Principles of Inventory Management: When You Are Down to Four, Order More PDF
Preview Principles of Inventory Management: When You Are Down to Four, Order More
Springer Series in Operations Research And Financial Engineering Series Editors: Thomas V. Mikosch Sidney I. Resnick Stephen M. Robinson F orothertitlespublishedinthisseries,goto h ttp://www.springer.com/series/3182 John A. Muckstadt Amar Sapra Principles of Inventory Management When You Are Down to Four, Order More 123 John A. Muckstadt Amar Sapra School of Operations Research Department of Quantitative Methods and Information Engineering and Information Systems Cornell University Indian Institute of Management 286 Rhodes Hall Bangalore Ithaca, NY 14853-3801 Bannerghatta Road USA Bangalore 560 076 [email protected] Indi a [email protected] Series Editors: Thomas V. Mikosch Stephen M. Robinson Department of Mathematical Sciences Department of Industrial and Systems Engineering University of Copenhagen University of Wisconsin-Madison DK-1017 Copenhagen Madision, WI 53706 Denmark USA [email protected] [email protected] Sidney I. Resnick Cornell University School of Operations Research and Information Engineering Ithaca, NY 14853 USA [email protected] ISSN 1431-8598 ISBN 978-0-387-24492-1 e-ISBN 978-0-387-68948-7 DOI 10.1007/978-0-387-68948-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009939430 Mathematics Subject Classification (2010): 90-01, 90B05, 90C39 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identifies as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To mywife, Linda,myparents,mychildren,and grandchildren,who havesupportedandinspiredme. —JackMuckstadt To myparentsandsiblingsfortheir continuedsupport andencouragement.Myparentshavelived adifficult lifeandhavedenied themselvesmost pleasuresinlife justtomakesurethattheirchildrenwereabletoobtain thebestpossibleeducation. —AmarSapra Preface The importance of managing inventories properly in global supply chains cannot be denied. Eachcomponent ofthese numerous supply chains mustfunction appropriately so that inventories are managed efficiently. To manage efficiently requires the leaders and staffs in each organization to comprehend certain basic principles and laws. The purpose ofthisbookistodiscuss theseprinciples. Thecontentsofthistextrepresentacollectionoflecturenotesthathavebeencreated overthepast33yearsatCornellUniversity.Assuch,thetopicsdiscussed,thesequence in which they are presented, and the level of mathematical sophistication required to understand the contents of this text are based on my interests and the backgrounds of mystudents. Clearly, notalltopics found inthe vastliterature onquantitative methods used to model and solve inventory management problems can be covered in a one- semestercourse. Consequently, thisbookislimitedinscopeanddepth. Thecontentsofthebookareorganized inamannerthatIhavefoundtobeeffective in teaching the subject matter. After an introductory chapter inwhich the fundamental issues pertaining to the management of inventories are discussed, we introduce a vari- ety of models and algorithms. Each such model is developed on the basis of a set of assumptions aboutthemannerinwhichanoperating environment functions. In Chapter 2 we study the classic economic order quantity problem. This type of problem isbased onthe assumption that demands occur ataconstant, continuous, and known rate over an infinite planning horizon. Furthermore, the cost structure remains constant over this infinite horizon as well. The focus is on managing inventories at a singlelocation. The material in Chapter 3 extends the topic covered in Chapter 2. Several multi- locationormulti-itemmodelsareanalyzed.Theseanalysesarebasedonwhatarecalled power-of-twopolicies. Again,theunderlying operatingenvironments areassuredtobe deterministic andunchanging overaninfinitehorizon. vii viii Preface The assumptions made about the operating environment are altered in Chapter 4. Here the planning horizon is finite in length and divided into periods. Demands and costs are assumed to be known in each period, although they may change from period toperiod. In all subsequent chapters, uncertainty is present in the operating environment. In Chapter 5 we study single-period problems in which customer demand is assumed to be described by a random variable. In Chapter 6, the analysis is extended to multiple periods.Thediscussionlargelyfocusesonestablishingpropertiesofoptimalpoliciesin finite-horizon settings when demand is described by a non-stationary process through time.Serialsystemsarealsodiscussed. Theobjectiveistominimizetheexpectedcosts ofholdinginventoriesandstockingout.Thus,thecoststructureinthischapterislimited tothecasewheretherearenofixedordering costs. In Chapter 7, we study environments in which demands can occur at any point in time over an infinite planning horizon. Whereas we assumed in Chapter 6 that inven- tory procurement decisions were made periodically, in this chapter we assume such decisions are made continuously in time. The underlying stochastic processes govern- ing the demand processes are stationary over the infinite planning horizon, as are the costs.AsinChapter6,weassumetherearenofixedordering costs. The analysis in Chapter 7 is confined to managing items in a single location. In Chapter 8 we extend the analysis to multi-echelon systems. Thus the underlying sys- tem is one in which inventory decisions are made continuously through time, but now in multiple locations. The importance of understanding the interactions of inventory policies betweenechelons isthemaintopicofthischapter. Chapters 9 and 10 contain extensions of the materials in Chapters 7 and 6, respec- tively. In