Inventory Control Under Stochastic Lead Time and Stochastic Demand
Inventory Control Under Stochastic Lead Time and Stochastic Demand

Author: Kenneth R Rand (Jr)

Publisher:

Published: 1965

Total Pages: 109

ISBN-13:

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An attempt is made to investigate the behavior of an inventory system in which lead time, the size of the demand order, and the time between successive demand orders are all random variables with known probability distributions. Since adequate analytical mathematical models are not existant, a computer-based simulation model is used to study the inventory system. An introduction to the inventory problem and a description of inventory systems currently in use are provided. The formulation of the model is described. Results are presented as graphs of stockout time as a function of reorder point.

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.

Analytics, Operations, and Strategic Decision Making in the Public Sector
Analytics, Operations, and Strategic Decision Making in the Public Sector

Author: Evans, Gerald William

Publisher: IGI Global

Published: 2019-02-15

Total Pages: 441

ISBN-13: 1522575928

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Analytics for the public sector involves the application of operations research and statistical techniques to solve various problems existing outside of the private sector. The use of analytics for the public sector results in more efficient and effective services for the clients and users of these systems. Analytics, Operations, and Strategic Decision Making in the Public Sector is an essential reference source that discusses analytics applications in various public sector organizations, and addresses the difficulties associated with the design and operation of these systems including multiple conflicting objectives, uncertainties and resulting risk, ill-structured nature, combinatorial design aspects, and scale. Featuring research on topics such as analytical modeling techniques, data mining, and statistical analysis, this book is ideally designed for academicians, educators, researchers, students, and public sector professionals including those in local, state, and federal governments; criminal justice systems; healthcare; energy and natural resources; waste management; emergency response; and the military.

Mathematics of Stochastic Manufacturing Systems
Mathematics of Stochastic Manufacturing Systems

Author: George Yin

Publisher: American Mathematical Soc.

Published: 1997-01-01

Total Pages: 420

ISBN-13: 9780821897027

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In this volume, leading experts in mathematical manufacturing research and related fields review and update recent advances of mathematics in stochastic manufacturing systems and attempt to bridge the gap between theory and applications. The topics covered include scheduling and production planning, modeling of manufacturing systems, hierarchical control for large and complex systems, Markov chains, queueing networks, numerical methods for system approximations, singular perturbed systems, risk-sensitive control, stochastic optimization methods, discrete event systems, and statistical quality control.

Capacity and Inventory Planning for Make-to-Order Production Systems
Capacity and Inventory Planning for Make-to-Order Production Systems

Author: Klaus Altendorfer

Publisher: Springer Science & Business Media

Published: 2013-07-31

Total Pages: 150

ISBN-13: 3319008439

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​The book presents different models for the simultaneous optimization problem of capacity investment and work release rule parameterization. The overall costs are minimized either including backorder costs or considering a service level constraint. The available literature is extended with the integration of a distributed customer required lead time in addition to the actual demand distribution. Furthermore, an endogenous production lead time is introduced. Different models for make-to-order production systems with one or multiple serial processing stages are developed. Capacity investment is linked to the processing rates of the machines or to the number of the machines. Results are equations for service level, tardiness, and FGI lead time in such a production system. For special cases with M/M/1 and M/M/s queues explicit solutions of the optimization problems or optimality conditions concerning capacity investment and work release rule parameterization are provided.

Management of Stochastic Demand in Make-to-Stock Manufacturing
Management of Stochastic Demand in Make-to-Stock Manufacturing

Author: Rainer Quante

Publisher: Peter Lang

Published: 2009

Total Pages: 138

ISBN-13: 9783631594094

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Up to now, demand fulfillment in make-to-stock manufacturing is usually handled by advanced planning systems. Orders are fulfilled on the basis of simple rules or deterministic planning approaches not taking into account demand fluctuations. The consideration of different customer classes as it is often done today requires more sophisticated approaches explicitly considering stochastic influences. This book reviews current literature, presents a framework that addresses revenue management and demand fulfillment at once and introduces new stochastic approaches for demand fulfillment in make-to-stock manufacturing based on the ideas of the revenue management literature.

Research Handbook on Inventory Management
Research Handbook on Inventory Management

Author: Jing-Sheng J. Song

Publisher: Edward Elgar Publishing

Published: 2023-08-14

Total Pages: 565

ISBN-13: 180037710X

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This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.