Real Optimization with SAP® APO

Josef KallrathThomas I. Maindl

Real Optimizationwith SAP® APO

With 73 Figuresand 30 Tables

123

Professor Dr. Josef Kallrath

E-mail: josef.kallrath@web.de

Dr. Thomas I. Maindl

E-mail: thomas.maindl@web.de

Cataloging-in-Publication Data

Library of Congress Control Number: 2006923242

ISBN-10 3-540-22561-7 Springer Berlin Heidelberg New YorkISBN-13 978-3-540-22561-4 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication orparts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, inits current version, and permission for use must always be obtained from Springer-Verlag.Violations are liablefor prosecution under the German Copyright Law.

Springer is a part of Springer Science+Business Mediaspringeronline.com

© Springer-Verlag Berlin Heidelberg 2006Printed in Germany

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,even in the absence of a specific statement, that such names are exempt from the relevant protective laws andregulations and therefore free for general use.

Cover design: design & production GmbHProduction: Helmut PetriPrinting: Strauss Offsetdruck

SPIN 11305699 Printed on acid-free paper – 42/3153 – 5 4 3 2 1 0

Trademarks

“SAP” and mySAP.com are trademarks of SAP Aktiengesellschaft, Systems, Applications and Products in DataProcessing, Dietmar-Hopp-Allee 16, D-69190 Walldorf, Germany. The publisher gratefully acknowledges SAP’skind permission to use its trademark in this publication. SAP AG is not the publisher of this book and is notresponsible for it under any aspect of press law.

SAP®, the SAP logo, mySAPTM, SAP NetWeaverTM, SAP® R/3®, SAP® BW, SAP® CRM, SAP® GUI,mySAPTM SCM, SAP® SCM, SAP® APO, ABAPTM, ABAP/4®, BAPI®, Drag&Relate, and mySAP.com® are trademarks or registered trademarks of SAP AG in Germany and in several other countries. All other products mentioned are trademarks or registered trademarks of their respective companies.

i2®, and the “i2 dot” logo are registered trademarks of i2 Technologies, Inc.

ILOG®, the ILOG design, CPLEX® and all other logos and product and service names of ILOG are registeredtrademarks or trademarks of ILOG in France, the U.S. and/or other countries.

Xpress-MPTM is a trademark of Dash Optimization.

TriMatrix® is a registered trademark of MATHESIS GmbH.

SCOR® is a registered trademark of the Supply-Chain Council in the United States and Europe.

Microsoft®, Excel®, MSN, and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries.

All other products or company names mentioned are used for identification purposes only and may be trademarks of their respective owners.

to our parents

Foreword

Optimization is a serious issue, touching many aspects of our life and activity.But it has not yet been completely absorbed in our culture. In this book theauthors point out how relatively young even the word “model” is. On top ofthat, the concept is rather elusive. How to deal with a technology that findsapplications in things as different as logistics, robotics, circuit layout, financialdeals and traffic control?

Although, during the last decades, we made significant progress, the broadpublic remained largely unaware of that. The days of John von Neumann,with his vast halls full of people frantically working mechanical calculatorsare long gone. Things that looked completely impossible in my youth, likesolving mixed integer problems are routine by now. All that was not justachieved by ever faster and cheaper computers, but also by serious progressin mathematics. But even in a world that more and more understands thatit cannot afford to waste resources, optimization remains to a large extentunknown.

It is quite logical and also fortunate that SAP R©, the leading supplier ofenterprise management systems has embedded an optimizer in his software.The authors have very carefully investigated the capabilities and the limits ofAPO. Remember that optimization is still a work in progress. We do not havethe tool that does everything for everybody. Some sales people will claim tohave such a miracle weapon every once in a while, out of enthusiasm so blindthat it turned into ignorance. But the serious technicians among us all knowthat such a thing does not exist, and never will.

For the creators of APO, I have the following advice. Do not get offendedby the fact that the authors discovered deficiencies. In some cases you willbe inspired to remove the weak points. In other cases you may decide not toaddress certain issues, because they are out of the league you want to play in.No matter what, the result is going to be an even better version of an alreadygood product.

Also for the users this book is a very important help. It is essential tounderstand the potential as well as the limits of a tool one is going to use. It

VIII Foreword

does not matter whether you are going to do furniture building or optimiza-tion. Without good solid information about the capabilities of your tool youare more likely to break something than to make something.

To those that would be disappointed by the fact that APO is not every-thing for everybody, I can only say in German: “Eine eierlegende Wollmilchsaubringt außer Bellen meistens nichts zustande!”

January 2006 Gerard De BeuckelaerMember of the BoardDirector of Strategic DevelopmentUTI SN, Bucharest, Romania

Preface

This book describes and demonstrates how SAP R© APO can be used to tackle“real” optimization problems arising in industry and focuses on optimization1

based on mixed integer linear programming (MILP). In a unique combinationit deals with the aspects of model-building and solving algorithms as well aswith the implementation in commercial supply chain management software,SAP APO being a typical example of an advanced planning system (APS).

