Matching Supply with Demand An Introduction to Operations Management (1)

Matching
Supply with
Demand

An Introduction to
Operations Management

This page intentionally left blank

Matching
Supply with
Demand

An Introduction to
Operations Management
Third Edition

Gérard Cachon

The Wharton School,
University of Pennsylvania

Christian Terwiesch

The Wharton School,
University of Pennsylvania

MATCHING SUPPLY WITH DEMAND: AN INTRODUCTION TO OPERATIONS MANAGEMENT,
THIRD EDITION

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Library of Congress Cataloging-in-Publication Data
Cachon, Gérard.

Matching supply with demand : an introduction to operations management / Gérard Cachon,
Christian Terwiesch.—3rd ed.

p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-07-352520-4 (alk. paper)
ISBN-10: 0-07-352520-0 (alk. paper)
1. Production management. I. Terwiesch, Christian. II. Title.
TS155.C13 2013
658.5—dc23

2011043859

www.mhhe.com

To the teachers, colleagues, and
professionals who shared with us their
knowledge.

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About the Authors

Gérard Cachon The Wharton School, University of Pennsylvania

Professor Cachon is the Fred R. Sullivan Professor of Operations and Information
Management at The Wharton School of the University of Pennsylvania, where he teaches
a variety of undergraduate, MBA, executive, and Ph.D. courses in operations management.
His research focuses on supply chain management, and operations strategy; in particu-
lar, how new technologies enhance and transform competitiveness via operations. He is
a Distinguished Fellow and past president of the Manufacturing and Service Operations
Society. His articles have appeared in Harvard Business Review, Management Science,
Marketing Science, Manufacturing & Service Operations Management, and Operations
Research. He has been on the editorial review board of five leading journals in operations
management, is a former editor of Manufacturing & Service Operations Management, and
is the current editor of Management Science. He has consulted with a wide range of com-
panies, including 4R Systems, Ahold, Americold, Campbell Soup, Gulfstream Aerospace,
IBM, Medtronic, and O’Neill.

Before joining The Wharton School in July 2000, Professor Cachon was on the faculty
at the Fuqua School of Business, Duke University. He received a Ph.D. from The Wharton
School in 1995.

He is an avid proponent of bicycle commuting (and other environmentally friendly
modes of transportation). Along with his wife and four children he enjoys hiking, skiing,
fishing, snorkeling, and scuba diving.

Christian Terwiesch The Wharton School, University of Pennsylvania

Professor Terwiesch is the Andrew M. Heller Professor at the Wharton School of the
University of Pennsylvania. He also is a professor in Wharton’s Operations and Informa-
tion Management Department as well as a Senior Fellow at the Leonard Davis Institute for
Health Economics. His research on operations management, research and development,
and innovation management appears in many of the leading academic journals, includ-
ing Management Science, Operations Research, Marketing Science, and Organization
Science. He has received numerous teaching awards for his courses in Wharton’s MBA
and executive education programs.

Professor Terwiesch has researched with and consulted for various organizations,
including a project on concurrent engineering for BMW, supply chain management for
Intel and Medtronic, and product customization for Dell. Most of his current work relates
to health care and innovation management. In the health care arena, some of Professor
Terwiesch’s recent projects include the analysis of capacity allocation for cardiac surgery
procedures at the University of California–San Francisco and at Penn Medicine, the impact
of emergency room crowding on hospital capacity and revenues (also at Penn Medicine),
and the usage of intensive care beds in the Children’s Hospital of Philadelphia. In the inno-
vation area, recent projects include the management of the clinical development portfolio
at Merck, the development of open innovation systems, and the design of patient-centered
care processes in the Veterans Administration hospital system.

Professor Terwiesch’s latest book, Innovation Tournaments, outlines a novel, process-
based approach to innovation management. The book was featured by BusinessWeek, the
Financial Times, and the Sloan Management Review.

vii

Acknowledgements

We would like to acknowledge the many people who have helped us in so many different
ways with this ongoing project.

We begin with the 2004 Wharton MBA class that weathered through our initial version
of the text. It is not practical for us to name every student that shared comments with
us, but we do wish to name the students who took the time to participate in our focus
groups: Gregory Ames, Maria Herrada-Flores, Justin Knowles, Karissa Kruse, Sandeep
Naik, Jeremy Stackowitz, Charlotte Walsh, and Thomas (TJ) Zerr. The 2005 MBA class
enjoyed a much more polished manuscript, but nevertheless contributed numerous sugges-
tions and identified remaining typos and errors (much to our chagrin). Since then, we have
continued to receive feedback from our undergraduate, MBA, and executive MBA students
at Wharton. In addition to Wharton students, we received helpful feedback from students at
Texas A&M, the University of Toronto, and INSEAD.

Along with our students, we would like to thank our co-teachers in the core: Naren
Agrawal, Krishnan Anand, Omar Besbes, Morris Cohen, Marshall Fisher, Richard Lai,
Chris Lee, Pranab Majumder, Serguei Netessine, Kathy Pearson, Taylor Randall, Nicolas
Reinecke, Daniel Snow, Stephan Spinler, Anita Tucker, Karl Ulrich, Senthil Veeraraghavan,
and Yu-Sheng Zheng. In addition to useful pedagogical advice and quality testing, they
shared many of their own practice problems and questions.

This book is not the first book in Operations Management, nor will it be the last. We
hope we have incorporated the best practices of existing books while introducing our own
innovations. The book by Anupindi et al. as well as the article by Harrison and Loch were
very helpful to us, as they developed the process view of operations underlying Chapters 2
through 8. The book by Chase and Aquilano was especially useful for Chapter 10. We
apply definitions and terminology from those sources whenever possible without sacrific-
ing our guiding principles.

We also have received some indirect and direct assistance from faculty at other univer-
sities. Garrett van Ryzin’s (Columbia) and Xavier de Groote’s (INSEAD) inventory notes
were influential in the writing of Chapters 2 and 14, and the revenue management note
by Serguei Netessine (Wharton) and Rob Shumsky (Dartmouth) was the starting point
for Chapter 16. The process analysis, queuing, and inventory notes and articles written
by Martin Lariviere (Northwestern), Michael Harrison (Stanford), and Christoph Loch
(INSEAD) were also influential in several of our chapters. Martin, being a particularly
clever question designer, was kind enough to share many of his questions with us.

Matthew Drake (Duquesne University) provided us with invaluable feedback during
his meticulous accuracy check of both the text and the solutions, and we thank him for his
contribution.

Several brave souls actually read the entire manuscript and responded with detailed
comments. These reviewers included Leslie M. Bobb (Bernard M. Baruch College), Sime
Curkovic (Western Michigan University–Kalamazoo), Scott Dobos (Indiana University–
Bloomington), Ricki Ann Kaplan (East Tennessee State University), and Kathy Stecke
(University of Texas at Dallas).

