(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:

DOWNLOAD EBOOK

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).

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

DOWNLOAD EBOOK

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.

Inventory Management with Stochastic Lead Times
Inventory Management with Stochastic Lead Times

Author: Kumar Muthuraman

Publisher:

Published: 2013

Total Pages: 34

ISBN-13:

DOWNLOAD EBOOK

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.

Inventory Management with Alternative Delivery Times
Inventory Management with Alternative Delivery Times

Author: Xiaoying Liang

Publisher: Springer

Published: 2016-11-24

Total Pages: 110

ISBN-13: 3319486357

DOWNLOAD EBOOK

This book develops a modeling framework to analyze the problem of inventory management with alternative delivery times. The general context considered here is that a seller replenishes its inventory in fixed intervals and, between replenishments, allocates the limited inventory to satisfy customers who are both price and delivery-time sensitive. On the demand side, customers have heterogeneous delivery-time requirements and choose either spot or late delivery. This theoretical modeling captures the essence of real-world business practices such as the delivery time market segmentation strategy adopted by automobile dealerships in China and many other similar examples. The book focuses on the seller’s optimal inventory replenishment and demand fulfillment policies, and our results provide managerial insights into the merits of flexible delivery-time options. Similar applications such as the group-buying mechanism are also examined. The main mathematical tool used in theoretical analysis is dynamic programming. This book is written for students, researchers, and practitioners in the areas of operations management and industrial engineering who are interested in understanding the rationale of flexible delivery times and designing successful applications.

Dynamic Management Decision and Stochastic Control Processes
Dynamic Management Decision and Stochastic Control Processes

Author: Toshio Odanaka

Publisher: World Scientific

Published: 1990

Total Pages: 240

ISBN-13: 9789810200923

DOWNLOAD EBOOK

This book treats stochastic control theory and its applications in management. The main numerical techniques necessary for such applications are presented. Several advanced topics leading to optimal processes are dismissed. The book also considers the theory of some stochastic control processes and several applications to illustrate the ideas.

Optimal Control and Optimization of Stochastic Supply Chain Systems
Optimal Control and Optimization of Stochastic Supply Chain Systems

Author: Dong-Ping Song

Publisher: Springer Science & Business Media

Published: 2012-11-29

Total Pages: 282

ISBN-13: 1447147243

DOWNLOAD EBOOK

Optimal Control and Optimization of Stochastic Supply Chain Systems examines its subject the context of the presence of a variety of uncertainties. Numerous examples with intuitive illustrations and tables are provided, to demonstrate the structural characteristics of the optimal control policies in various stochastic supply chains and to show how to make use of these characteristics to construct easy-to-operate sub-optimal policies. In Part I, a general introduction to stochastic supply chain systems is provided. Analytical models for various stochastic supply chain systems are formulated and analysed in Part II. In Part III the structural knowledge of the optimal control policies obtained in Part II is utilized to construct easy-to-operate sub-optimal control policies for various stochastic supply chain systems accordingly. Finally, Part IV discusses the optimisation of threshold-type control policies and their robustness. A key feature of the book is its tying together of the complex analytical models produced by the requirements of operational practice, and the simple solutions needed for implementation. The analytical models and theoretical analysis propounded in this monograph will be of benefit to academic researchers and graduate students looking at logistics and supply chain management from standpoints in operations research or industrial, manufacturing, or control engineering. The practical tools and solutions and the qualitative insights into the ideas underlying functional supply chain systems will be of similar use to readers from more industrially-based backgrounds.