As many enterprises have implemented SAP R© software for Enterprise Re-source Planning (ERP) in a global scale successfully we feel that a logicalextension of this backbone is to be seen in optimization for procurement, pro-duction and distribution. Decision makers become more and more convincedof the benefits of using optimization techniques and to formulate and imple-ment models that address the actual problems that cannot be solved usingjust ERP software. This book bridges the domains of economists and businessengineers who deal mostly with ERP-like solutions on the one hand and theoperation research experts and mathematicians who typically deal with moreor less isolated optimization applications on the other hand. The availabilityof APS software that is fully integrated into the ERP software and systemlandscapes provides a unique opportunity to utilize these two domains in theform of a tightly integrated symbiosis. Certainly there is still some work todo to convince “business people” of the huge potentials of optimization tech-niques and at the same time convincing the “optimization practitioners” ofthe potential value of APS that are based on a predefined mathematical modeland allow for changing optimization model settings by changing pre-set para-meters. One of the biggest challenges is to work towards better understandingeach other, a seemingly obvious issue that nevertheless is very much neglectedin the real world. Especially this last task is made increasingly difficult be-cause the term optimization, as outlined on page 23 is often used in differentmeanings. In this book we speak of real optimization – meaning that in an1 See Sect. 2.2 for a definition of the term optimization which has different meaning

in mathematics, computers science, economy and its colloquial usage.

X Preface

exact, mathematical sense the result derived from the input data is optimal orthat strict and tight bounds are computed quantifying the maximal differencebetween the objective function of the current feasible solution to the optimum.Thus, from the mathematical point of view this leads to incorrect labeling ofsome supply chain management (SCM) and ERP systems as optimizationproviders where in reality just certain rules are applied to real world prob-lems resulting in possibly feasible, but by no means optimal recommendationsfor solving supply chain problems. The value and consequences of obtainingoptimal solutions or solutions with safe bounds are discussed in Sect. 10.2.1.

We address readers involved in optimization projects in which SAP and,particularly, SAP APO are implemented in companies. These are the projectdesigners, projects leaders, the IT personnel inside the companies, but alsooperations research practitioners, supply chain management consultants, anddecision makers in the area of tool selection for optimization tasks. Grad-uates in the economic sciences, business and operations research, but alsomathematicians and physicists with interest in solving real optimization prob-lems might benefit from reading this book. We do not expect a strong back-ground in mathematics and optimization but rather a certain openness tobecome familiar with the concepts and nomenclature of optimization andto acquire the skills necessary to understand the described algorithms andmodels. Our book is not supposed to introduce the reader into SAP, SAP R©R/3 R©, mySAPTMERP, or SAP APO in general. The reader is advised to keepin mind that the optimization engine is just one part of SAP APO and thatthe software supports a wealth of other functionalities and business processes.This book rather summarizes when optimization is useful (Sect. 10.2.1), itprovides a sound overview of optimization model formulation and solving aswell as implementation in SAP APO and leads to interpreting the results inthe right way. At the same time we demonstrate the strengths and weaknessesof the two possible approaches2 – using an integrated advanced planning3 and2 The reader should keep in mind that many statements we make about SAP APO

when comparing it to tailored optimization approaches hold – cum grano salis –for other commercial advanced planning systems as well.

3 The number of case studies using SAP APO (SNP optimizer) discussed in thisbook is most likely not representative for the number of companies using SAPAPO (SNP optimizer) successfully. Current SNP live implementations we areaware of at the time of the writing using the SNP optimizer are with clients inplastics, and in surgical and hygiene items. Current SNP project implementa-tions (with optimizer) planned to go live in the first quarter of 2006 are witha catalyst manufacturer and an automotive supplier. Planned SNP projects tobegin in the first quarter 2006 are with a windmill manufacturer (SNP optimizer)and industrial automation products manufacturer (constraint propagation-basedalgorithm Capable-To-Match, CTM). All these projects have been implementedor will be implemented by axentiv AG (Darmstadt). As it is very difficult toobtain publishable references on precisely SNP optimizer applications, we would

Preface XI

scheduling system or building a customized optimization model or application– hoping to work towards building the bridge described above.

In order to set the right expectations we would like to summarize what wejust said and explicitly stress what this book is and what it is not :

• it is a book on mathematical optimization in SAP APO for operationsresearch practitioners, consultants, or project team members involved inSAP APO projects

• it is a book on mathematical optimization in SCM• it is a book on real life issues associated with decision taking in real world

problems supported by mathematical optimization in SCM• it is a book from which one can learn the relevant conceptual ideas of

SCM related to planning from the mathematical point of view• it is an introduction to linear and mixed integer linear programming (LP,

MILP) for non-mathematicians• it is an introduction to setting up and running the SNP optimizer in SAP

APO helpful to any novice• it is a book containing selective case studies on optimization in and in

connection with SAP APO; the selection criteria were mostly availabil-ity (permission to write about it in this book) and suitability (didacticalissues)

