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Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
The author considers a single server queueing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and a linear cost structure is assumed. The problem is to decide, at the completion of each service and given the state of system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (non-preemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy which is optimal, and a simple algorithm for its computation is presented. (Modified author abstract).
Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
The author considers a single server queueing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and a linear cost structure is assumed. The problem is to decide, at the completion of each service and given the state of system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (non-preemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy which is optimal, and a simple algorithm for its computation is presented. (Modified author abstract).
Author: Stanford University. Department of Operations Research Publisher: ISBN: Category : Languages : en Pages : 34
Book Description
The author continues the study of the dynamic scheduling problem introduced and formulated in the paper's predecessor. The positive interest rate is considered fixed throughout. It is shown that there exists a static optimal policy, and the corresponding optimal priority ranking is exhibited. Broadening the formulation to allow inserted idel time, it is shown that the previous optimal policy need be changed only be refusing to serve (under any circumstances) a certain number of the lowest priority classes. (Author).
Author: Stanford University. Department of Operations Research Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
The author considers an M/G/1 queue with several customer classes. It is not required that the queue be stable or even that the mean service time be finite for any class. The economic framework is linear, featuring a holding cost per unit time and fixed service reward for each class. Future costs and rewards are continuously discounted using a positive interest rate. The problem is to decide, at the completion of each service and given the state of the system, which class to admit next. The objective is to maximize expected net present value over an infinite planning horizon. The problem is formulated as a Markov renewal decision process. One very special type of scheduling rule, called a static policy, simply enforces a specified priority ranking. The return function under a static policy is explicity presented. In a subsequent paper it will be shown that there exists a static optimal policy. (Author).
Author: Lawrence M. Wein Publisher: Forgotten Books ISBN: 9780666231024 Category : Business & Economics Languages : en Pages : 48
Book Description
Excerpt from Dynamic Scheduling of a Multiclass Make-to-Stock Queue The goal of this paper is to investigate the scheduling problem faced by a single machine, make-to - stock production facility in a dynamic stochastic environment. This facility is pictured in Figure 1, where it is assumed that there is an ample amount of raw material inventory of product k, for k 1, K. The scheduler decides when to release a raw product k job onto the shop floor, at which time the job becomes a unit of product k work-in-process (wip) inventory. These decisions will be referred to as release decisions. There is a single machine that transforms units of product k wip inventory into units of product k finished goods inventory. The machine is modeled as a multiclass queue, in that the machine may work on only one unit at a time, and each product has its own general processing time distribution. Demand for each product can be any arbitrary point process that satisfies a functional central limit theorem (for example, a compound Poisson process). About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
The author considers a single server queueing system with two classes of customers who arrive according to independent Poisson processes. The two service time distributions are arbitrary, and a linear holding cost and fixed service reward for each class is considered. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. (Modified author abstract).
Author: Eren Cil Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper investigates an optimal sequencing and dynamic pricing prob- lem for a two-class queueing system. Using a Markov Decision Process based model, we obtain structural characterizations of optimal policies. In particular, it is shown that the optimal pricing policy depends on the entire queue length vector but some monotonicity results prevail as the composition of this vector changes. A numerical study finds that static pricing policies may have significant suboptimality but simple dynamic pricing policies perform well in most situations.
Author: John Gittins Publisher: John Wiley & Sons ISBN: 1119990211 Category : Mathematics Languages : en Pages : 233
Book Description
In 1989 the first edition of this book set out Gittins' pioneering index solution to the multi-armed bandit problem and his subsequent investigation of a wide of sequential resource allocation and stochastic scheduling problems. Since then there has been a remarkable flowering of new insights, generalizations and applications, to which Glazebrook and Weber have made major contributions. This second edition brings the story up to date. There are new chapters on the achievable region approach to stochastic optimization problems, the construction of performance bounds for suboptimal policies, Whittle's restless bandits, and the use of Lagrangian relaxation in the construction and evaluation of index policies. Some of the many varied proofs of the index theorem are discussed along with the insights that they provide. Many contemporary applications are surveyed, and over 150 new references are included. Over the past 40 years the Gittins index has helped theoreticians and practitioners to address a huge variety of problems within chemometrics, economics, engineering, numerical analysis, operational research, probability, statistics and website design. This new edition will be an important resource for others wishing to use this approach.
Author: Quan-Lin Li Publisher: Springer Nature ISBN: 981150864X Category : Computers Languages : en Pages : 497
Book Description
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book. The contributors are leading researchers with diverse research perspectives. The research areas of the book iclude a broad range of topics related to reliability models, queueing theory, manufacturing systems, supply chain finance, risk management, Markov decision processes, blockchain and so forth. The book consists of a brief Preface describing the main achievements of Professor Cao; followed by congratulations from Professors Way Kuo and Wei Wayne Li, and by Operations Research Society of China, and Reliability Professional Society of China; and further followed by 25 articles roughly grouped together. Most of the articles are written in a style understandable to a wide audience. This book is useful to anyone interested in recent developments in reliability, network security, system safety, and their stochastic modeling and analysis.
Author: Christoph Loch Publisher: Routledge ISBN: 0750685522 Category : Business & Economics Languages : en Pages : 560
Book Description
This text provides a comprehensive view of the challenges in managing the development of new products from well-known and leading contributors in the field.
Author: J. Michael Harrison
Author: J. Michael Harrison
Author: Stanford University. Department of Operations Research
Author: Stanford University. Department of Operations Research
Author: Lawrence M. Wein
Author: J. Michael Harrison
Author: Eren Cil
Author: Gustav Feichtinger
Author: John Gittins
Author: Quan-Lin Li
Author: Christoph Loch