Our Ph.D. student “volunteers,” Karan Girotra, Diwas KC, Marcelo Olivares, and Fuq-
iang Zhang, as well as Ruchika Lal and Bernd Terwiesch, took on the tedious job of qual-
ity testing. Robert Batt, Santiago Gallino, Antonio Moreno, Greg Neubecker, Michael Van
Pelt, and Bethany Schwartz helped to collect and analyze data and could frequently solve
practice problems faster than we could. The text is much cleaner due to their efforts.

viii

Acknowledgements ix

The many cases and practical examples that illustrate the core concepts of this book
reflect our extensive collaboration with several companies, including the University of
Pennsylvania Hospital System in the Philadelphia region, the Circored plant in Trinidad,
the Xootr factory in New Hampshire, the An-ser call center in Wisconsin, the operations
group at O’Neill in California, and the supply chain group at Medtronic in Minnesota. We
have benefited from countless visits and meetings with their management teams. We thank
the people of these organizations, whose role it is to match supply and demand in the “real
world,” for sharing their knowledge, listening to our ideas, and challenging our models.
Special thanks go to Jeff Salomon and his team (Interventional Radiology), Karl Ulrich
(Xootr), Allan Fromm (An-ser), Cherry Chu and John Pope (O’Neill), and Frederic Marie
and John Grossman (Medtronic). Allan Fromm deserves extra credit, as he was not only
willing to share with us his extensive knowledge of service operations that he gathered as a
CEO of a call center company but also proofread the entire manuscript and tackled most of
the practice problems. Special thanks also to the McKinsey operations practice, in particu-
lar Stephen Doig, John Drew, and Nicolas Reinecke, for sharing their practical experience
on Lean Operations and the Toyota Production System.

We especially thank our friend, colleague, and cycling partner Karl Ulrich, who has
been involved in various aspects of the book, starting from its initial idea to the last details
of the design process, including the cover design.

Through each edition of this text we have been supported by a fantastic team at
McGraw Hill: Scott Isenberg, Cynthia Douglas, Colin Kelley, Karthryn Mikulic,
Dick Hercher, Danielle Andries, and Erin Melloy.

Finally, we thank our family members, some of whom were surely unwilling reviewers
who nevertheless performed their family obligation with a cheerful smile.

Gérard Cachon

Christian Terwiesch

Preface

This book represents our view of the essential body of knowledge for an introductory
operations management course. It has been successfully used with all types of students,
from freshmen taking an introductory course in operations management, to MBAs, to
executive MBAs, and even PhD students.

Our guiding principle in the development of Matching Supply with Demand has been
“real operations, real solutions.” “Real operations” means that most of the chapters in this
book are written from the perspective of a specific company so that the material in this
text will come to life by discussing it in a real-world context. Companies and products are
simply easier to remember than numbers and equations. We have chosen a wide variety
of companies, small and large, representing services, manufacturing, and retailing alike.
While obviously not fully representative, we believe that—taken together—these cases
provide a realistic picture of operations management problems today.

“Real solutions” means that we do not want equations and models to merely provide
students with mathematical gymnastics for the sake of an intellectual exercise. We feel
that professional training, even in a rigorous academic setting, requires tools and strategies
that students can implement in practice. We achieve this by demonstrating how to apply
our models from start to finish in a realistic operational setting. For example, we do not
assume the existence of inputs such as a demand forecast or a cost parameter; we actually
explain how these inputs can be obtained in practice. Furthermore, we openly address the
implementation challenges of each model/strategy we discuss so that students know what
to expect when the “rubber hits the pavement.”

To fully deliver on “real operations, real solutions,” we also must adhere to the prin-
ciple of “real simple.” Do not worry; “real simple” does not mean plenty of “blah-blah”
without any analytical rigor. Quite the contrary. To us, “real simple” means hard analy-
sis that is made easy to learn. This is crucial for an operations text. Our objective is to
teach business leaders, not tacticians. Thus, we need students to be able to quickly develop
a foundation of formal models so that they have the time to explore the big picture, that is,
how operations can be transformed to provide an organization with sustainable competi-
tive advantage and/or superior customer service. Students that get bogged down in details,
equations, and analysis are not fully capturing the valuable insights they will need in their
future career.

So how do we strive for “real simple”? First, we recognize that not every student comes
to this material with an engineering/math background. As a result, we tried to use as little
mathematical notation as possible, to provide many real-world examples, and to adhere to
consistent terminology and phrasing. Second, we provide various levels of detail for each
analysis. For example, every little step in an analysis is described in the text via an explicit
example; then a summary of the process is provided in a “how to” exhibit, a brief listing of
key notation and equations is provided at the end of each chapter, and, finally, solved prac-
tice problems are offered to reinforce learning. While we do humbly recognize, given the
quantitative sophistication of this text, that “much simpler” might be more accurate than
“real simple,” we nevertheless hope that students will be pleasantly surprised to discover
that their analytical capabilities are even stronger than they imagined.

x

Preface xi

The initial version of Matching Supply with Demand made its debut in portions of the
operations management core course at Wharton in the 2002–2003 academic year. This
edition incorporates the feedback we have received over the last 10 years from many
students, executives, and colleagues, both at Wharton and abroad.

Gérard Cachon

Christian Terwiesch

Changes to This Edition

The third edition has benefited from the comments and suggestions from students, faculty,
and practitioners from around the world. The book is now translated into Chinese and
Korean, and what once was written as an MBA textbook has been taught to undergraduate
students, MBA students, doctoral students, and executives.

The changes that we implemented were substantial, touching almost every chapter of
the book. The changes can be broken up into three categories: an update of data and case
examples, the addition of three chapters related to content that was not previously covered
in the book, and an overall streamlining of the exposition of the existing content.

Many things have happened since we wrote the second edition three years ago. Compa-
nies have gone out of business, and new business models were invented. Toyota, the only
company that has a chapter dedicated to it in this book, has gone through a major crisis
with quality problems in it vehicles. Sadly enough, history also repeated itself: We used
the 2007 Japanese earthquake as a motivating example on the first page of the second edi-
tion. Now, as we write the third edition, we had to witness the devastating effects of the
2011 earthquake and the effects it had on people and business. To respond to the need to
stay current, we have updated data and case examples throughout the book.

We decided to add three new chapters to this book. The first new chapter is about proj-
ect management—a topic that is taught in many operations courses but was previously
absent from the book. The second new chapter is about sustainable operation, a topic of
rapidly growing interest in academia and in practice. We also added a chapter on business
model innovation. Just like the chapter on lean operations and the Toyota Production Sys-
tem was added as a capstone chapter for the first half of the book in the second edition, for
the third edition we wanted to bring together a set of ideas that enable companies to build
new business models using the lessons of matching supply with demand. The chapter was
fun to write, and we hope it will also be fun to read.

We have seen many textbooks grow thick over multiple editions—nothing is more
painful to an author than deleting text he or she wrote before. As much as we were com-
mitted to update the content of the book and to add fresh and relevant content, we also
wanted to keep the time constraints of our readers in mind. We took some content out of
the book (we will make it available on our book website, www.cachon-terwiesch.net) and
streamlined the exposition of several tools. It is all about lean after all.

xii

Brief Contents

1 Introduction 1 16 Revenue Management with Capacity
Controls 353
2 The Process View of the
Organization 10 17 Supply Chain Coordination 373
18 Sustainable Operations 401
3 Understanding the Supply Process: 19 Business Model Innovation 410
Evaluating Process Capacity 32
APPENDIXES
4 Estimating and Reducing Labor A Statistics Tutorial 424
Costs 56 B Tables 433
C Evaluation of the Loss Function 445
5 Project Management 80 D Equations and Approximations 448
E Solutions to Selected Practice
6 The Link between Operations and
Finance 96 Problems 456

7 Batching and Other Flow Interruptions: GLOSSARY 482
Setup Times and the Economic Order
Quantity Model 114 REFERENCES 492