both chapters, we introduce the impact that fixed ordering costs have on the form of optimal operating policies as well as on the methods used to model and solve theresultingoptimization problems. Bothexactandapproximate modelsarepresented alongwithappropriatealgorithmsandheuristics.Aproofoftheoptimalityofso-called (s,S)policies isgiven,too. Asmentioned, thematerials contained inthis text areones that have been taught to Cornell students. These students are seniors and first year graduate students. As such, they have studied optimization methods, probability theory (non-measure-theoretic) and stochastic processes in undergraduate level courses prior to taking the inventory management course. In addition to presenting fundamental principles to them, the in- tent ofthe course isalsotodemonstrate theapplication ofthetopics they havestudied previously. The text is written so that sections can be read mostly independently. To make this possible, notation ispresented ineachmajorsection ofeachchapter. Thetextcouldbe used in different ways. For example, a half semester course could consist of material in Chapter 2, Section 4.1, Sections 5.1–5.2, Sections 6.2–6.3, most of Sections 9.1– Preface ix 9.2,Sections10.1–10.2,andSection10.5.Whilewehavechosentoexaminestochastic lot sizing problems at the end of the text, these materials could easily be studied in a different sequence. For example, Chapter 9 could be studied after Chapter 3, and Chapter 10 could be studied after Chapter 6. Rearranging the sequence in which the textcanbereadispossiblebecause ofthewayithasbeenwritten. I have mentioned that the scope of this text is limited. I encourage readers to study other textstocomplete their understanding ofthebasic principles underlying thetopic of inventory management. These texts include those authored by Sven Axsa¨ter; Ed Silver and Rein Peterson; Steve Nahmias; Craig Sherbrooke; Paul Zipkin; and Evan Porteus. Each of these authors has made exceptional contributions to the science and practiceofinventory management. Ithaca, NY JohnA.Muckstadt May2009 Acknowledgments I began my study of inventories while a student at the University of Michigan. My teachers there, Richard C. Wilson and Herbert P. Galliher, taught me the basics of the subject. These two were great teachers and engineers. They prodded and encouraged meduringandaftermystudentyears. Iamdeeplyindebtedtothem. As is often the case in a person’s life, an event occurred that altered every profes- sional activity I have undertaken thereafter. This event occurred for me in the early 1970s when I was asked to develop an approach for computing procurement quanti- ties for engines and other repairable items for the U.S. Air Force’s F-15 aircraft. At that time I was an active duty Air Force Officer. Suddenly, I had to truly learn and then apply the principles of inventory theory. The people with whom I worked on this projectwerecapable,dedicated, andtrulyofgreatcharacter.AttheAirForceLogistics CommandHeadquarters,whereIworked,thesepeopleincludedMajorGeneralGeorge Rhodes,ColonelFredGluck,MajorGenePerkins,CaptainJonReynolds,CaptainMike Pearson, MSgt Robert Kinsey, Tom Harruff, Vic Presutti, and Perry Stewart. I learned much from my friends and colleagues at the RAND Corporation: Irv Cohen, Gordon Crawford, Steve Drezner, Murray Geisler, Jack Abel, Mort Berman, Lou Miller, Bob Paulson, Hy Shulman, and John Lu. I also benefited greatly from research conducted at RAND by Craig Sherbrooke. Many of the ideas presented in Chapter 8 are directly related tohisefforts. Also, Ihad thedistinct privilege oflearning about thepractice of inventory management from Bernie Rosenman, who headed the Army Inventory Re- searchOffice,andhiscolleagues KarlKruseandAlanKaplan. Since 1974 I have been on the faculty at Cornell and have had the opportunity to work with some of the finest scholars in the field of operations research. Peter Jack- son, Bill Maxwell, Paat Rusmevichientong, and Robin Roundy all have greatly influ- enced my thinking about the principles of inventory management. I have been fortu- natetohavetaughtandworkedwithmanygiftedstudents. Almost1,000students have xi xii Acknowledgments been taught inventory management principles at Cornell since 1974. I am especially indebted to many former Ph.D. students, who, without exception, have been wonder- ful people and a great joy to work with. They include Kripa Shanker, Peter Knepell, Mike Isaac, Jim Rappold, Kathryn Caggiano, Andy Loerch, Bob Sheldon, Ed Chan, Alan Bowman, David Murray, Jong Chow, Eleftherios Iacovou, Susan Alten, Chuck Sox, Howard Singer, Sophia Wang, Juan Pereira, and, most recently, Retsef Levi, Tim Huh, and Ganesh Janakiraman. Major sections of Chapter 10 are due to these latter three. Thanks also to Tim Huh, Retsef Levi, Ganesh Janakiraman, and Joseph Geunes fortheirearlyadoptionofthebookandhelpful feedback. AmarSapra, myco-author and formerCornell student, urged mefor manyyears to writethisbook.Withouthisencouragement andsubstantial assistance, thebookwould nothavebeencompleted. IcannotexpresswithmerewordshowthankfulIamtoallofthesetrulyexceptional people. I also appreciate the heroic efforts of June Meyermann, who had to decipher my handwriting as she typed the manuscript. Sheis ajewel. Kathleen King and PaatRus- mevichientong have provided substantial support in the preparation of this book, as well. Lastly, and most importantly, my wife Linda has been very supportive of the time I have spent working on the text. The many hours that I have not been available for activities withheraretoonumeroustocount.Ideeplyappreciate herconstantloveand support.
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