; os dados sócio-demográficos, e a instituição a que cada indivíduo pertence não têm relação com a percepção do estado de saúde destas pessoas; existe relação significativa entre a percepção do estado de saúde das pessoas idosas institucionalizadas e a saúde dos seus pares, essencialmente quando se abordam itens relacionados com aspectos físicos; no que concerne aos hábitos de vida, não existe relação entre a percepção do estado de saúde das pessoas idosas e os hábitos tabágicos e os hábitos alcoólicos. Os dados obtidos nem sempre são os dados que se esperavam efectivamente, porém fazem sentido ao serem consolidados com a teoria.--------ABSTRACT: The aging of the Portuguese population is a reality. It is imperative that society has the capacity to face the specific necessities of those who are in this phase of their lives. Therefore, this change in the demographics requires investment in scientific knowledge in order to know the consequences at levels such as: the economic, social cultural, biological and physical, mainly related to health. The main purpose of this study has been to evaluate the perceptions of elderly people concerning their health conditions. There were nine institutions involved, which are referred to as nursing homes, and a sample of 75 people between 66 and 100 years-old, from both genders, cooperated. Data has been collected through social-demographic, Mini Mental State and also through the questionnaire of the self-evaluation of health and physical well-being (from Fonseca and Paúl, 1999). The obtained data was worked within a perspective of descriptive/ inference statistic. From this analysis, it was determined that the great majority of the sample describes their perception of health as “acceptable” or “weak”, in general; the social-demographic information and the institution to where each person belongs do not show a connection with their perception of their health condition; however, there seems to be a significant relation between an institutionalized elderly person´s perception of their health condition and their spouse’s health, mainly when related to physical issues. In as far as life styles are concerned, do not show a connection between elderly people’s perception of health and smoking habits and alcohol habits. The obtained data does not always match expectations; nevertheless they make sense when being complemented by the theory.

The interrogation of witnesses abroad in execution of a european investigation order: an examination from eyes of the defence

European Master Human Rights and Democratisation

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Fractional order describing functions

This paper addresses limit cycles and signal propagation in dynamical systems with backlash. The study follows the describing function (DF) method for approximate analysis of nonlinearities and generalizes it in the perspective of the fractional calculus. The concept of fractional order describing function (FDF) is illustrated and the results for several numerical experiments are analysed. FDF leads to a novel viewpoint for limit cycle signal propagation as time-space waves within system structure.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

Fractional Order Description of DNA

This study addresses the deoxyribonucleic acid (DNA) and proposes a procedure based on the association of statistics, information theory, signal processing, Fourier analysis and fractional calculus for describing fundamental characteristics of the DNA. In a first phase the 24 chromosomes of the Human are evaluated. In a second phase, 10 chromosomes for different species are also processed and the results compared. The results reveal invariance in the description and close resemblances with fractional Brownian motion.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Control and Dynamics of Fractional Order Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

Short-Circuit Impedance of Power Transformers: the Fractional Order Calculus Approach

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04