8 Variability and Its Impact on Process INDEX OF KEY “HOW TO”
Performance: Waiting Time Problems 144 EXHIBITS 495

9 The Impact of Variability on Process SUMMARY OF KEY NOTATION
Performance: Throughput Losses 183 AND EQUATIONS 496

10 Quality Management, Statistical Process INDEX 500
Control, and Six-Sigma Capability 198

11 Lean Operations and the Toyota
Production System 222

12 Betting on Uncertain Demand: The
Newsvendor Model 240

13 Assemble-to-Order, Make-to-Order,
and Quick Response with Reactive
Capacity 270

14 Service Levels and Lead Times in Supply
Chains: The Order-up-to Inventory
Model 287

15 Risk-Pooling Strategies to Reduce and
Hedge Uncertainty 319

xiii

Table of Contents

Chapter 1 4.5 Scale Up to Higher Volume 66
Introduction 1 Increasing Capacity by Replicating the
Line 67
1.1 Learning Objectives and Framework 3 Increasing Capacity by Selectively Adding
1.2 Road Map of the Book 6 Workers 67
Increasing Capacity by Further Specializing
Chapter 2 Tasks 69
The Process View of the Organization 10
4.6 Summary 72
2.1 Presbyterian Hospital in Philadelphia 10 4.7 Further Reading 74
2.2 Three Measures of Process Performance 15 4.8 Practice Problems 74
2.3 Little’s Law 16
2.4 Inventory Turns and Inventory Costs 19 Chapter 5
2.5 Five Reasons to Hold Inventory 23 Project Management 80

Pipeline Inventory 23 5.1 Motivating Example 80
5.2 Critical Path Method 82
Seasonal Inventory 24 5.3 Computing Project Completion Time 83
5.4 Finding the Critical Path and Creating a Gantt
Cycle Inventory 25
Decoupling Inventory/Buffers 26 Chart 84
5.5 Computing Slack Time 85
Safety Inventory 26 5.6 Dealing with Uncertainty 88
2.6 The Product–Process Matrix 27
2.7 Summary 29 Random Activity Times 88
2.8 Further Reading 29 Potential Iteration/Rework Loops 91
2.9 Practice Problems 29 Decision Tree/Milestones/Exit Option 91
Unknown Unknowns 92
Chapter 3 5.7 How to Accelerate Projects 92
Understanding the Supply Process: 5.8 Literature/Further Reading 94
Evaluating Process Capacity 32 5.9 Practice Problems 94

3.1 How to Draw a Process Flow Diagram 33 Chapter 6
3.2 Bottleneck, Process Capacity, and Flow Rate The Link between Operations and
Finance 96
(Throughput) 38
3.3 How Long Does It Take to Produce a Certain 6.1 Paul Downs Cabinetmakers 97
6.2 Building an ROIC Tree 98
Amount of Supply? 40 6.3 Valuing Operational Improvements 103
3.4 Process Utilization and Capacity 6.4 Analyzing Operations Based on Financial

Utilization 41 Data 106
3.5 Workload and Implied Utilization 43 6.5 Summary 111
3.6 Multiple Types of Flow Units 44 6.6 Further Reading 112
3.7 Summary 48 6.7 Practice Problems 112
3.8 Practice Problems 50
Chapter 7
Chapter 4 Batching and Other Flow Interruptions:
Estimating and Reducing Labor Costs 56 Setup Times and the Economic Order
Quantity Model 114
4.1 Analyzing an Assembly Operation 56
4.2 Time to Process a Quantity X Starting with an 7.1 The Impact of Setups on Capacity 115
Empty Process 58
4.3 Labor Content and Idle Time 60
4.4 Increasing Capacity by Line Balancing 63

xiv

Table of Contents xv

7.2 Interaction between Batching and Chapter 9
Inventory 118 The Impact of Variability on Process
Performance: Throughput Losses 183
7.3 Choosing a Batch Size in the Presence of
Setup Times 121 9.1 Motivating Examples: Why Averages Do Not
Work 183
7.4 Setup Times and Product Variety 124
7.5 Setup Time Reduction 125 9.2 Ambulance Diversion 184
7.6 Balancing Setup Costs with Inventory Costs: 9.3 Throughput Loss for a Simple Process 185
9.4 Customer Impatience and Throughput
The EOQ Model 126
7.7 Observations Related to the Economic Order Loss 189
9.5 Several Resources with Variability in
Quantity 130
7.8 Other Flow Interruptions: Buffer or Sequence 191

Suffer 134 The Role of Buffers 192
7.9 Summary 136 9.6 Summary 194
7.10 Further Reading 137 9.7 Further Reading 195
7.11 Practice Problems 137 9.8 Practice Problems 195

Chapter 8 Chapter 10
Variability and Its Impact on Process Quality Management, Statistical Process
Performance: Waiting Time Problems 144 Control, and Six-Sigma Capability 198

8.1 Motivating Example: A Somewhat Unrealistic 10.1 Controlling Variation: Practical Motivation 199
Call Center 145 10.2 The Two Types of Variation 200
10.3 Constructing Control Charts 202
8.2 Variability: Where It Comes From and How It 10.4 Control Chart Example from a Service
Can Be Measured 147
Setting 205
8.3 Analyzing an Arrival Process 149 10.5 Design Specifications and Process
Stationary Arrivals 151
Exponential Interarrival Times 153 Capability 208
Nonexponential Interarrival Times 154 10.6 Attribute Control Charts 210
Summary: Analyzing an Arrival 10.7 Robust Process Design 211
Process 155 10.8 Impact of Yields and Defects on Process

8.4 Processing Time Variability 155 Flow 214
8.5 Predicting the Average Waiting Time for the
Rework 215
Case of One Resource 157
8.6 Predicting the Average Waiting Time for the Eliminating Flow Units from the Process 216

Case of Multiple Resources 161 Cost Economics and Location of Test Points 217
8.7 Service Levels in Waiting Time
Defects and Variability 218
Problems 164 10.9 A Process for Improvement 218
8.8 Economic Implications: Generating a Staffing 10.10 Further Reading 220
10.11 Practice Problems 220
Plan 165
8.9 Impact of Pooling: Economies of Scale 168 Chapter 11
8.10 Priority Rules in Waiting Lines 172 Lean Operations and the Toyota Production
System 222
Processing-Time-Dependent Priority Rules 172
Processing-Time-Independent Priority 11.1 The History of Toyota 222
Rules 172 11.2 TPS Framework 224
8.11 Reducing Variability 173 11.3 The Seven Sources of Waste 225
Ways to Reduce Arrival Variability 173 11.4 JIT: Matching Supply with Demand 228
Ways to Reduce Processing Time Variability 174
8.12 Summary 176 Achieve One-Unit-at-a-Time Flow 228
8.13 Further Reading 177 Produce at the Rate of Customer Demand 229
8.14 Practice Problems 177 Implement Pull Systems 229

xvi Table of Contents

11.5 Quality Management 231 Chapter 14
11.6 Exposing Problems through Inventory Service Levels and Lead Times in Supply
Chains: The Order-up-to Inventory
Reduction 233 Model 287
11.7 Flexibility 234
11.8 Standardization of Work and Reduction of 14.1 Medtronic’s Supply Chain 288
14.2 The Order-up-to Model Design and
Variability 236
11.9 Human Resource Practices 236 Implementation 291
11.10 Lean Transformation 237 14.3 The End-of-Period Inventory Level 294
11.11 Further Reading 239 14.4 Choosing Demand Distributions 295
11.12 Practice Problems 239 14.5 Performance Measures 299

Chapter 12 In-Stock and Stockout Probability 299
Betting on Uncertain Demand: The
Newsvendor Model 240 Expected Back Order 301

