Algorithmes d'approximation pour la gestion de stock

Nous considérons des problèmes de gestion des stocks multi-échelon à temps périodique avec des demandes non stationnaires. Ces hypothèses sur la demande apparaissent notamment lorsque des prévisions sur la demande sont utilisées dynamiquement (de nouvelles prévisions sont fournies à chaque période). La structure des coûts comprend des coûts fixes et variables d approvisionnement, des coûts de stockage et des coûts de mise en attente des demandes. Le délai d approvisionnement est supposé constant. Le problème consistant à déterminer la politique optimale qui minimise les coûts sur un horizon fini peut être formulé grâce à un programme dynamique. Dans le cadre déterministe, les problèmes auxquels nous nous intéressons sont le plus souvent NP-difficiles, ce qui fait rapidement exploser l espace d état. Il devient alors nécessaire de recourir à des heuristiques. Nous nous orientons vers la recherche d'algorithmes d'approximation combinatoires pour le problème One Warehouse Multi Retailers et plus généralement pour des systèmes de distribution divergents. Nous nous intéresserons dans un premier temps à des systèmes de distribution à deux étages avec un entrepôt central et des entrepôts secondaires qui voient la demande finale. Dans un deuxième temps, des structures logistiques plus complexes pourront être considérées. L objectif sera de proposer des heuristiques originales, basées sur des techniques de répartition des coûts, de les comparer numériquement à la politique optimale sur de petites instances et, si possible, d établir des garanties de performance.Inventory management has always been a major component of the field of operations research and numerous models derived from the industry aroused the interest of both the researchers and the practitioners. Within this framework, our work focuses on several classical inventory problems, for which no tractable method is known to compute an optimal solution. Specifically, we study deterministic models, in which the demands of the customers are known in advance, and we propose approximation techniques for each of the corresponding problems that build feasible approximate solutions while remaining computationally tractable. We first consider continuous-time models with a single facility when demand and holding costs are time-dependent. We present a simple technique that balances the different costs incurred by the system and we use this concept to build approximation methods for a large class of such problems. The second part of our work focuses on a discrete time model, in which a central warehouse supplies several retailers facing the final customers demands. This problem is known to be NP-hard, thus finding an optimal solution in polynomial time is unrealistic unless P=NP. We introduce a new decomposition of the system into simple subproblems and a method to recombine the solutions to these subproblems into a feasible solution to the original problem. The resulting algorithm has a constant performance guarantee and can be extended to several generalizations of the system, including more general cost structures and problems with backlogging or lost-sales.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

Optimizing the Performance of Robotic Mobile Fulfillment Systems

A robotic mobile fulfillment system is a novel type of automated part-to-picker material handling system. In this type of system, robots transport mobile shelves, called pods, containing items between the storage area and the workstations. It is well suited to e-commerce, due to its modularity and it's ability to adapt to changing orders patterns. Robots can nearly instantaneously switch between inbound and outbound tasks, pods can be continually repositioned to allow for automatic sorting of the inventory, pods can contain many different types of items, and unloaded robots can drive underneath pods, allowing them to use completely different routes than loaded robots. This thesis studies the performance of robotic mobile fulfillment systems by solving decision problems related to warehouse design, inventory and resource allocation, and real-time operations. For warehouse design, a new queueing network is developed that incorporates realistic robot movement, storage zones, and multi-line orders. For inventory allocation, we develop a new type of queueing network, the cross-class matching multi-class semi-open queueing network, which can be applied to other systems as well. Resource (re)allocation is modeled by combining queueing networks with Markov decision processes while including time-varying demand. This model compares benchmark policies from practice wit

Optimal Inventory Control and Distribution Network Design of Multi-Echelon Supply Chains