• it is a technical book (in the sense of mathematics)• it is a book for readers who want to establish an independent opinion

based on a deeper technical understanding of the underlying mathematicalassumptions enabling to select the best planning philosophy and approachfor a real world optimization problem at hand

• it is a book for readers in companies having selected SAP APO and whowant to improve their cooperation with external consultants by an im-proved understanding of technical issues and foundations

• it is a book for consultants who specialized on introducing SAP APO tocompanies and exploiting SAP APO optimization facilities to its best

• it is a book encouraging the reader to think and to establish an own andindependent opinion

• it is a book which tries to provide clear answers and ideas to real worldoptimization projects involving SAP APO

• it is not an SCM book• it is not a textbook on mySAPTMSCM• it is not an introduction to LP and MILP optimization techniques for

mathematicians• it is not a description of processes supported by SAP APO beyond the

SNP optimizer• it is not a marketing book for SAP APO or any other APS

appreciate readers making references to such positive cases available to us – wewould consider them in a future edition of this book.

XII Preface

• it is not a marketing book for Dash Optimization, ILOG, or any otherprovider of optimization algorithms, nor for AUDI, axentiv, Ferrari, orMathesis

We hope it is a book the reader will enjoy reading!

Structure of the Book

SAP APO is introduced as a commercial supply chain management tool inChap. 1. This chapter deals with the role of optimization in supply chainmanagement (SCM) and introduces the concept of commercially availablesoftware products, so-called advanced planning systems (APS).

In Chap. 2 we give an introduction into models, model building and op-timization. We introduce the main objects of optimization: variables, con-straints and objective function and give a brief sketch of optimization projects.We conclude this chapter by highlighting the basic ideas and intention of op-timization in SAP APO.

The Chapters 3 and 4 provide a step-by-step introduction into how anoptimization model is built in SAP APO. The more general steps of buildinga supply chain model are explained in Chap. 3 along with an idea how amathematical formulation might look like. Chap. 4 demonstrates how theoptimizer-specific settings are made and the optimization is actually run inSAP APO. By adjusting the parameters we treat this example supply chainmodel as both an LP and an MILP problem.

In Chap. 5 we use supply chain planning in the semiconductor industry asan example of advanced planning in high technology industries. In additionto optimization we discuss a constraint propagation approach that is verypopular in this particular industry. Chap. 6 focuses on consumer goods.

Chap. 7 has been contributed by Ruth Wassermann, Matthias Lauten-schlager, Boris Reuter, and Christian Steiner (axentiv AG, Darmstadt, Ger-many) and discusses a planning problem in the automotive industry and ascheduling problem occurring in the chemical industry. The detailed schedul-ing is part of the overall planning process including SAP R/3, the SAP APOcomponents Demand Planning, Supply Network Planning, and ProductionPlanning/Detailed Scheduling, and ILOG R© cartridge.

Chap. 8 deals with a planning problem in the process industry: a multi-location, multi-period planning problem of a network of multi-purpose reac-tors used in the chemical industry to derive optimal production plans. Thisproduction planning case study focuses strongly on the MILP model and de-scribes a typical situation in which a complete optimization solution has beenimplemented in industry prior to the introduction of SAP APO. The questionsthen arises whether it is possible to replace the system by SAP APO or tointerface it as an individual model. In order to do so, we add appropriate SAPAPO related comments to the mathematical model description. In addition,this case provides a good example of what is needed in terms of documentationif a model external to SAP APO is to be developed or maintained.

Preface XIII

In Chap. 9 we find case studies in which individual optimization modelshave been interfaced to SAP APO. This chapter indicates alternative tracksand focuses on problems and issues to be considered when taking the approachof interfacing own optimization models to SAP APO. In two of the threecases both the SAP APO optimizer and an external solver are used to tackledifferent planning tasks in one SAP implementation. Section 9.2 and 9.3 havebeen contributed by Remi Lequette (ILOG, Gentilly Cedex, France) and AxelHecker (Mathesis GmbH, Mannheim, Germany), respectively.

A summary of what can be learned from this book and many years ofexperience in SAP APO and optimization projects is given in Chap. 10. Herewe also discuss which impact advanced planning and scheduling systems suchas SAP APO have in larger companies and which possible consequences thishas for optimization in the future.

In the appendix we give an overview of the different SAP APO componentsfollowed by some of the mathematical foundations of optimization enablingthe reader to develop a deeper understanding and to be able to fully exploitthe benefits of mathematical optimization. Finally, we provide a glossary anda subject index for easy reference.