12.1 O’Neill Inc. 241 Expected On-Hand Inventory 302
12.2 An Introduction to the Newsvendor
Pipeline Inventory/Expected On-Order
Model 243
12.3 Constructing a Demand Forecast 243 Inventory 303
12.4 The Expected Profit-Maximizing Order 14.6 Choosing an Order-up-to Level to Meet a

Quantity 250 Service Target 304
12.5 Performance Measures 254 14.7 Choosing an Appropriate Service

Expected Lost Sales 255 Level 304
14.8 Controlling Ordering Costs 308
Expected Sales 256 14.9 Managerial Insights 311
14.10 Summary 313
Expected Leftover Inventory 257 14.11 Further Reading 314
14.12 Practice Problems 314
Expected Profit 257
Chapter 15
In-Stock Probability and Stockout Risk-Pooling Strategies to Reduce and
Hedge Uncertainty 319
Probability 258
12.6 Choosing an Order Quantity to Meet a Service 15.1 Location Pooling 319
Pooling Medtronic’s Field Inventory 320
Objective 259 15.2 Medtronic’s Distribution Center(s) 324
12.7 Managerial Lessons 259 15.3 Electronic Commerce 325
12.8 Summary 262
12.9 Further Reading 263 15.4 Product Pooling 326
12.10 Practice Problems 263 15.5 Lead Time Pooling: Consolidated Distribution
15.6 and Delayed Differentiation 333
Chapter 13 15.7
Assemble-to-Order, Make-to-Order, Consolidated Distribution 333
and Quick Response with Reactive Delayed Differentiation 338
Capacity 270 Capacity Pooling with Flexible
Manufacturing 341
13.1 Evaluating and Minimizing the Summary 347
Newsvendor’s Demand–Supply Mismatch Further Reading 348
13.2 Cost 271 Practice Problems 348
13.3 When Is the Mismatch Cost High? 273
Reducing Mismatch Costs with Make-to- Chapter 16
13.4 Order 276 Revenue Management with Capacity
Quick Response with Reactive Controls 353
13.5 Capacity 277
13.6 Summary 281 16.1 Revenue Management and Margin
13.7 Further Reading 282 Arithmetic 353
Practice Problems 282
16.2 Protection Levels and Booking Limits 355

Table of Contents xvii

16.3 Overbooking 361 18.2 Material 404
16.4 Implementation of Revenue 18.3
Management 363 Agriculture, Fishing, and Forestry 404
16.5 18.4
16.6 Demand Forecasting 363 18.5 People 405
16.7 Dynamic Decisions 364 18.6 Sustainability: The Business Case 405
Variability in Available Capacity 364 Sustainability and Operations
Reservations Coming in Groups 364 Management 406
Effective Segmenting of Customers 364 Summary 409
Multiple Fare Classes 364 Further Reading 409
Software Implementation 365 Practice Problems 409
Variation in Capacity Purchase: Not All
Customers Purchase One Unit of Capacity 365 Chapter 19
Summary 367 Business Model Innovation 410
Further Reading 368
Practice Problems 368 19.1 Zipcar and Netflix 410
19.2 Innovation and Value Creation 412
Chapter 17 19.3 The Customer Value Curve:
Supply Chain Coordination 373 The Demand Side of Business Model
19.4 Innovation 414
17.1 The Bullwhip Effect: Causes and Solutions: The Supply Side of Business Model
Consequences 373 19.5 Innovation 417
17.2 19.6
Order Synchronization 376 19.7 Process Timing 418
17.3 Order Batching 377
17.4 Trade Promotions and Forward Buying 378 Process Location 419
17.5 Reactive and Overreactive Ordering 382
Shortage Gaming 383 Process Standardization 421
17.6 Bullwhip Effect: Mitigating Strategies 384 Unsuccessful Business Model
17.7 Sharing Information 384 Innovation 422
17.8 Smoothing the Flow of Product 385 Summary 423
Eliminating Pathological Incentives 385 Further Reading 423
Using Vendor-Managed Inventory 386
The Countereffect to the Bullwhip Effect: Appendix A Statistics Tutorial 424
Production Smoothing 388
Incentive Conflicts in a Sunglasses Supply Appendix B Tables 433
Chain 389
Buy-Back Contracts 392 Appendix C Evaluation of the Loss
More Supply Chain Contracts 395 Function 445
Quantity Discounts 395
Options Contracts 395 Appendix D Equations and
Revenue Sharing 396 Approximations 448
Quantity Flexibility Contracts 396
Price Protection 397 Appendix E Solutions to Selected Practice
Summary 397 Problems 456
Further Reading 398
Practice Problems 398 Glossary 482

References 492

Index of Key “How to” Exhibits 495

Chapter 18 Summary of Key Notation and
Sustainable Operations 401 Equations 496

18.1 Sustainability: Background 401 Index 500
Energy 401
Water 404

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1Chapter
Introduction

A central premise in economics is that prices adjust to match supply with demand: if there
is excess demand, prices rise; if there is excess supply, prices fall. But while an economist
may find comfort with this theory, managers in practice often do not. To them excess
demand means lost revenue and excess supply means wasted resources. They fully under-
stand that matching supply with demand is extremely difficult and requires more tools than
just price adjustments.

Consider the following examples:

• In 2006, Nintendo launched the Wii game console with much success—so much suc-
cess that the company could not make enough units to keep up with demand. Some entre-
preneurs would wait in long lines to purchase scarce units only to turn around and sell them
online for several hundred dollars over the retail price.

• In 2007, Dell lost its worldwide market share leadership to HP. Trying to regain
momentum, Dell offered laptop computers to consumers in various colors. Unfortunately,
problems with dust contamination in the painting process prevented Dell from ramping up
production, causing long delays, which in turn caused some customers to cancel their order.

• At 4 p.m. on weekdays, it is hard to find a taxi in Manhattan because that is when taxis
tend to change between shifts. Consequently, customers wait longer for a cab.

• In March 2011, a massive earthquake hit Japan, followed by devastating tsunamis.
Supplies for some key automobile and electronic components were unavailable or scarce
for months, disrupting production around the globe.

• In 2008, Boeing was unable to deliver on time its new 777s to Emirates Airlines because
growth in demand caught its supplier of kitchen galleys off guard and short on capacity.

• In early 2002, a victim of a car crash in Germany died in a rescue helicopter after the
medical team together with their dispatcher had unsuccessfully attempted to find a slot in
an operating room at eight different hospitals. In the United States, every day there are
thousands of patients requiring emergency care who cannot be transported to the nearest
emergency room and/or have to wait considerable time before receiving care.

• The average customer to Disney World experiences only nine rides per day, in part
because of long queues. To give customers a better experience (read, “more rides”), Disney
developed several mechanisms to encourage customers to find rides with short or no queues.

All of these cases have in common that they suffer from a mismatch between demand
and supply, with respect either to their timing or to their quantities.

This book is about how firms can design their operations to better match supply with
demand. Our motivation is simply stated: By better matching supply with demand, a firm
gains a significant competitive advantage over its rivals. A firm can achieve this better

1

2 Chapter 1

match through the implementation of the rigorous models and the operational strategies
we outline in this book.

