Optimal Flow Control in Manufacturing Systems Production Planning an
This book presents a unified optimal control approach to a large class of problems arising in the field of production planning and scheduling. It introduces a leading optimal flow control paradigm which results in efficient solutions for planning and sche
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Applied Optimization Volume 18
Series Editors:
Panos M. Pardalos University 01 Florida, U.S.A. Donald Hearn University 01 Florida, U.S.A.
The titles published in this series are listed at the end 0/ this volume.
Optimal Flow Control in Manufacturing Systems Production Planning and Scheduling
by
OdedMaimon Department ollndustrial Engineering, Tel-Aviv University, Tel-Aviv, Israel
Eugene Khmelnitsky Department ollndustrial Engineering, Tel-Aviv University, Tel-Aviv, Israel
and
Konstantin Kogan Department ollndustrial Engineering, Tel-Aviv University, Tel-Aviv, Israel
Springer-Science+Business Media, B.V.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4757-2834-7 (eBook) ISBN 978-1-4419-4799-4 DOI 10.1007/978-1-4757-2834-7
Printed on acid-free paper
Additional material to this book can be downloaded from http://extras.springer.com. All Rights Reserved © 1998 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1998. Softcover reprint ofthe hardcover 1st edition 1998 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
To ourlamilies
When a ship does not arrive to a certain port neither by due-date, nor later, the Company's Boss exclaims: "The Devil !", the Admiralty: "My God !" (loosely translated from "New Jules Veme", a poem by Joseph Brodsky)
CONTENTS
Preface
xv
PART I: BASIC CONCEPTS CHAPTER 1.
INTRODUCTION
3
1.3.1 Advantages 1.3.2 Limitations
3 4 6 7 7
1.4 Outline of the Book
8
1.1 Top-Down Production Planning Hierarchy 1.2 Planning and Scheduling Approaches 1.3 Why Specifically Optimal Control ?
Bibliography
CHAPTER2.
MATHEMATICAL FUNDAMENTALS OF OPTIMAL CONTROL
2.1 Calculus ofVariations in Optimization Problems 2.1.1 Nature ofDynamic Systems 2.1.2 Modeling ofManufacturing Environment 2.1.3 Optimization of a Single-Time-Step Dynamic System 2.l.4 Optimization ofa Multi-Time-Step Dynamic System with Mixed Controland State Variables Constraints
2.2 Maximum Principle Formulation for Optimal Control Problems 2.2.1 Statement of the Canonical Form of an Optimal Control Problem 2.2.2 Construction of aDescent Variation 2.2.3 Necessary Optimality Conditions
11 11 11 12 13
16 25 26 28 39
2.3 Maximum Principle-Based Numerical Methods
46
2.3.1 Shooting Method 2.3.2 Time-Decomposition Method Bibliography
52
47
x
PART 11: FLOW CONTROL IN PRODUCTION PLANNING CHAPTER3.
ONE-ITEM SINGLE-FACILITY AGGREGATE PRODUCTION PLANNING PROBLEMS
3.1 Introduction 3.2 Production Smoothing with Capacity Expansion 3.2.1 Problem Fonnulation 3.2.2 Analysis ofthe Optimal Production Plan 3.2.3 Analytical Rules for Managing Production Cases 3.2.4 Numerical Algorithm for Arbitrary Demands
3.3 Capacity Evolution Planning: Expansion, Deterioration and Selling 3.3.1 Problem Fonnulation 3.3.2