Reading Recommendations

The book has been structured in such a way that the chapters, especiallyChapters 1 to 4 depend on each other while Chapters 5 to 9 are independentfrom each other and thus can be read in any sequence. Chap. 10 providesa summary which for some readers might be the first part to look at (thereare, believe it or not, detective story readers who first want to know whowas the murderer). Of course, the chapters of the book can be read in thesequence arranged in this book. But, depending on the interest of the reader,deviations from this sequence might be appropriate. As the book addressesdifferent types of readers we suggest the following paths. These paths dependon background, interest and goal [Orientation and Real World Optimization(1); SAP APO and mathematical foundations (2), Support of own work inSAP APO projects or when producing a master or PhD thesis (3)]:

XIV Preface

profession background goal path

mathematician

scientists

no SCM

no SAP

(1)

(2)

(3)

1 (A) (2) 3 4 (5) (6) (7) (8) (9) 10 (B)

1 (2) A 3 4 (5) (6) (7) (8) (9) 10 (B)

1 (A) (2) 3 4 (5) (6) (7) (8) (9) 10 (B)

economist

SCMno SAP APO

(1)

(2)

(3)

1 (A) 2 3 4 10 (B) (5) (6) (7) (8) (9)

1 2 3 4 (5) (6) (7) (8) (9) 10 (A) (B)

(1) (2) A 3 4 (5) (6) (7) (8) (9) 10 (B)

economist

SCM

good knowledge

in mathematics

(1)

(2)

(3)

(1) 2 3 4 (5) (6) (7) (8) (9) 10 (A) (B)

(1) (2) 3 4 (5) (6) (7) (8) (9) 10 (A) (B)

(1) (2) 3 4 (5) (6) (7) (8) (9) 10 (A) (B)

economist

SCM

poor knowledge

in mathematics

(1)

(2)

(3)

(1) 2 3 4 (5) (6) (7) (8) (9) 10 (A) B

(1) 2 3 4 (5) (6) (7) (8) (9) 10 (A) (B)

(1) 2 (B) (A) 3 4 (5) (6) (7) (8) (9) 10

practitioner

consultants

good knowledge

in mathematics

(1)

(2)

(3)

(1) (2) 3 4 10 (5) (6) (7) (8) (9) (A) (B)

3 4 (5) (6) (7) (8) (9) 10 (1) (A) (2) (B)

(1) (A) (2) 3 4 10 (5) (6) (7) (8) (9) (B)

practitioner

consultants

poor knowledge

in mathematics

(1)

(2)

(3)

(1) 2 3 4 10 (5) (6) (7) (8) (9) (A) B

2 3 4 (5) (6) (7) (8) (9) 10 (1) (A) B

(1) (A) 2 B 3 4 10 (5) (6) (7) (8) (9)

Most chapters, especially the application Chapters 5 to 9 are written in sucha way that they can be read separately in spite of the many cross-references.Hence reading this book selectively is well possible. Finally we want to mentionthat in most cases the book is starting off a topic in an elementary way thatis easy to understand, but might increase in difficulty to a level that mightnot seem adequate to all readers. We choose this proceeding for being able todeal with the topics to a sufficient level of detail, address a wide variety ofreaders, and provide each of them some interesting aspects making this booka companion for quite some time of their work on optimization. We hope thatevery reader will find at least parts of the book useful and will come to theconclusion it was worthwhile to read this book.

This book is partly based on lectures at the University of Heidelberg, Uni-versity of Cologne, and the University of Florida (Gainesville, FL), conferencepapers and experience from industrial projects. We particularly stress the dif-ferent approaches when tackling optimization problems with mathematicalmodel formulation tools and with commercial advanced planning systems. Byshowing the strengths and limitations of both approaches we hope to givenovices and practitioners in supply chain management an orientation andsupport decision makers when they have to decide which way to go.

Preface XV

Acknowledgements

This book would never have been published without the common interest bothauthors had in celestial mechanics, experiencing the inspiring atmosphere ofthe Vienna Observatory and the interaction with Prof. Dr. Rudolf Dvorak4

who encouraged both of us to do some more scientific work also during ourindustrial life. This is not to say that one could not write a book on supplychain issues without a celestial mechanics background – but it definitely helps,especially when watching M13 through the observatory’s large refractor aftera few hours spending at a local wine restaurant in one of Vienna’s suburbs.Therefore, a word of thanks to Prof. Dr. Rudolf Dvorak.

We would like to thank Prof. Dr. Michael Pinedo5 for providing a draft ofhis book. This contributed to Chap. 6.

We are grateful to Ms. Melanie Seliger6 who contributed to Chap. 1, helpedin defining the example model (Chap. 3), and contributed to researching re-sults for Sect. 8.3 and Mr. Clemens M. Merk who helped with translating work-ing manuscripts on Supply Chain Management. We thank Prof. Dr. HartmutStadtler7 for his interest and constructive criticism of the book manuscript.His long-year appreciation of many activities of JK, not only during the workof this book, but also other optimization activities such as the GOR workinggroup “Praxis der mathematischen Optimierung” was always very encour-aging. A special word of thanks is directed to Prof. Dr. Martin Grotschel8

for numerous discussions on supporting mathematical optimization in indus-try. JK thanks Prof. Dr. Robert Daniel9 for giving more detailed insight intoXpress-MPTM.