To somewhat soften our challenge to economic theory, we do acknowledge it is pos-
sible to mitigate demand–supply mismatches by adjusting prices. For example, the effec-
tive market price of the Wii game console did rise due to the strong demand. But this price
adjustment was neither under Nintendo’s control, nor did Nintendo (or its retailers) collect
the extra surplus. In other words, we view that price adjustment as a symptom of a prob-
lem, rather than evidence of a healthy system. Moreover, in many other cases, price adjust-
ments are impossible. The time period between the initiation of demand and the fulfillment
through supply is too short or there are too few buyers and sellers in the market. There
simply is no market for emergency care in operating rooms, waiting times in call centers,
or piston rings immediately after an earthquake.

Why is matching supply with demand difficult? The short answer is that demand can vary,
in either predictable or unpredictable ways, and supply is inflexible. On average, an organiza-
tion might have the correct amount of resources (people, product, and/or equipment), but most
organizations find themselves frequently in situations with resources in the wrong place, at the
wrong time, and/or in the wrong quantity. Furthermore, shifting resources across locations or
time is costly, hence the inflexibility in supply. For example, physicians are not willing to rush
back and forth to the hospital as they are needed and retailers cannot afford to immediately
move product from one location to another. While it is essentially impossible to always achieve
a perfect match between supply and demand, successful firms continually strive for that goal.

Table 1.1 provides a sample of industries that we will discuss in this book and describes
their challenge to match supply with demand. Take the airline industry (last column in
Table 1.1.). For fiscal year 2007, British Airways achieved a 76.1 percent utilization; that is,
a 160-seat aircraft (the average size in their fleet) had, on average, 122 seats occupied with
a paying passenger and 38 seats flying empty. If British Airways could have had four more
(paying) passengers on each flight, that is, increase its utilization by about 2.5 percent, its
corporate profits would have increased by close to £242 million, which is about 44 percent
of its operating profit for 2007. This illustrates a critical lesson: Even a seemingly small

TABLE 1.1 Examples of Supply–Demand Mismatches

Supply Retailing Iron Ore Plant Emergency Room Pacemakers Air Travel
Demand Iron ore Medical service Seats on specific
Consumer Medical flight
electronics Steel mills Urgent need for equipment Travel for specific
medical service time and
Consumers buying Heart surgeon destination
a new video Doctors, nurses, requiring pace-
system and infrastructure maker at exact Empty seat
are underutilized time and location
Supply exceeds High inventory Prices fall Crowding and
demand costs; few delays in the ER; Pacemaker sits
inventory turns Prices rise potential diversion in inventory
of ambulances
Demand exceeds Forgone profit If prices fall too Staffing to Forgone profit Overbooking;
low, production predicted demand; (typically not customer has to
supply opportunity; facility is shut priorities associated with take different
down medical risk) flight (profit loss)
consumer

dissatisfaction

Actions to match Forecasting; quick Distribution Dynamic pricing;

supply and response system holding booking policies

demand pacemakers at vari-

ous locations

(continued )

Introduction 3

TABLE 1.1 Concluded

Managerial Per-unit inventory Prices are so Delays in treat- Most products About 30% of all
importance costs for consumer competitive that ment or transfer (valued $20k) seats fly empty;
electronics retailing the primary have been linked to spend 4–5 months a 1–2% increase
Reference all too often exceed emphasis is on death waiting in a trunk in seat utilization
net profits reducing the cost of a salesperson makes the difference
of supply before being used between profits
and losses

Chapter 2, Chapter 3, Chapter 8, Chapter 14, Chapter 16,
The Process View Service Levels and Revenue
of the Organization; Understanding the Variability and Its Lead Times in Management with
Chapter 12, Betting Supply Chains: Capacity Controls
on Uncertain Supply Process: Impact on Process The Order-up-to
Demand: The Inventory Model
Newsvendor Evaluating Process Performance:
Model; Chapter 13,
Assemble-to-Order, Capacity; Waiting Time
Make-to-Order,
and Quick Chapter 4, Problems;
Response with
Reactive Capacity Estimating and Chapter 9, The

Reducing Labor Impact of Vari-

Costs ability on Process

Performance:

Throughput Losses

improvement in operations, for example, a utilization increase of 2.5 percent, can have a sig-
nificant effect on a firm’s profitability precisely because, for most firms, their profit (if they
have a profit) is a relatively small percentage of their revenue. Hence, improving the match
between supply and demand is a critically important responsibility for a firm’s management.

The other examples in Table 1.1 are drawn from a wide range of settings: health care
delivery and devices, retailing, and heavy industry. Each suffers significant consequences
due to demand–supply mismatches, and each requires specialized tools to improve and
manage its operations.

To conclude our introduction, we strongly believe that effective operations management
is about effectively matching supply with demand. Organizations that take the design of
their operations seriously and aggressively implement the tools of operations management
will enjoy a significant performance advantage over their competitors. This lesson is espe-
cially relevant for senior management given the razor-thin profit margins firms must deal
with in modern competitive industries.

1.1 Learning Objectives and Framework

In this book, we look at organizations as entities that must match the supply of what they
produce with the demand for their product. In this process, we will introduce a number of
quantitative models and qualitative strategies, which we collectively refer to as the “tools
of operations management.” By “quantitative model” we mean some mathematical proce-
dure or equation that takes inputs (such as a demand forecast, a processing rate, etc.) and
outputs a number that either instructs a manager on what to do (how much inventory to
buy, how many nurses to have on call, etc.) or informs a manager about a relevant perfor-
mance measure (e.g., the average time a customer waits for service, the average number of
patients in the emergency room, etc.). By “qualitative strategy” we mean a guiding princi-
ple: for example, increase the flexibility of your production facilities, decrease the variety
of products offered, serve customers in priority order, and so forth. The next section gives
a brief description of the key models and strategies we cover. Our learning objective for

4 Chapter 1

this book, put as succinctly as we can, is to teach students how and when to implement the
tools of operations management.

Just as the tools of operations management come in different forms, they can be applied
in different ways:

1. Operations management tools can be applied to ensure that resources are used as effi-
ciently as possible; that is, the most is achieved with what we have.

2. Operations management tools can be used to make desirable trade-offs between com-
peting objectives.

3. Operations management tools can be used to redesign or restructure our operations so
that we can improve performance along multiple dimensions simultaneously.

We view our diverse set of tools as complementary to each other. In other words, our
focus is neither exclusively on the quantitative models nor exclusively on the qualitative
strategies. Without analytical models, it is difficult to move beyond the “blah-blah” of
strategies and without strategies, it is easy to get lost in the minutia of tactical models. Put
another way, we have designed this book to provide a rigorous operations management
education for a strategic, high-level manager or consultant.

We will apply operations tools to firms that produce services and goods in a variety
of environments—from apparel to health care, from call centers to pacemakers, and from
kick scooters to iron ore fines. We present many diverse settings precisely because there
does not exist a “standard” operational environment. Hence, there does not exist a single
tool that applies to all firms. By presenting a variety of tools and explaining their pros and
cons, students will gain the capability to apply this knowledge no matter what operational
setting they encounter.

Consider how operations tools can be applied to a call center. A common problem
in this industry is to find an appropriate number of customer service representatives to
answer incoming calls. The more representatives we hire, the less likely incoming calls
will have to wait; thus, the higher will be the level of service we provide. However, labor is
the single largest driver of costs in a call center, so, obviously, having more representatives
on duty also will increase the costs we incur per call.

The first use of operations management tools is to ensure that resources are used as
effectively as possible. Assume we engage in a benchmarking initiative with three other call
centers and find that the performance of our competitors behaves according to Figure 1.1:
Competitor A is providing faster response times but also has higher costs. Competitor B has
longer response times but has lower costs. Surprisingly, we find that competitor C outper-
forms us on both cost and service level. How can this be?

