The aim of this study is to analyze the formulations set out on mathematical textbooks designed for fifth grade in order to identify and to diagnose elements and possible factors that may hinder or mislead the understanding and interpretation of mathematical formulations set out, which can cause an inadequate mental representation, thereby undermining the reflective capacity of students. To that end, we carried out a field survey with fifty-two (52) teachers in training in order to diagnose the construct of these enunciations. It is assumed that the textual construction of the set out, that is the structure of the language and the words, should be made and submitted to the student/reader so that they would understand them clearly, as well as respond to them with autonomy in the absence of a teacher. Were chosen textbooks of Mathematics on the basis of the methodological approach of Discursive Textual Analysis, which works with meanings constructed from a set of texts in order to achieve a description and interpretation of some senses the reading can inspire. In this way, the study emphasizes not only the importance of contextualizing the content to assist and facilitate the understanding of mathematical statements that can influence and interfere with the learning process of students, but, also, the use of a clear and explicit language necessary for a correct understanding and interpretation of the student/reader. Therefore, on the basis of the factors analyzed, were identified that the difficulty to interpret and understand the mathematical statements are associated with the language used by the authors of the textbook, by omission of information or for presenting ambiguity and polysemy. In this sense this research proposes a reflection and invites the professionals of education, both, educators and authors of textbooks to (re) think about the form of the preparation and construction of these formulated set out, so that they observe attentively the juxtaposed elements or the absence of them, without which the student/reader can not understand what he reads due to the deficit in the structure of the formulated set outs. / No presente estudo buscou-se analisar os enunciados matemáticos propostos pelos Livros Didáticos do 5ºano, a fim de identificar e diagnosticar elementos e fatores possíveis que podem dificultar na intelecção e interpretação de leitura desses enunciados, os quais podem provocar uma representação mental inadequada, prejudicando assim, a capacidade reflexiva do aluno. Para tanto, realizou-se uma pesquisa de campo com 52 professores em formação, a fim de diagnosticar o constructo desses enunciados. Parte-se do princípio de que a construção textual dos enunciados, isto é, a estrutura da linguagem e dos vocábulos precisa estar posta e apresentada para o aluno/leitor de forma que este possa entendê-los claramente, bem como respondê-los com autonomia, na ausência do professor. Foram escolhidos livros didáticos de Matemática com base na abordagem metodológica da Análise Textual Discursiva, que trabalha com significados construídos a partir de um conjunto de textos de modo a alcançar uma descrição e interpretação de alguns sentidos que a leitura pode suscitar. Dessa forma, o estudo ressalta não só a importância de se contextualizar o conteúdo para auxiliar e facilitar a compreensão dos enunciados matemáticos que podem influenciar e interferir na aprendizagem do aluno, mas também a utilização de uma linguagem que nela esteja explícita os subsídios necessários para a intelecção e interpretação do aluno/leitor. Portanto, com base nos fatores analisados do corpus em questão, identifica-se que a dificuldade para interpretar e compreender os enunciados matemáticos está associada com a linguagem utilizada pelos autores do livro didático, seja por lacuna de informações ou por apresentar ambiguidade e polissemia. Assim, esta pesquisa propõe uma reflexão e convida os profissionais da educação, tanto educadores como autores dos livros didáticos a (re)pensarem sobre a forma de elaboração e construção dos enunciados das atividades escolares de modo que observem os elementos justapostos ou a ausências de elementos, que sem os quais o aluno/leitor não poderá compreender o que lê devido ao déficit na estrutura dos enunciados.

Les activités de transport et de gestion des stocks ont un impact important les unes sur les autres. Assurer un niveau de stock idéal peut demander des livraisons fréquentes, ce qui entraîne des coûts logistiques élevés. Pour optimiser les compromis entre les coûts de stock et de transport, des systèmes VMI (Vendor Managed Inventory) ont été développés pour gérer ensemble les opérations de stock et de transport. Pour un ensemble de clients ayant des demandes sur un horizon de temps, le problème de détermination des tournées et des quantités à livrer avec un coût minimum de gestion de stock et de transport est connu sous le nom de Inventory Routing Problem (IRP). Les systèmes à deux échelons ont également été étudiés pour améliorer le flux de véhicules dans les zones urbaines. étant donné que des nouvelles politiques de gestion sont apparues, dans le but de limiter le trafic des gros véhicules et leur vitesse dans les centres urbains, des Centres de Distribution (DC) sont mis en place pour coordonner les flux de marchandises à l'intérieur et à l'extérieur des zones urbaines. Les produits sont donc livrés aux clients par les fournisseurs via les DC.Nous proposons de combiner un système à deux échelons avec le IRP. Nous introduisons un Operational Two-Echelon Inventory Routing Problem (O-2E-IRP), ce qui est une nouvelle extension du IRP à notre connaissance. Dans le O-2E-IRP proposé, les clients doivent être servis par un fournisseur strictement via des DC et les tournées doivent être définis dans les deux échelons sur un horizon de temps donné. Trois politiques de réapprovisionnement et de configurations de routage différentes sont modélisées pour ce problème. Nous développons deux formulations mathématiques, ainsi qu'un algorithme Branch-and-Cut (B&C) combiné à une matheuristique pour résoudre le problème. De plus, nous analysons plusieurs inégalités valides disponibles pour le IRP et nous introduisons de nouvelles inégalités valides inhérentes au IRP à deux échelons. Des expériences de calcul approfondies ont été effectuées sur un ensemble d'instances générées de manière aléatoire. Les résultats obtenus montrent que les performances des méthodes sont liées à la politique de stock et à la configuration de routage.Dans le contexte d'un IRP à deux échelons, deux décisions tactiques importantes doivent être prises en plus des décisions de livraison de routage et de quantité de livraison: à partir de quel DC sera fourni chaque client et en utilisant quels véhicules ? Répondre à ces questions est extrêmement difficile car cela implique de pouvoir minimiser les coûts opérationnels d'un système de livraison VMI à deux échelons à long-terme et avec des demandes incertaines. Pour faire face à cela, nous présentons le Tactical Two-Echelon Inventory Routing Problem (T-2E-IRP) qui optimise les décisions en fonction d'un horizon à long-terme et en tenant compte des demandes stochastiques. Trois politiques de gestion des stocks sont modélisées et appliquées à un ou aux deux échelons. Nous développons une approche de simulation pour résoudre le T-2E-IRP sur un horizon de temps à long-terme. Nous proposons quatre formulations et deux algorithmes B&C pour définir l'affectation des clients et des véhicules aux DC en fonction d'un horizon de temps court. Ensuite, nous évaluons ces décisions d'affectation via un outil de simulation qui résout un sous-problème du T-2E-IRP, qui consiste en les décisions de livraisons du fournisseur aux DC et des DC aux clients, sur un horizon glissant. De nombreuses expériences sont effectuées pour un ensemble d'instances générées aléatoirement. L'impact de plusieurs paramètres utilisés pour déterminer l'affectation des clients et des véhicules aux DC sur le coût total est analysé. Basé sur des expériences, nous définissons la combinaison de paramètres qui fournit généralement les meilleurs résultats sur les instances générées. / Transport and inventory management activities have a great impact on each other. Ensuring an ideal inventory level can require frequent deliveries, leading to high logistics costs. To optimize the trade-offs between inventory and transportation costs, VMI (Vendor Managed Inventory) systems have been developed to manage inventory and transportation operations together. Given a set of customers with demands over a time horizon, the problem of determining routes and delivery quantities at a minimum inventory holding and transportation costs is known as Inventory Routing Problem (IRP). Two-echelon systems have also been studied to improve the freight vehicle flow inside urban areas. As new management policies have emerged, with the goal of limiting the traffic of large vehicles and their speed in urban centers, Distribution Centers (DC) are introduced to coordinate freight flows inside and outside the urban areas. Products are then delivered from the suppliers to the customers through the DC.We propose to combine a two-echelon system with the IRP. We introduce an Operational Two-Echelon Inventory Routing Problem (O-2E-IRP), which is a new extension of the IRP to the best of our knowledge. On the proposed O-2E-IRP, the customers must be served by a supplier strictly through DC and routes must be defined in both echelons over a given time horizon. Three different replenishment policies and routing configurations are modeled for this problem. We develop two mathematical formulations, and a Branch-and-Cut (B&C) algorithm combined with a matheuristic to solve the problem. In addition, we analyze several valid inequalities available for IRP, and we introduce new ones inherent to the IRP within two echelons. Extensive computational experiments have been carried out on a set of randomly generated instances. The obtained results show that the performance of the methods is related to the inventory policy and routing configuration.In the context of a two-echelon IRP, two important tactical decisions have to be taken in addition to route and quantity delivery decisions: from which DC will be supplied each customer and using which vehicles? Answering these questions is extremely difficult as it implies being able to minimize operational costs for a two-echelon VMI delivery system on long-term and with uncertain demands. In order to deal with this, we introduce the Tactical Two-Echelon Inventory Routing Problem (T-2E-IRP) that optimizes the decisions based on a long-term horizon and considering stochastic demands. Three inventory management policies are modeled and applied at one or both echelons. We develop a simulation approach to solve the T-2E-IRP on a long-term time horizon. We propose four formulations and two B&C algorithms to define the assignment of customers and vehicles to the DC based on a short time horizon. Then, we evaluate these assignment decisions through a simulation tool that solves a subproblem of the T-2E-IRP, which consists of the decisions of deliveries from the supplier to the DC and from the DC to the customers, on a rolling-horizon framework. Extensive computational experiments are performed for a set of randomly generated instances. The impact of several parameters used to determine the assignment of customers and vehicles to DC on the total cost is analyzed. Based on the experiments, we define the combination of parameters that generally provides the best results on the generated instances.