We are grateful to a number of colleagues who read the manuscript criti-cally and made many valuable suggestions, especially Dr. Ulrich Eberhard10,Dr. Hans-Joachim Pitz11, Steffen Rebennack12, Dr. Anna Schreieck13, againProf. Dr. Hartmut Stadtler14, and Dr. Ruth Wassermann15.4 Institut fur Astronomie, Universitat Wien, Turkenschanzstr. 17, A-1180 Wien,

Austria5 NYU Stern, New York, NY, USA6 POM Prof. Tempelmeier GmbH, Leichlingen, Germany7 Universitat Hamburg, Hamburg, Germany8 Zuse Institut Berlin, Berlin, Germany9 Dash Optimization, Blisworth House Blisworth, GB-Northamptonshire NN7

3BX, England10 BASF Aktiengesellschaft, D-67056 Ludwigshafen, Germany11 BASF Aktiengesellschaft, KTE/P-J630, D-67056 Ludwigshafen, Germany12 Universitat Heidelberg, Heidelberg, Germany13 BASF Aktiengesellschaft, Scientific Computing (GVC/S-B009), D-67056 Lud-

wigshafen, Germany14 Universitat Hamburg, Hamburg, Germany15 axentiv AG, Darmstadt, Germany

XVI Preface

We appreciate the permission granted by Ruth Tellis (Palgrave/Macmillan)and John M. Wilson16 to use and reproduce some material (especially, pp. 39-43, pp. 105-120, pp. 128-131) from Josef Kallrath & John M. Wilson, BusinessOptimisation Using Mathematical Programming, (1997, [55]), Macmillan PressLtd., Houndsmill, Basingstoke, Hamsphire RG21 6XS, UK.

We thank Dr. Werner A. Muller17, the publishing director of Springer’sEconomics and Management Science section for his constructive support, thetime he spent with us in several meetings, all his advise during various phasesof this book project, and for being a patient editor. Thanks is also directed toBarbara Karg18 for her clear answers, instructions and help regarding variouslayout issues in the final production phase of this book.

Overall we thank everybody in the acknowledgement list and also othersproviding minor comments or suggestions who preferred not to be listed forcontributing to this three years project producing this book. It was an in-teresting project and we hope that the reader feels encouraged by the spiritof this book – the reader’s feedback will be appreciated and will likely beconsidered in a future edition of this book.

Weisenheim am Berg, January 2006 Josef Kallrath19

Mannheim, January 2006 Thomas I. Maindl20

16 Loughborough University, Loughborough, UK17 Springer-Verlag GmbH, Tiergartenstrasse 17, 69121 Heidelberg, Germany18 Springer-Verlag GmbH, Tiergartenstrasse 17, 69121 Heidelberg, Germany19 Contact this author by sending an e-mail to josef.kallrath@web.de20 Contact this author by sending an e-mail to thomas.maindl@web.de

Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX

Conventions and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXV

Part I Introduction

1 Supply Chain Management and Advanced PlanningSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Supply Chain Planning – a Brief Introduction . . . . . . . . . . . . . . . 3

1.1.1 The Supply-Chain Operations Reference Model . . . . . . . 41.1.2 Supply Chain Planning and Advanced Planning Systems 61.1.3 Advanced Planning Systems and Optimization . . . . . . . . 8

1.2 SAP APO as an Advanced Planning System . . . . . . . . . . . . . . . . 91.2.1 Components of SAP APO . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 Optimization in SAP APO . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Fundamentals of Supply Network Planning in SAP APO . . . . . 121.4 Planning Methods in SAP APO Supply Network Planning . . . . 15

1.4.1 SNP Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.4.2 SNP Capable-to-Match . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.3 SNP Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Introduction: Models, Model Building and Optimization . . . 212.1 An Important Warning on Modeling and Optimization . . . . . . . 212.2 Mathematical Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 The Main Ingredients of Optimization Models . . . . . . . . . . . . . . . 26

2.3.1 Indices and Index Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3.3 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

XVIII Contents

2.3.4 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.3.5 The Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4 Classes of Problems in Mathematical Optimization . . . . . . . . . . 322.4.1 A Deterministic Standard MINLP Problem . . . . . . . . . . . 32

2.4.1.1 Comments on Solution Algorithms . . . . . . . . . . . 332.4.1.2 Optimization Versus Simulation . . . . . . . . . . . . . 35

2.4.2 Multi-objective Optimization . . . . . . . . . . . . . . . . . . . . . . . 352.4.3 Optimization Under Uncertainty . . . . . . . . . . . . . . . . . . . . 36

2.5 Implementing Models and Solving Optimization Problems . . . . 382.5.1 Implementing Optimization Models . . . . . . . . . . . . . . . . . . 382.5.2 Solving Optimization Problems . . . . . . . . . . . . . . . . . . . . . 39

2.6 Optimization and SAP APO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Model Building in SAP APO Supply Network Planning . . . 413.1 The Example Supply Chain Model . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.1 The Supply Chain Structure . . . . . . . . . . . . . . . . . . . . . . . . 423.1.2 Constraints and Costs in the Example Model . . . . . . . . . 433.1.3 A Mathematical Formulation of the Example Model . . . 45