It must be that there is something that competitor C does in the operation of the call
center that is smarter than what we do. Or, in other words, there is something that we do
in our operations that is inefficient or wasteful. In this setting, we need to use our tools
to move the firm toward the frontier illustrated in Figure 1.1. The frontier is the line that
includes all benchmarks to the lower left; that is, no firm is outside the current frontier. For
example, a premium service might be an important element of our business strategy, so we
may choose not to compromise on service. And we could have a target that at least 90 per-
cent of the incoming calls will be served within 10 seconds or less. But given that target,
we should use our quantitative tools to ensure that our labor costs are as low as possible,
that is, that we are at least on the efficiency frontier.

The second use of operations management tools is to find the right balance between our
competing objectives, high service and low cost. This is similar to what is shown in Fig-
ure 1.2. In such a situation, we need to quantify the costs of waiting as well as the costs of
labor and then recommend the most profitable compromise between these two objectives.

Introduction 5

FIGURE 1.1 Responsiveness
High
Local Improvement
of Operations by
Eliminating
Inefficiencies

Competitor A
Eliminate
Inefficiencies

Current Frontier
Competitor C in the Industry

Low Competitor B Labor Productivity
(e.g., $/Call)
Low Labor High Labor
Productivity Productivity

Moving to the frontier of efficiency and finding the right spot on the frontier are
surely important. But outstanding companies do not stop there. The third use for our
operations management tools is to fundamentally question the design of the current
system itself. For example, a call center might consider merging with or acquiring
another call center to gain scale economies. Alternatively, a call center might consider
an investment in the development of a new technology leading to shorter call durations.

FIGURE 1.2 Responsiveness
High
Trade-off between
Labor Productivity
and Responsiveness

Shorter Waiting Times
but More Operator Idle Time

Current Position Longer Waiting Times,
on the Frontier Yet Operators Are More
Fully Utilized

Low High Labor Labor Productivity
Productivity (e.g., $/Call)
Low Labor
Productivity

6 Chapter 1

FIGURE 1.3 Responsiveness
High
Redesigning the
Process to Operate at
an Improved Frontier

Redesign
Process

New Frontier

Current Frontier
in the Industry

Low High Labor Labor Productivity
Productivity (e.g., $/Call)
Low Labor
Productivity

In such cases, a firm pushes the envelope, that is, moves the frontier of what previ-
ously was feasible (see Figure 1.3). Hence, a firm is able to achieve faster responsiveness
and higher labor productivity. But, unfortunately, there are few free lunches: while we have
improved both customer service and labor productivity, pushing out the frontier generally
requires some investments in time and effort. Hence, we need to use our tools to quantify
the improvements we can achieve so that we can decide whether the effort is justifiable. It is
easy to tell a firm that investing in technology can lead to shorter call durations, faster service,
and higher labor productivity, but is that investment worthwhile? Our objective is to educate
managers so that they can provide “big ideas” and can back them up with rigorous analysis.

1.2 Road Map of the Book

This book can be roughly divided into five clusters of closely related chapters.

The first cluster, Chapters 2–7, analyzes business processes (the methods and proce-
dures by which a service is completed or a good is produced). For the most part, the
view taken in those chapters is one of process without variability in service times, pro-
duction times, demand arrival, quality, and so forth. Hence, the objective is to orga-
nize the business process to maximize supply given the resources available to the firm.

Chapters 8–11 introduce variability into business process analysis. Issues include the
presence of waiting times, lost demand due to poor service, and lost output due to poor
quality. This cluster concludes with an overview of the Toyota Production System.

Chapters 12–15 discuss inventory control, information management, and process flex-
ibility. Issues include demand forecasting, stocking quantities, performance measures,
product design, and production flexibility.

Chapter 16 departs from a focus on the supply process and turns attention to the
demand process. In particular, the chapter covers the tools of revenue management
that allow a firm to better match its demand to its fixed supply.

Introduction 7

TABLE 1.2 Chapters Theme
A High-Level 2–7
Grouping of Process analysis without variability in service times, production rates, demand arrival,
Chapters 8–11 quality, etc.
Process analysis with variability in service times, production rates, demand arrival,
12–15 quality, etc.
16 Inventory control, information management, process flexibility
Revenue management
17–19 Strategic operations management: supply chains, sustainability, and business models

Chapters 17–19 conclude the book with several strategic topics, including the manage-
ment and control of the supply chain, sustainability, and business model innovation.

Table 1.2 summarizes these clusters.
The following provides a more detailed summary of the contents of each chapter:

• Chapter 2 defines a process, introduces the basic process performance metrics, and
provides a framework for characterizing processes (the product–process matrix). Little’s
Law is introduced, an essential formula for understanding business processes and the link
between operations management and financial accounting.

• Chapter 3 introduces process analysis tools from the perspective of a manager (as
opposed to an engineer): how to determine the capacity of a process and how to compute
process utilization.

• Chapter 4 looks at assembly operations with a specific focus on labor costs, an
extremely important performance metric. It frequently drives location decisions (consider
the current debate related to offshoring) and has—especially in service operations—a
major impact on the bottom line. We define measures such as labor content, labor utiliza-
tion, and idle time. We also introduce the concept of line balancing.

• Chapter 5 investigates project management, a process that is designed for a single,
somewhat unique, project such as a ship, a new building, or a satellite.

• Chapter 6 connects the operational details of process analysis with key financial per-
formance measures for a firm, such as return on invested capital. Through this chapter we
discover how to make process improvement translate into enhanced financial performance
for the organization.

• Chapter 7 studies production in the presence of setup times and setup costs (the EOQ
model). A key issue is the impact of product variety on production performance.

• Chapter 8 explores the consequences of variability on a process. As we will dis-
cuss in the context of a call center, variability can lead to long customer waiting times
and thereby is a key enemy in all service organizations. We discuss how an organization
should handle the trade-off between a desire for minimizing the investment into capacity
(e.g., customer service representatives) while achieving a good service experience for the
customer.

• Chapter 9 continues the discussion of variability and its impact on service quality. As
we will discuss in the context of emergency medicine, variability frequently can lead to
situations in which demand has to be turned away because of insufficient capacity. This
has substantial implications, especially in the health care environment.

• Chapter 10 details the tools of quality management, including statistical process con-
trol, six-sigma, and robust design.

• Chapter 11 describes how Toyota, via its world-famous collection of production
strategies called the Toyota Production System, achieves high quality and low cost.

8 Chapter 1

• Chapter 12 focuses on the management of seasonal goods with only one supply oppor-
tunity. The newsvendor model allows a manager to strike the correct balance between too
much supply and too little supply.

• Chapter 13 expands upon the setting of the previous chapter by allowing additional
supply to occur in the middle of the selling season. This “reactive capacity” allows a firm
to better respond to early season sales information.

• Chapter 14 continues the discussion of inventory management with the introduc-
tion of lead times. The order-up-to model is used to choose replenishment quantities that
achieve target availability levels (such as an in-stock probability).

• Chapter 15 highlights numerous risk-pooling strategies to improve inventory man-
agement within the supply chain: for example, location pooling, product pooling, universal
design, delayed differentiation (also known as postponement), and capacity pooling.

• Chapter 16 covers revenue management. In particular, the focus is on the use of book-
ing limits and overbooking to better match demand to supply when supply is fixed.

• Chapter 17 identifies the bullwhip effect as a key issue in the effective operation of
a supply chain and offers coordination strategies for firms to improve the performance of
their supply chain.

• Chapter 18 applies operations management thinking to the challenge of sustainability.

• Chapter 19 concludes the book with how operations management enables new busi-
ness models. A framework is presented for understanding business model innovation that
can assist in the creation of new business models.

Some of the chapters are designed to be “entry level” chapters, that is, chapters that
can be read independently from the rest of the text. Other chapters are more advanced, so
they at least require some working knowledge of the material in another chapter. Table 1.3
summarizes the contents of the chapters and indicates prerequisite chapters.

TABLE 1.3 Chapter Summaries and Prerequisites

Chapter Managerial Issue Key Qualitative Key Quantitative Prerequisite
2: The Process View of Framework Tool Chapters
the Organization Understanding business Product–process matrix;
processes at a high level; focus on process flows Little’s Law None
3: Understanding the process performance
Supply Process: measures, inventory, flow Process flow diagram; Inventory turns and
Evaluating Process time, and flow rate finding and removing a inventory costs
Capacity bottleneck
4: Estimating and Understanding the details Computing process Chapter 2
Reducing Labor Costs of a process
capacity and utilization

Labor costs Line balancing; division Computing labor costs, Chapters 2, 3
of labor labor utilization
Chapters 2, 3
5: Project Management Time to project completion Critical path Minimizing idle time Chapters 2, 3

6: The Link between Process improvement Return on Invested Critical path analysis
Operations and Finance to enhance corporate Capital (ROIC) tree
performance Computing ROIC
7: Batching and Other
Flow Interruptions: Setup time and setup Achieving a smooth EOQ model Chapters 2, 3
Setup Times and the costs; managing product process flow; deciding
Economic Order variety about setups and Determining batch sizes
Quantity Model ordering frequency

(continued )

Introduction 9

TABLE 1.3 Concluded

Chapter Managerial Issue Key Qualitative Key Quantitative Prerequisite
Framework Tool Chapters

8: Variability and Its Waiting times in service Understanding congestion; Waiting time formula None
Impact on Process processes pooling service capacity
Performance: Waiting
Time Problems

9: The Impact of Lost demand in service Role of service buffers; Erlang loss formula Chapter 8
Variability on Process processes pooling
Performance:
Throughput Losses Probability of diverting
demand

10: Quality Management, Defining and improving Statistical process control; Computing process None
Statistical Process quality six-sigma capability; creating a
Control, and Six-Sigma control chart
Capability

11: Lean Operations Process improvement for Lean operations; Toyota — None
and the Toyota competitive advantage Production System
Production System

12: Betting on Uncertain Choosing stocking levels Improving the forecasting Forecasting demand None
Demand: The for seasonal-style goods process
Newsvendor Model
The newsvendor model
for choosing stocking
quantities and evaluating
performance measures

13: Assemble-to-Order, How to use reactive Value of better demand Reactive capacity models Chapter 12
Make-to-Order, and capacity to reduce information; assemble-to-
Quick Response with demand–supply mismatch order and make-to-order
Reactive Capacity costs strategies

14: Service Levels and Inventory management Impact of lead times on The order-up-to model Chapter 12 is
Lead Times in Supply with numerous performance; how to for inventory manage- highly
Chains: The Order-up- replenishments choose an appropriate ment and performance- recom-
to Inventory Model objective function measure evaluation mended

15: Risk Pooling How to better design the Quantifying, reducing, Newsvendor and order- Chapters 12
Strategies to Reduce supply chain or a product avoiding, and hedging
and Hedge Uncertainty or a service to better uncertainty up-to models and 14
match supply with
demand

16: Revenue Manage- How to manage demand Reserving capacity for Booking limit/protection Chapter 12
ment with Capacity when supply is fixed high-paying customers; level model; overbooking
Controls accepting more reserva- model
tions than available
capacity

17: Supply Chain How to manage demand Bullwhip effect; supply Supply chain contract Chapter 12
Coordination variability and inventory chain contracts model
across the supply chain

18: Sustainability How to employ operations Measuring resource use — None
management techniques and emissions
to a sustainability initiative

19: Business Model How to create a business Customer value curve — None
Innovation model innovation and supply process
transformation

2Chapter
The Process View of
the Organization

Matching supply and demand would be easy if business processes would be instantaneous
and could immediately create any amount of supply to meet demand. Understanding the
questions of “Why are business processes not instantaneous?” and “What constrains pro-
cesses from creating more supply?” is thereby at the heart of operations management. To
answer these questions, we need to take a detailed look at how business processes actually
work. In this chapter, we introduce some concepts fundamental to process analysis. The
key idea of the chapter is that it is not sufficient for a firm to create great products and ser-
vices; the firm also must design and improve its business processes that supply its products
and services.

To get more familiar with the process view of a firm, we now take a detailed look
behind the scenes of a particular operation, namely the Department of Interventional Radi-
ology at Presbyterian Hospital in Philadelphia.

2.1 Presbyterian Hospital in Philadelphia

Interventional radiology is a subspecialty field of radiology that uses advanced imaging
techniques such as real-time X-rays, ultrasound, computed tomography, and magnetic
resonance imaging to perform minimally invasive procedures.

Over the past decade, interventional radiology procedures have begun to replace an
increasing number of standard “open surgical procedures” for a number of reasons. Instead
of being performed in an operating room, interventional radiology procedures are per-
formed in an angiography suite (see Figure 2.1). Although highly specialized, these rooms
are less expensive to operate than conventional operating rooms. Interventional procedures
are often safer and have dramatically shorter recovery times compared to traditional sur-
gery. Also, an interventional radiologist is often able to treat diseases such as advanced
liver cancer that cannot be helped by standard surgery.

Although we may not have been in the interventional radiology unit, many, if not most,
of us have been in a radiology department of a hospital at some point in our life. From the
perspective of the patient, the following steps need to take place before the patient can go
home or return to his or her hospital unit. In process analysis, we refer to these steps as
activities:

• Registration of the patient.
• Initial consultation with a doctor; signature of the consent form.

10

The Process View of the Organization 11

FIGURE 2.1

Example of a
Procedure in an
Interventional
Radiology Unit

Reprinted with permission of
Arrow International, Inc.

• Preparation for the procedure.

• The actual procedure.

• Removal of all equipment.

• Recovery in an area outside the angiography suite.

• Consultation with the doctor.

Figure 2.2 includes a graphical representation of these steps, called a Gantt diagram
(named after the 19th-century industrialist Henry Gantt). It provides several useful pieces
of information.

First, the Gantt chart allows us to see the process steps and their durations, which are
also called activity times or processing times.The duration simply corresponds to the
length of the corresponding bars. Second, the Gantt diagram also illustrates the depen-
dence between the various process activities. For example, the consultation with the doctor
can only occur once the patient has arrived and been registered. In contrast, the preparation
of the angiography suite can proceed in parallel to the initial consultation.

You might have come across Gantt charts in the context of project management. Unlike
process analysis, project management is typically concerned with the completion of one sin-
gle project (See Chapter 5 for more details on project management.) The most well-known
concept of project management is the critical path. The critical path is composed of all those
activities that—if delayed—would lead to a delay in the overall completion time of the proj-
ect, or—in this case—the time the patient has completed his or her stay in the radiology unit.