Optimale Bestandskontrolle und Gestaltung von Vertriebsnetzen mehrstufiger Supply Chains Aufgrund von Global Sourcing, Outsourcing der Produktion und Versorgung weltweiter Kunden innerhalb eines komplexen Vertriebsnetzes, in welchem mehrere Anlagen durch verschiedene Aktivitäten miteinander vernetzt sind, haben die meisten Unternehmen heutzutage immer komplexere Supply Chain-Netzwerke in einer immer unbeständiger werdenden Geschäftsumgebung. Mehr beteiligte Unternehmen in der Wertschöpfungskette bedeuten mehr Knoten und Verbindungen im Netzwerk. Folglich bringt die Globalisierung Komplexität und neue Herausforderungen, obwohl Unternehmen immer stärker von globalen Supply Chains profitieren. In einer solchen Geschäftsumgebung müssen sich die Akteure innerhalb der Supply Chain (SC) auf die effiziente Verwaltung und Koordination des Materialflusses im mehrstufigen System fokussieren, um diesen Herausforderungen handhaben zu können. In vielen Fällen beinhaltet die Supply Chain eines Unternehmens unterschiedliche Entscheidungen auf verschiedenen Planungsebenen, wie der Anlagenstandort, die Bestände und die Verkehrsmittel. Jede dieser Entscheidungen spielt eine bedeutende Rolle hinsichtlich der Gesamtleistung und das Verhältnis zwischen ihnen kann nicht ignoriert werden. Allerdings wurden diese Entscheidungen meist einzeln untersucht. In den letzten Jahren haben zahlreiche Studien die Bedeutung der Integration von beteiligten Entscheidungen in Supply Chains hervorgehoben. In diesem Zusammenhang sollten Entscheidungen über Anlagenstandort, Bestand und Verkehrsmittel gemeinsam in einem Optimierungsproblem des Vertriebsnetzes betrachtet werden, um genauere Ergebnisse für das Gesamtsystem zu erzeugen. Darüber hinaus ist ein effektives Management des Materialflusses über die gesamte Lieferkette hinweg, aufgrund der dynamischen Umgebung mit mehreren Zielen, ein schwieriges Problem. Die Lösungsansätze, die in der Vergangenheit verwendet wurden, um Probleme mehrstufiger Supply Chains zu lösen, basierten auf herkömmlichen Verfahren unter der Verwendung von analytischen Techniken. Diese sind jedoch nicht ausreichend, um die Dynamiken in Lieferketten zu bewältigen, aufgrund ihrer Unfähigkeit, mit den komplexen Interaktionen zwischen den Akteuren der Supply Chain umzugehen und das stochastische Verhalten zu repräsentieren, das in vielen Problemen der realen Welt besteht. Die Simulationsmodellierung ist in letzter Zeit zu einem wichtigen Instrument geworden, da ein analytisches Modell nicht in der Lage ist, ein System abzubilden, das sowohl der Variabilität als auch der Komplexität unterliegt. Allerdings erfordern Simulationen umfangreiche Laufzeiten, um möglichst viele Lösungen zu bewerten und die optimale Lösung für ein definiertes Problem zu finden. Um mit dieser Schwierigkeit umzugehen, muss das Simulationsmodell in Optimierungsalgorithmen integriert werden. In Erwiderung auf die oben genannten Herausforderungen, ist eines der Hauptziele dieser Arbeit, ein Modell und ein Lösungsverfahren für die optimale Gestaltung von Vertriebsnetzwerken integrierter Supply Chains vorzuschlagen, das die Beziehung zwischen den Entscheidungen der verschiedenen Planungsebenen berücksichtigt. Die Problemstellung wird mithilfe von Zielfunktionen formuliert, um die Kundenabdeckung zu maximieren, den maximalen Abstand von den Anlagenstandorten zu den Bedarfspunkten zu minimieren oder die Gesamtkosten zu minimieren. Um die optimale Anzahl, Kapazität und Lage der Anlagen zu bestimmen, kommen der Nondominated Sorting Genetic Algorithm II (NSGA-II) und der Quantum-based Particle Swarm Optimization Algorithm (QPSO) zum Einsatz, um dieses Optimierungsproblem im Spannungsfeld verschiedener Ziele zu lösen. Aufgrund der Komplexität mehrstufiger Systeme und der zugrunde liegenden Unsicherheiten, wurde die Optimierung von Beständen über die gesamte Lieferkette hinweg zur wesentlichen Herausforderung, um die Kosten zu reduzieren und die Serviceanforderungen zu erfüllen. In diesem Zusammenhang ist das andere Ziel dieser Arbeit die Darstellung eines simulationsbasierten Optimierungs-Frameworks, in dem die Simulation, basierend auf der objektorientierten Programmierung, entwickelt wird und die Optimierung metaheuristische Techniken mit unterschiedlichen Kriterien, wie NSGA-II und MOPOSO, verwendet. Insbesondere das geplante Framework regt einen großen Nutzen an, sowohl für das Bestandsoptimierungsproblem in mehrstufigen Supply Chains, als auch für andere Logistikprobleme.Today, most companies have more complex supply chain networks in a more volatile business environment due to global sourcing, outsourcing of production and serving customers all over the world with a complex distribution network that has several facilities linked by various activities. More companies involved within the value chain, means more nodes and links in the network. Therefore, globalization brings complexities and new challenges as enterprises increasingly benefit from global supply chains. In such a business environment, Supply Chain (SC) members must focus on the efficient management and coordination of material flow in the multi-echelon system to handle with these challenges. In many cases, the supply chain of a company includes various decisions at different planning levels, such as facility location, inventory and transportation. Each of these decisions plays a significant role in the overall performance and the relationship between them cannot be ignored. However, these decisions have been mostly studied individually. In recent years, numerous studies have emphasized the importance of integrating the decisions involved in supply chains. In this context, facility location, inventory and transportation decisions should be jointly considered in an optimization problem of distribution network design to produce more accurate results for the whole system. Furthermore, effective management of material flow across a supply chain is a difficult problem due to the dynamic environment with multiple objectives. In the past, the majority of the solution approaches used to solve multi-echelon supply chain problems were based on conventional methods using analytical techniques. However, they are insufficient to cope with the SC dynamics because of the inability to handle to the complex interactions between the SC members and to represent stochastic behaviors existing in many real world problems. Simulation modeling has recently become a major tool since an analytical model is unable to formulate a system that is subject to both variability and complexity. However, simulations require extensive runtime to evaluate many feasible solutions and to find the optimal one for a defined problem. To deal with this problem, simulation model needs to be integrated in optimization algorithms. In response to the aforementioned challenges, one of the primary objectives of this thesis is to propose a model and solution method for the optimal distribution network design of an integrated supply chain that takes into account the relationship between decisions at the different levels of planning horizon. The problem is formulated with objective functions to maximize the customer coverage or minimize the maximal distance from the facilities to the demand points and minimize the total cost. In order to find optimal number, capacity and location of facilities, the Nondominated Sorting Genetic Algorithm II (NSGA-II) and Quantum-based Particle Swarm Optimization Algorithm (QPSO) are employed for solving this multiobjective optimization problem. Due to the complexities of multi-echelon system and the underlying uncertainty, optimizing inventories across the supply chain has become other major challenge to reduce the cost and to meet service requirements. In this context, the other aim of this thesis is to present a simulation-based optimization framework, in which the simulation is developed based on the object-oriented programming and the optimization utilizes multi-objective metaheuristic techniques, such as the well-known NSGA-II and MOPSO. In particular, the proposed framework suggests a great utility for the inventory optimization problem in multi-echelon supply chains, as well as for other logistics-related problems