3.2 Supply Chain Model Master Data . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.1 Models and Planning Versions in SAP APO . . . . . . . . . . 513.2.2 Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.3 Products and Location Products . . . . . . . . . . . . . . . . . . . . 553.2.4 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2.4.1 General Resource Data . . . . . . . . . . . . . . . . . . . . . 593.2.4.2 Resource Capacity Variants . . . . . . . . . . . . . . . . . 61

3.2.5 Production Process Models . . . . . . . . . . . . . . . . . . . . . . . . . 613.2.5.1 General PPM Data . . . . . . . . . . . . . . . . . . . . . . . . 623.2.5.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.5.3 Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.2.5.4 Product Plan Assignment . . . . . . . . . . . . . . . . . . . 673.2.5.5 PPM Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2.5.6 PPM Data in the Example Model . . . . . . . . . . . . 68

3.2.6 Assembling the Parts with the Supply Chain Engineer . 693.2.7 Transportation Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4 Optimization in SAP APO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.1 Recap of the Supply Chain Model . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Optimizer Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2.1 The Optimization Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2.2 Scaling the Costs in the Master Data – the SNP Cost

Profile and SNP Cost Maintenance . . . . . . . . . . . . . . . . . . 864.2.3 Working Towards Steady Results – the SNP

Optimization Bound Profile . . . . . . . . . . . . . . . . . . . . . . . . . 874.2.4 Lot Sizes for Shipments – the SNP Lot Size Profile . . . . 884.2.5 Decomposition Methods and the SNP Priority Profile . . 89

Contents XIX

4.2.6 Settings in SAP APO Customizing – the SNPPlanning and Parallel Processing Profiles . . . . . . . . . . . . . 89

4.2.7 The Time Bucket Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.3 The Planning Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.3.1 SNP Planning Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.3.2 Continuous Variant of the Model . . . . . . . . . . . . . . . . . . . . 934.3.3 Discrete Variant of the Model . . . . . . . . . . . . . . . . . . . . . . . 98

4.4 Some Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.4.1 A Mathematician’s View . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.4.2 The Standard Business Software View . . . . . . . . . . . . . . . 101

Part II Detailed Case-Studies

5 Planning in Semiconductor Manufacturing . . . . . . . . . . . . . . . . . 1055.1 Semiconductor Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.1.1 The Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . 1065.1.2 Semiconductor Business Challenges . . . . . . . . . . . . . . . . . . 107

5.2 Supply Chain Business Practices . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.2.1 Semiconductor Capacity and Master Planning . . . . . . . . 1095.2.2 Semiconductor Supply Chain Modeling . . . . . . . . . . . . . . . 1105.2.3 Semiconductor Supply Chain Planning and SAP APO . 111

5.2.3.1 Capable-to-Match for Semiconductor . . . . . . . . . 1115.2.3.2 Optimization for Semiconductor . . . . . . . . . . . . . 113

5.3 The Semiconductor Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.3.1 The Business Objectives and Project Scope . . . . . . . . . . . 1155.3.2 The Supply Chain Structure . . . . . . . . . . . . . . . . . . . . . . . . 1165.3.3 SNP Implementation in SAP APO . . . . . . . . . . . . . . . . . . 117

6 Consumer Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.1 Supply Chain Challenges Characterizing the Consumer

Products Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.2 The Carlsberg Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.2.1 The Carlsberg Business Objectives and Project Scope . . 1216.2.2 The Supply Chain Structure in the Carlsberg Case . . . . 1216.2.3 SNP Optimization Implementation in SAP APO . . . . . . 123

7 Customized Optimization Solutions for the Automotiveand Chemical Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.1 Automotive Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.1.1 The Complete Planning System . . . . . . . . . . . . . . . . . . . . . 1267.1.2 Strategic Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1267.1.3 Mid-Range (Budget and Master Production) Planning . 128

7.1.3.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.1.3.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

XX Contents

7.1.3.3 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307.1.3.4 Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307.1.3.5 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.1.4 Order-driven Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.1.4.1 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.1.4.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.1.4.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.1.4.4 Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.1.4.5 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1347.2 Chemical Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2.1 The Architecture of the Complete Planning System . . . . 1357.2.2 Production Planning and Detailed Scheduling . . . . . . . . . 1367.2.3 Approximation Methods in SAP APO PP/DS . . . . . . . . 138

7.2.3.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387.2.3.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.2.4 Cartridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387.2.4.1 Cartridge Planning Scenario . . . . . . . . . . . . . . . . 1397.2.4.2 Optimization Problem (Overview) . . . . . . . . . . . 1397.2.4.3 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397.2.4.4 Smelter/Simple Extruder Model . . . . . . . . . . . . . 1407.2.4.5 Extruder Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.2.4.6 Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.2.4.7 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.3 The Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

8 Operative Planning in the Process Industry . . . . . . . . . . . . . . . 1438.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438.2 A Tailored MILP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

8.2.1 Basic Assumptions and Limitations of the Model . . . . . . 1478.2.2 General Framework of the Mathematical Model . . . . . . . 147

8.2.2.1 Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.2.2.2 Index Sets and Indicator Tables . . . . . . . . . . . . . 1488.2.2.3 The Problem Data . . . . . . . . . . . . . . . . . . . . . . . . . 1498.2.2.4 Time Discretization . . . . . . . . . . . . . . . . . . . . . . . . 1518.2.2.5 The Concept of Modes . . . . . . . . . . . . . . . . . . . . . 1538.2.2.6 The Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

8.2.3 The Mathematical Model – the System of Constraints . . 1568.2.3.1 Modeling the Production . . . . . . . . . . . . . . . . . . . 1568.2.3.2 Modeling Mode-changing Reactors . . . . . . . . . . . 1578.2.3.3 Multi-stage Production . . . . . . . . . . . . . . . . . . . . . 1628.2.3.4 Minimum Production Requirements . . . . . . . . . . 1648.2.3.5 Batch and Campaign Production . . . . . . . . . . . . 1678.2.3.6 Modeling Stock Balances and Inventories . . . . . 169

Contents XXI

8.2.3.7 Dedicated Inventories at Sites (Free Origin) . . . 1698.2.3.8 Modeling Transport . . . . . . . . . . . . . . . . . . . . . . . . 1768.2.3.9 Keeping Track of the Origin of Products . . . . . . 1798.2.3.10 Including Demands and Demand Constraints . . 180

8.2.4 Defining the Objective Functions . . . . . . . . . . . . . . . . . . . . 1818.2.4.1 Maximizing Contribution Margin . . . . . . . . . . . . 1828.2.4.2 Maximizing Margin – Satisfying Demand . . . . . 1858.2.4.3 Minimizing Cost While Satisfying Full Demand 1858.2.4.4 Maximizing Total Sales . . . . . . . . . . . . . . . . . . . . . 1858.2.4.5 Maximizing Net Profit . . . . . . . . . . . . . . . . . . . . . . 1878.2.4.6 Multi-criteria Objectives . . . . . . . . . . . . . . . . . . . . 1878.2.4.7 Maximizing Total Production . . . . . . . . . . . . . . . 1888.2.4.8 Maximizing Production of Requested Products 188

8.2.5 Implementation of the Model . . . . . . . . . . . . . . . . . . . . . . . 1888.2.5.1 Estimating the Quality of the Solution . . . . . . . 1898.2.5.2 Comparing Solutions of Different Scenarios . . . . 1908.2.5.3 Description of the Output . . . . . . . . . . . . . . . . . . 191

8.2.6 Real Life Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1938.2.6.1 Diagnosing Infeasibilities . . . . . . . . . . . . . . . . . . . . 1938.2.6.2 Seemingly Implausible Results . . . . . . . . . . . . . . . 1958.2.6.3 Relaxation of Constraints . . . . . . . . . . . . . . . . . . . 195

8.3 The SAP APO View on this Problem . . . . . . . . . . . . . . . . . . . . . . 1968.3.1 (Non)linear Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1978.3.2 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1978.3.3 Demand Satisfaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1988.3.4 Detailed Comments on the Tailored MILP Model . . . . . . 199

8.3.4.1 Basic Assumptions and Limitations . . . . . . . . . . 2008.3.4.2 General Framework of the Model . . . . . . . . . . . . 2008.3.4.3 The Mathematical Model – the Constraints . . . 2018.3.4.4 Description of the Outputs . . . . . . . . . . . . . . . . . . 2038.3.4.5 Diagnosing Infeasibilities . . . . . . . . . . . . . . . . . . . . 203

8.3.5 Concluding Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

9 Case Studies – Interfacing Tailored Models to SAP APO . . 2059.1 Developing Tailored Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.2 The ILOG Cartridge Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

9.2.1 ILOG Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2079.2.1.1 The Optimization Development Framework

and Cartridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2089.2.2 The Bulk Distribution Case . . . . . . . . . . . . . . . . . . . . . . . . . 208

9.2.2.1 Business Context . . . . . . . . . . . . . . . . . . . . . . . . . . 2089.2.2.2 SAP APO Project . . . . . . . . . . . . . . . . . . . . . . . . . 2099.2.2.3 Cartridge Motivations . . . . . . . . . . . . . . . . . . . . . . 2099.2.2.4 Solution Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.2.2.5 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

XXII Contents

9.2.2.6 Project Information . . . . . . . . . . . . . . . . . . . . . . . . 2159.2.3 The Load Builder Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

9.2.3.1 Business Context . . . . . . . . . . . . . . . . . . . . . . . . . . 2169.2.3.2 SAP APO Project . . . . . . . . . . . . . . . . . . . . . . . . . 2189.2.3.3 Cartridge Motivations . . . . . . . . . . . . . . . . . . . . . . 2189.2.3.4 Solution Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 2199.2.3.5 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2229.2.3.6 Project Information . . . . . . . . . . . . . . . . . . . . . . . . 222

9.2.4 The Cartridge Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 2239.2.4.1 External Architecture . . . . . . . . . . . . . . . . . . . . . . 2249.2.4.2 Data Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 2279.2.4.3 Internal Architecture . . . . . . . . . . . . . . . . . . . . . . . 227

9.2.5 About Cartridge Projects . . . . . . . . . . . . . . . . . . . . . . . . . . 2289.2.5.1 The Team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2289.2.5.2 The Inception Phase . . . . . . . . . . . . . . . . . . . . . . . 2309.2.5.3 Elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2339.2.5.4 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2339.2.5.5 Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2349.2.5.6 Risks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

9.3 Production and Sales Planning in the Chemical Industry . . . . . 2379.3.1 Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2379.3.2 Task and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2379.3.3 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

9.3.3.1 Data Download from SAP R/3 and SAP APO. 2399.3.3.2 Checks on Completeness and Consistency . . . . . 2409.3.3.3 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2409.3.3.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2419.3.3.5 Iterations and Adjustments . . . . . . . . . . . . . . . . . 2419.3.3.6 Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

9.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2429.3.4.1 The “Human Factor” . . . . . . . . . . . . . . . . . . . . . . . 2439.3.4.2 “Plug-in” Solution Versus SNP . . . . . . . . . . . . . . 243

9.3.5 Future Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2459.3.5.1 Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2459.3.5.2 Task and Objectives . . . . . . . . . . . . . . . . . . . . . . . 2469.3.5.3 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

Part III Concluding Considerations - The Future

10 Summary, Visions and Perspective . . . . . . . . . . . . . . . . . . . . . . . . . 25310.1 What Can Be Learned from this Book? . . . . . . . . . . . . . . . . . . . . 25310.2 A Summary of Experience in Optimization Projects . . . . . . . . . 255

10.2.1 When Is Optimization Useful at All? . . . . . . . . . . . . . . . . . 25510.2.2 Data and Optimization Model . . . . . . . . . . . . . . . . . . . . . . 261

Contents XXIII

10.2.3 Rules in Planning and Scheduling Problems. . . . . . . . . . . 26210.2.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26310.2.5 Interfacing Tailored Models . . . . . . . . . . . . . . . . . . . . . . . . . 265

10.3 Further Developments in Real World Optimization . . . . . . . . . . 26510.3.1 Simultaneous Operative and Strategic Optimization . . . 26610.3.2 Rigorous Approaches to Scheduling . . . . . . . . . . . . . . . . . . 26710.3.3 Planning and Scheduling Under Uncertainty . . . . . . . . . . 26810.3.4 A Mathematician’s Dream . . . . . . . . . . . . . . . . . . . . . . . . . . 26810.3.5 SAP APO as a Modeling Tool . . . . . . . . . . . . . . . . . . . . . . 269

10.4 The Future of Optimization with SAP APO . . . . . . . . . . . . . . . . 269

Part IV Appendix

A The Hitchhiker’s Guide to SAP APO . . . . . . . . . . . . . . . . . . . . . . 273A.1 SAP APO Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273A.2 Hierarchical Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

B Mathematical Foundations of Optimization . . . . . . . . . . . . . . . . 277B.1 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

B.1.1 A Primal Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 279B.1.2 Computing Initial Feasible LP Solutions . . . . . . . . . . . . . . 283B.1.3 LP Problems with Upper Bounds . . . . . . . . . . . . . . . . . . . . 284B.1.4 Dual Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 286B.1.5 Interior-point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

B.2 Mixed Integer Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . 290B.3 Multicriteria Optimization and Goal Programming . . . . . . . . . . 294

C Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

Conventions and Abbreviations

The following table contains in alphabetic order the abbreviations used in thisbook.

Abbreviation Meaning

APS Advanced Planning SystemATP Available-to-Promise

BAPI R© Business Application Programming InterfaceBOM Bill of MaterialB&B Branch and Boundcf. confer (compare)CIF Core Interfacecu currency unitCP Constraint ProgrammingCTM Capable-to-MatchCTP Capable-to-PromiseDP Demand Planninge.g. exempli gratia (for example)ERP Enterprise Resource PlanningGUI Graphical User Interfacei.e. id est (that is)IP Integer ProgrammingLP Linear ProgrammingMILP Mixed Integer Linear ProgrammingMIP Mixed Integer ProgrammingMIQP Mixed Integer Quadratic ProgrammingMINLP Mixed Integer Nonlinear ProgrammingMPEC Mathematical Programming with Equilibrium ConstraintsMRP Material Requirements PlanningNLP Nonlinear ProgrammingODBC Open DataBase ConnectivityOR Operations ResearchPDS Product Data StructurePP/DS Production Planning and Detailed Scheduling

XXVI Conventions and Abbreviations

PPM Production Process ModelQP Quadratic ProgrammingSAP APO SAP Advanced Planning and OptimizationSCM Supply Chain ManagementSNP Supply Network Plannings.t. subject tow.r.t. with respect to