Mathematics in the Supply Chain

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Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

Classification of the Existing Knowledge Base of OR/MS Research and Practice (1990-2019) using a Proposed Classification Scheme

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordOperations Research/Management Science (OR/MS) has traditionally been defined as the discipline that applies advanced analytical methods to help make better and more informed decisions. The purpose of this paper is to present an analysis of the existing knowledge base of OR/MS research and practice using a proposed keywords-based approach. A conceptual structure is necessary in order to place in context the findings of our keyword analysis. Towards this we first present a classification scheme that relies on keywords that appeared in articles published in important OR/MS journals from 1990-2019 (over 82,000 articles). Our classification scheme applies a methodological approach towards keyword selection and its systematic classification, wherein approximately 1300 most frequently used keywords (in terms of cumulative percentage, these keywords and their derivations account for more than 45% of the approx. 290,000 keyword occurrences used by the authors to represent the content of their articles) were selected and organised in a classification scheme with seven top-level categories and multiple levels of sub-categories. The scheme identified the most commonly used keywords relating to OR/MS problems, modeling techniques and applications. Next, we use this proposed scheme to present an analysis of the last 30 years, in three distinct time periods, to show the changes in OR/MS literature. The contribution of the paper is thus twofold, (a) the development of a proposed discipline-based classification of keywords (like the ACM Computer Classification System and the AMS Mathematics Subject Classification), and (b) an analysis of OR/MS research and practice using the proposed classification

Evaluation et gestion de la flexibilité dans les chaînes logistiques : nouveau cadre général et applications

This thesis focuses on flexibility issues in supply chain. These issues are becoming more and more important for firms because of the increasingly changing business environment and customer behaviors. Although some of these issues have been tackled in academic research in recent years, but studies have mainly concentrated in conceptual levels and there is little consensus even on the definition of flexibility. This thesis aims at defining a new framework for the supply chain flexibility, proposing quantitative measures of the flexibility and optimizing the use of flexibility, especially in an integrated production and transportation planning context. The new framework of supply chain flexibility is based on classification of different flexibility aspects in a supply chain into three main categories - manufacturing flexibility,logistic chain flexibility and system flexibility. These flexibility types are further distinguished into major flexibility dimension and other flexibility dimension.In order to measure supply chain flexibility from a quantitative point of view, Mechanical Analogy method is particularly discussed. A procedure is established to enlarge and carry out this method in supply chain, provided with a case study to evaluate the flexibility of Louis Vuitton stores.One of the most important issues is to optimally make use of the available flexibility. We investigate an Integrated Production and Transportation Planning problem with given flexibility tolerances, where the production and transportation activities are intimately linked to each other and must be scheduled in a synchronized way. Particularly, heterogeneous vehicles are taken into account. Two mixed integer linear programming models are constructed.Three algorithms are developed and compared with linear relaxation bounds for large sized real life instances and with optimal solutions for small sized instances. These comparisons show the effectiveness of our heuristics in solving real life problemsCette thèse étudie la problématique de la flexibilité dans les chaînes logistiques. La recherche académique a commencé à s’intéresser à cette problématique depuis quelques années, mais les études existantes restent pour la plupart au niveau conceptuel et il y a peu de consensus sur la définition même de la flexibilité. Cette thèse a pour ambition de définir un nouveau cadre pour la flexibilité dans les chaînes logistiques, proposer des mesures quantitatives pour la flexibilité et enfin optimiser l’utilisation de la flexibilité, en particulier dans un contexte de planification intégrée de la production et du transport.Ce travail de thèse vise tout d’abord à établir un nouveau cadre pour la flexibilité de la chaîne logistique, où les différents aspects de la flexibilité sont classifiés en trois catégories principales: flexibilité de la production, flexibilité de la chaîne logistique et flexibilité du système. Dans chacune de ces catégories, on peut trouver des dimensions primordiales et des dimensions moins importantes.Afin d’évaluer la flexibilité de manière quantitative, nous faisons appel à la méthode Analogie Mécanique. Cette méthode propose une analogie entre un système mécanique vibratoire et une chaîne logistique. Dans ce contexte, nous avons développé une étude de cas pour Louis Vuitton afin d’évaluer la flexibilité de leurs magasins, et nous avons établi une procédure pour implémenter cette méthode.Une autre problématique importante est l’utilisation optimale de la flexibilité existante.Nous nous sommes particulièrement intéressés à la planification intégrée de la production et du transport avec des flexibilités sur la capacité de transport, où la production et le transport sont intimement liés du fait du manque de capacité de stockage et doivent être planifiées conjointement. Particulièrement, les véhicules hétérogènes sont pris en compte.Nous avons construit deux modèles de programmation linéaire en nombres mixtes et développé trois algorithmes qui ont été comparées par rapport à la relaxation linéaire pour les instances de grande taille et aux solutions optimales pour des instances de petite taille. Ces comparaisons montrent que les heuristiques proposées sont efficaces pour résoudre des problèmes réels, aussi bien en termes de qualité de solution qu’en termes de temps de calcul

Multi-period distribution networks with purchase commitment contracts

Retailers which deliver products directly to their customer locations often rely on Logistics Service Intermediaries (LSI) for order management, warehousing, transportation and distribution services. Usually, the LSI acts as a shipper and subcontracts the transportation to carriers for longhaul and last-mile delivery services. All agents interact and are connected through cross-docking facilities. As the demand from customers may vary significantly over time, the shipper's requirements for transportation evolve accordingly at the tactical level. This creates opportunities for the LSI to take advantage of medium-term contracts with the carriers at prices lower than those offered by the spot market. In this article, we propose a MILP formulation for the multi-period planning problem with minimum purchase commitment contracts faced by the LSI. The study focuses on designing dynamically, at a tactical level, a suitable network of cross-docking facilities and related transportation capacities (belonging to different carriers) to reduce the LSI operational costs in the long term. We propose several exact and heuristic decomposition methods for the the model, respectively, based on combinatorial Benders cuts and on relax-and-repair approaches. The performance of these algorithms is experimentally compared to that of commercial solvers (brand-and-cut and classical Benders). The numerical results show that our methods bring benefits for the solution of large size instances

Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume