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

Inventory models with lateral transshipments : a review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satised from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level denition, all in uence the best method of transshipping. Models of many dierent systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these dierences can be understood and gaps within the literature can be identied

Multi-Echelon Models for Repairable Items: A Review

We review multi-echelon inventory models for repairable items. Such models have been widely applied to the management of critical spare parts for military equipment for around three decades, but the application to manufacturing and service industries seems to be much less documented. We feel that the appropriate use of models in the management of spare parts for heavily utilized equipment in industry can result in significant cost savings, in particular in those settings where repair facilities are resource constrained. In our review, we provide a strategic framework for making these decisions, place the modeling problem in the broader context of inventory control, and review the prominent models in the literature under a unified setting, highlighting some key relationships. We concentrate on describing those models which we feel are most applicable for practical application, revisiting in detail the Multi-Echelon Technique for Recoverable Item Control (METRIC) model and its variations, and then discussing a variety of more general queueing models. We then discuss the components which we feel must be addressed in the models in order to apply them practically to industrial settings

Performance Analysis of Multi-Echelon Inventory Systems.

A two-echelon inventory and distribution system consisting of a centralized warehouse and N stores is considered in this paper. The inventories of the warehouse as well as the stores are controlled by periodic review (s,S) ordering policies. The expected levels of capital investment, storage space needs, capacity requirements for delivery vehicles, and reliable customer service are issues of great importance to practitioners when considering the introduction of a central warehouse and transportation system. Helmut Schneider, Dan Rinks, and Peter Kelle have developed a methodology that has been shown to provide approximately optimal (s,S) policies under various demand conditions, and are easy to handle computationally. The approximations of Schneider et al., are used to generate ordering policies for the two-echelon system in order to observe the behavior of the aggregate inventories generated by the (s,S) policies using computer simulation. The simulation results are used to evaluate the accuracy of the analytic models in predicting the aggregate inventory behavior, and simple computational formulas are proposed to calculate confidence limits for aggregate inventory levels and for shipping volumes and weights

Service Inventory Management : Solution techniques for inventory systems without backorders

Koole, G.M. [Promotor]Vis, I.F.A. [Copromotor

Gestion optimale des pièces de rechange dans un réseau logistique multi-échelon flexible

Ce mémoire aborde la problématique de planification et contrôle des inventaires des pièces de rechange pour des systèmes assujettis à des défaillances aléatoires. Nous décrivons une série de modèles de décision pour gérer une gamme de pièces de rechange pour des réseaux constitués de plusieurs équipements en opération. Chaque équipement est composé d’une ou de plusieurs pièces qui sont nécessaires à son bon fonctionnement. Lorsqu’une pièce tombe en panne, elle est remplacée par une rechange, si disponible en stock, elle sera ensuite acheminée vers l’atelier de réparation pour la remettre en état de fonctionnement. Les modèles étudiés dans ce travail sont adaptés à une organisation disposant d’un réseau d’équipements, de canaux de transport, de stocks de pièces de rechange et de plusieurs stations de réparation. Les stocks et les stations sont déployés pour desservir un territoire, une zone ou une région, afin de garantir un niveau de service requis. Les modèles mathématiques proposés, décrivant les processus de défaillance, de réparation et de transport, utilisent la théorie des files d’attente. Celle-ci traduit fidèlement le phénomène de défaillance et de réparation provoqué par la contrainte de capacité des stations de réparation et des canaux de transport. Le processus stochastique qui engendre les arrivées des pièces défaillantes aux stations de réparation est supposé être un processus de Poisson. Les délais de traitement et de transit d’une pièce ne sont pas connus avec certitude, ils sont considérés comme des variables aléatoires qui suivent des distributions générales. Le système de gestion de stock des pièces de rechanges adopte une politique de transaction continue à réapprovisionnement unitaire (S-1, S). Dans ce travail, nous nous intéressons à l’analyse de l’évolution du système dans un régime permanent afin de trouver une politique de contrôle optimale qui dépend essentiellement de la quantité de pièces de rechange à garder en stock et de la capacité de traitement des stations de réparation. Nous développons aussi des modèles approximatifs pour traiter des configurations logistiques multi-échelon, ainsi que des demandes en urgence dans un échelon supérieur, et des transferts latéraux entre magasins de même échelon. Ces modèles sont ajustés pour faire face à des mesures de services différentes et pour traiter plusieurs références de pièces de rechange. Plusieurs algorithmes ont été proposés et implémentés, ils ont donné lieu à des résultats numériques dégageant des courbes d’efficiences (Coût, Niveau de service, Capacité) permettant aux gestionnaires de prendre des décisions éclairées le long du cycle de vie du système. En outre, une étude comparative très poussée a permis de démontrer l’exactitude des résultats obtenus par nos algorithmes avec les meilleures contributions publiées dans la littérature. Mots clés : pièces de rechange, gestion des stocks, politiques de maintenance, politiques de contrôle des stocks, fonction de renouvellement, files d’attente, chaînes logistiques, systèmes multi-échelon.This paper deals with the problem of planning and control of spare parts inventory for systems subject to random failures. We describe a series of decision models to manage a range of spare parts for networks made up of several equipment in operation. Each equipment is composed of one or more parts that are necessary for its proper functioning. When part breaks down, it is replaced by another, if available in stock., it will then be taken to the repair station to restore it to its working condition. The models studied in this work are adapted to an organization with a network of equipment, transport channels, stocks of spare parts and several repair stations. Inventories and stations are deployed to serve a territory, zone or region to ensure a required level of service. The proposed mathematical models, describing the failure, the repair and the transport processes, use the queuing theory. It accurately reflects the phenomenon of failure and repair caused by the capacity constraints of repair stations and transport channels. The stochastic process that generates the arrival of failure parts at repair stations is assumed to be a Poisson process. The processing and transit times of a part are not known with certainty, they are considered as random variables, which follow general distributions. The spare parts inventory management system adopts a continuous transaction policy with unit replenishment (S-1, S). In this thesis, we are interested in analyzing the evolution of the system in a permanent regime, in order to find an optimal control policy which depends essentially on the number of spare parts to be kept in stock and the processing capacity of repair stations. We also develop approximate models to deal with multi-echelon logistic configurations, as well as emergency requests in a higher echelon, and lateral transfers between stores of the same echelon level. These models are adjusted to deal with different service measures and to handle several spare parts references. Several algorithms have been proposed and implemented, giving rise to numerical results yielding efficiency curves (Cost, Service Level, Capacity) allowing managers to make informed decisions throughout the life cycle of the system. In addition, a very detailed comparative study has been conducted to demonstrate the accuracy of the results obtained by our algorithms with the best contributions published in the literature. Keywords: Spare parts inventory management, maintenance policies, inventory control policies, renewal function, queuing system, supply chains, multi-echelon networks

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

Holdout transshipment policy in two-location inventory systems

In two-location inventory systems, unidirectional transshipment policies are considered when an item is not routinely stocked at a location in the system. Unlike the past research in this area which has concentrated on the simple transshipment policies of complete pooling or no pooling, the research presented in this thesis endeavors to develop an understanding of a more general class of transshipment policy. The research considers two major approaches: a decomposition approach, in which the two-location system is decomposed into a system with independent locations, and Markov decision process approach. For the decomposition approach, the transshipment policy is restricted to the class of holdout transshipment policy. The first attempt to develop a decomposition approach assumes that transshipment between the locations occurs at a constant rate in order to decompose the system into two independent locations with constant demand rates. The second attempt modifies the assumption of constant rate of transshipment to take account of local inventory levels to decompose the system into two independent locations with non-constant demand rates. In the final attempt, the assumption of constant rate of transshipment is further modified to model more closely the location providing transshipments. Again the system is decomposed into two independent locations with non-constant demand rates. For each attempt, standard techniques are applied to derive explicit expressions for the average cost rate, and an iterative solution method is developed to find an optimal holdout transshipment policy. Computational results show that these approaches can provide some insights into the performance of the original system. A semi-Markov decision model of the system is developed under the assumption of exponential lead time rather than fixed lead time. This model is later extended to the case of phase-type distribution for lead time. The semi-Markov decision process allows more general transshipment policies, but is computationally more demanding. Implicit expressions for the average cost rate are derived from the optimality equation for dynamic programming models. Computational results illustrate insights into the management of the two-location system that can be gained from this approach