(S, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

(S, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

Author: Richard Ehrhardt

Publisher:

Published: 1980

Total Pages: 29

ISBN-13:

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A stochastic lead time inventory model is analyzed under the assumptions that (1) replenishment orders do not cross in time and (2) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. This study corrects errors in the existing literature on the finite-horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalized easily. Conditions for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies. (Author).


Inventory Management with Stochastic Lead Times

Inventory Management with Stochastic Lead Times

Author: Kumar Muthuraman

Publisher:

Published: 2013

Total Pages: 34

ISBN-13:

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This article analyzes a continuous time back-ordered inventory system with stochastic demand and stochastic delivery lags for placed orders. This problem in general has an infinite dimensional state space and is hence intractable. We first obtain the set of minimal conditions for reducing such a system's state space to one-dimension and show how this reduction is done. Next, by modeling demand as a diffusion process, we reformulate the inventory control problem as an impulse control problem. We simplify the impulse control problem to a Quasi-Variation Inequality (QVI). Based on the QVI formulation, we obtain the optimality of the (s, S) policy and the limiting distribution of the inventory level. We also obtain the long run average cost of such an inventory system. Finally, we provide a method to solve the QVI formulation. Using a set of computational experiments, we show that significant losses are incurred in approximating a stochastic lead time system with a fixed lead time system, thereby highlighting the need for such stochastic lead time models. We also provide insights into the dependence of this value loss on various problem parameters.


Continuous-Review (s, S) Inventory Models with State-Dependent Leadtimes

Continuous-Review (s, S) Inventory Models with State-Dependent Leadtimes

Author: Donald Gross

Publisher:

Published: 1971

Total Pages: 29

ISBN-13:

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The paper describes the development of a continuous-review (s, S) inventory model with state-dependent and stochastic leadtimes. The demand on the inventory system is assumed to be a Posson random variable, and order-filling portion of the replenishment leadtime is allowed to depend on the number of outstanding orders (i.e., to be state dependent). The inventory state probabilities which are required in order to optimize the cost function with respect to s and S can be obtained via a queuing analysis on the order-filling process. Orders are assumed to arrive at a single-channel service facility, where the service may be state dependent in either one of two ways. (Author).


Foundations of Stochastic Inventory Theory

Foundations of Stochastic Inventory Theory

Author: Evan L. Porteus

Publisher: Stanford University Press

Published: 2002

Total Pages: 330

ISBN-13: 9780804743990

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This book has a dual purpose?serving as an advanced textbook designed to prepare doctoral students to do research on the mathematical foundations of inventory theory, and as a reference work for those already engaged in such research. All chapters conclude with exercises that either solidify or extend the concepts introduced.


On Replenishment Rules, Forecasting, and the Bullwhip Effect in Supply Chains

On Replenishment Rules, Forecasting, and the Bullwhip Effect in Supply Chains

Author: Stephen M. Disney

Publisher: Now Publishers Inc

Published: 2008

Total Pages: 95

ISBN-13: 1601981325

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In this review we focus on supply coordination and use the bullwhip effect as the key example of supply chain inefficiency. We emphasize the managerial relevance of the bullwhip effect and the methodological issues so that both managers and researchers can benefit.


Stochastic Inventory Models with Bulk Demand and State-dependent Leadtimes

Stochastic Inventory Models with Bulk Demand and State-dependent Leadtimes

Author: Carl A. Harris

Publisher:

Published: 1969

Total Pages: 32

ISBN-13:

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The paper describes several one-for-one ordering (S - 1,S) inventory models in which the time required for order replenishment is state dependent. The demand is assumed to follow a compound Poisson distribution. That portion of the leadtime dealing with the actual filling of orders is assumed to depend on the number of outstanding orders. Several models are investigated. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory costs as a function of S in order to obtain an optimal value of S. (Author).


Fundamentals of Supply Chain Theory

Fundamentals of Supply Chain Theory

Author: Lawrence V. Snyder

Publisher: John Wiley & Sons

Published: 2019-07-01

Total Pages: 956

ISBN-13: 1119024978

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Comprehensively teaches the fundamentals of supply chain theory This book presents the methodology and foundations of supply chain management and also demonstrates how recent developments build upon classic models. The authors focus on strategic, tactical, and operational aspects of supply chain management and cover a broad range of topics from forecasting, inventory management, and facility location to transportation, process flexibility, and auctions. Key mathematical models for optimizing the design, operation, and evaluation of supply chains are presented as well as models currently emerging from the research frontier. Fundamentals of Supply Chain Theory, Second Edition contains new chapters on transportation (traveling salesman and vehicle routing problems), integrated supply chain models, and applications of supply chain theory. New sections have also been added throughout, on topics including machine learning models for forecasting, conic optimization for facility location, a multi-supplier model for supply uncertainty, and a game-theoretic analysis of auctions. The second edition also contains case studies for each chapter that illustrate the real-world implementation of the models presented. This edition also contains nearly 200 new homework problems, over 60 new worked examples, and over 140 new illustrative figures. Plentiful teaching supplements are available, including an Instructor’s Manual and PowerPoint slides, as well as MATLAB programming assignments that require students to code algorithms in an effort to provide a deeper understanding of the material. Ideal as a textbook for upper-undergraduate and graduate-level courses in supply chain management in engineering and business schools, Fundamentals of Supply Chain Theory, Second Edition will also appeal to anyone interested in quantitative approaches for studying supply chains.