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications

Pooling and polling : creation of pooling in inventory and queueing models

The subject of the present monograph is the ‘Creation of Pooling in Inventory and Queueing Models’. This research consists of the study of sharing a scarce resource (such as inventory, server capacity, or production capacity) between multiple customer classes. This is called pooling, where the goal is to achieve cost or waiting time reductions. For the queueing and inventory models studied, both theoretical, scientific insights, are generated, as well as strategies which are applicable in practice. This monograph consists of two parts: pooling and polling. In both research streams, a scarce resource (inventory or server capacity, respectively production capacity) has to be shared between multiple users. In the first part of the thesis, pooling is applied to multi-location inventory models. It is studied how cost reduction can be achieved by the use of stock transfers between local warehouses, so-called lateral transshipments. In this way, stock is pooled between the warehouses. The setting is motivated by a spare parts inventory network, where critical components of technically advanced machines are kept on stock, to reduce down time durations. We create insights into the question when lateral transshipments lead to cost reductions, by studying several models. Firstly, a system with two stock points is studied, for which we completely characterize the structure of the optimal policy, using dynamic programming. For this, we formulate the model as a Markov decision process. We also derived conditions under which simple, easy to implement, policies are always optimal, such as a hold back policy and a complete pooling policy. Furthermore, we identified the parameter settings under which cost savings can be achieved. Secondly, we characterize the optimal policy structure for a multi-location model where only one stock point issues lateral transshipments, a so-called quick response warehouse. Thirdly, we apply the insights generated to the general multi-location model with lateral transshipments. We propose the use of a hold back policy, and construct a new approximation algorithm for deriving the performance characteristics. It is based on the use of interrupted Poisson processes. The algorithm is shown to be very accurate, and can be used for the optimization of the hold back levels, the parameters of this class of policies. Also, we study related inventory models, where a single stock point servers multiple customers classes. Furthermore, the pooling of server capacity is studied. For a two queue model where the head-of-line processor sharing discipline is applied, we derive the optimal control policy for dividing the servers attention, as well as for accepting customers. Also, a server farm with an infinite number of servers is studied, where servers can be turned off after a service completion in order to save costs. We characterize the optimal policy for this model. In the second part of the thesis polling models are studied, which are queueing systems where multiple queues are served by a single server. An application is the production of multiple types of products on a single machine. In this way, the production capacity is pooled between the product types. For the classical polling model, we derive a closedform approximation for the mean waiting time at each of the queues. The approximation is based on the interpolation of light and heavy traffic results. Also, we study a system with so-called smart customers, where the arrival rate at a queue depends on the position of the server. Finally, we invent two new service disciplines (the gated/exhaustive and the ??-gated discipline) for polling models, designed to yield ’fairness and efficiency’ in the mean waiting times. That is, they result in almost equal mean waiting times at each of the queues, without increasing the weighted sum of the mean waiting times too much

Dual sourcing : with arbitrary stochastic demand and stochastic lead times

Companies with high-performing supply chains enjoy essential competitive ad- vantages. However, supply chain management faces an environment of rising risk that endangers these competitive advantages. One of the reasons is to outsource parts of their business. This bears the risk of significantly increased lead times and lead time variability. It is the impact of lead time variability on inventory management that is the central aspect of this book. It describes a mathematical model for dual sourcing with two reorder points, shows the deviation between stochastic and deterministic calculations in a sensitivity analysis, and investigates different relaxations of a traditional dual-sourcing policy

Multilocation Inventory Systems With Centralized Information.

The management of multi-echelon inventory systems has been both an important and challenging research area for many years. The rapid advance in information technology and the emphasis on integrated supply chain management have new implications for the successful operation of distribution systems. This research focuses on the study of some fundamental issues related to the operation of a multilocation inventory system with centralized information. First, we do a comparative analysis to evaluate the overall performance of individual versus centralized ordering policies for a multi-store distribution system where centralized information is available. This study integrates the existing research and clarifies one of the fundamental questions facing inventory managers today: whether or not ordering decisions should be centralized. Next, we consider a multi-store distribution system where emergency transshipments are permitted among these stores. Based on some simplifying assumptions, we develop an integrated model with a joint consideration of inventory and transshipment components. An approximately optimal (s, S) policy is obtained through a dynamic programming technique. This ordering policy is then compared with a simplified policy that assumes free and instantaneous transshipments. We also examine the relative performance of base stock policies for a centralized-ordering distribution system. Numerical studies are provided to give general guidelines for use of the policies