In addition to the eight steps described in the Gantt chart of Figure 2.2, most of us asso-
ciate another activity with hospital care: waiting. Strictly speaking, waiting is not really

12 Chapter 2 Registration
Initial Consultation
FIGURE 2.2 Preparation of Room
Preparation of Patient
Gantt Chart
Summarizing the Procedure
Activities for Removal of Equipment
Interventional
Radiology Recovery
Consultation

Time
7:45 8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00

Activity Taking Place in Angiography Suite

an activity, as it does not add any value to the process. However, waiting is nevertheless
relevant. It is annoying for the patient and can complicate matters for the hospital unit. For
this reason, waiting times take an important role in operations management. Figure 2.3
shows the actual durations of the activities for a patient arriving at 12:30, as well as the
time the patient needs to wait before being moved to the angiography suite.

FIGURE 2.3 Registration Patient Waits
Initial Consultation
Gantt Chart
Summarizing the Preparation of Room
Activities for a
Patient Arriving
at 12:30

Preparation of Patient

Procedure

Removal of Equipment

Recovery

Consultation

Time
12:30 12:45 13:00 13:15 13:30 13:45 14:00 14:15 14:30 14:45 15:00

Activity Taking Place in Angiography Suite

The Process View of the Organization 13

But why is there waiting time? Waiting is—to stay in the medical language for the
moment—a symptom of supply–demand mismatch. If supply would be unlimited, our
visit to the hospital would be reduced to the duration of the activities outlined in Figure 2.2
(the critical path). Imagine visiting a hospital in which all the nurses, technicians, doctors,
and hospital administrators would just care for you!

Given that few of us are in a position to receive the undivided attention of an entire hos-
pital unit, it is important that we not only take the egocentric perspective of the patient, but
look at the hospital operations more broadly. From the perspective of the hospital, there
are many patients “flowing” through the process.

The people and the equipment necessary to support the interventional radiology process
deal with many patients, not just one. We refer to these elements of the process as the pro-
cess resources. Consider, for example, the perspective of the nurse and how she/he spends
her/his time in the department of interventional radiology. Obviously, radiology from the
viewpoint of the nurse is not an exceptional event, but a rather repetitive endeavor. Some
of the nurse’s work involves direct interaction with the patient; other work—while required
for the patient—is invisible to the patient. This includes the preparation of the angiography
suite and various aspects of medical record keeping.

Given this repetitive nature of work, the nurse as well as the doctors, technicians, and
hospital administrators think of interventional radiology as a process, not a project. Over
the course of the day, they see many patients come and go. Many hospitals, including the
Presbyterian Hospital in Philadelphia, have a “patient log” that summarizes at what times
patients arrive at the unit. This patient log provides a picture of demand on the correspond-
ing day. The patient log for December 2, is summarized by Table 2.1.

Many of these arrivals were probably scheduled some time in advance. Our analysis
here focuses on what happens to the patient once he/she has arrived in the interventional
radiology unit. A separate analysis could be performed, looking at the process starting with
a request for diagnostics up to the arrival of the patient.

Given that the resources in the interventional radiology unit have to care for 11 patients
on December 2, they basically need to complete the work according to 11 Gantt charts of
the type outlined in Figure 2.2. This—in turn—can lead to waiting times. Waiting times
arise when several patients are “competing” for the same limited resource, which is illus-
trated by the following two examples.

First, observe that the critical path for a typical patient takes about 2 hours. Note further
that we want to care for 11 patients over a 10-hour workday. Consequently, we will have
to take care of several patients at once. This would not be a problem if we had unlim-
ited resources, nurses, doctors, space in the angiography suites, and so forth. However,

TABLE 2.1 Number Patient Name Arrival Time Room Assignment
Patient Log on Main room
December 2 1 7:35
2 7:45 Main room
3 8:10 Main room
4 9:30 Main room
5 10:15
6 10:30 Main room
7 11:05 Main room
8 12:35
9 14:30
10 14:35
11 14:40

14 Chapter 2

FIGURE 2.4 Patient 9 Patient
Patient 8 Wait
Time Patient Spent in
the Interventional Patient 6
Radiology Unit (for
Patients Treated in
Main Room Only),
Including Room
Preparation Time

Patient 5

Patient 4 Room Prepared
Patient 1 Before Patient Arrives

Time
7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Activity Taking Place in Angiography Suite

given the resources that we have, if the Gantt charts of two patients are requesting the
same resource simultaneously, waiting times result. For example, the second patient might
require the initial consultation with the doctor at a time when the doctor is in the middle
of the procedure for patient 1. Note also that patients 1, 4, 5, 6, 8, and 9 are assigned to the
same room (the unit has a main room and a second room used for simpler cases), and thus
they are also potentially competing for the same resource.

A second source of waiting time lies in the unpredictable nature of many of the activi-
ties. Some patients will take much longer in the actual procedure than others. For example,
patient 1 spent 1:50 hours in the procedure, while patient 9 was in the procedure for 2:30
hours (see Figure 2.4). As an extreme case, consider patient 5, who refused to sign the
consent form and left the process after only 15 minutes.

Such uncertainty is undesirable for resources, as it leaves them “flooded” with work at
some moments in the day and “starved” for work at other moments. Figure 2.5 summa-
rizes at what moments in time the angiography suite was used on December 2.

By now, we have established two views to the interventional radiology:

• The view of the patient for whom the idealized stay is summarized by Figure 2.2.
Mismatches between supply and demand from the patient’s perspective mean having a
unit of demand (i.e., the patient) wait for a unit of supply (a resource).

• The view of the resources (summarized by Figure 2.5), which experience demand–
supply mismatches when they are sometimes “flooded” with work, followed by periods of
no work.

As these two perspectives are ultimately two sides of the same coin, we are interested in
bringing these two views together. This is the fundamental idea of process analysis.

FIGURE 2.5 Patient 1 Patient 4 Patient 6 Patient 8 Patient 9

Usage of the Main
Room

Time

7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

The Process View of the Organization 15

2.2 Three Measures of Process Performance

At the most aggregate level, a process can be thought of as a “black box” that uses resources
(labor and capital) to transform inputs (undiagnosed patients, raw materials, unserved cus-
tomers) into outputs (diagnosed patients, finished goods, served customers). This is shown
in Figure 2.6. Chapter 3 explains the details of constructing figures like Figure 2.6, which
are called process flow diagrams. When analyzing the processes that lead to the supply of
goods and services, we first define our unit of analysis.

In the case of the interventional radiology unit, we choose patients as our flow unit.
Choosing the flow unit is typically determined by the type of product or service the supply
process is dealing with; for example, vehicles in an auto plant, travelers for an airline, or
gallons of beer in a brewery.

As suggested by the term, flow units flow through the process, starting as input and
later leaving the process as output. With the appropriate flow unit defined, we next can
evaluate a process based on three fundamental process performance measures:

• The number of flow units contained within the process is called the inventory (in a
production setting, it is referred to as work-in-process, WIP). Given that our focus is not
only on production processes, inventory could take the form of the number of insurance
claims or the number of tax returns at the IRS. There are various reasons why we find
inventory in processes, which we discuss in greater detail below. While many of us might
initially feel uncomfortable with the wording, the inventory in the case of the interven-
tional radiology unit is a group of patients.

• The time it takes a flow unit to get through the process is called the flow time. The flow
time takes into account that the item (flow unit) may have to wait to be processed because
there are other flow units (inventory) in the process potentially competing for the same
resources. Flow time is an especially important performance metric in service environments
or in other business situations that are sensitive to delays, such as make-to-order production,
where the production of the process only begins upon the arrival of the customer order. In a
radiology unit, flow time is something that patients are likely to care about: it measures the
time from their arrival at the interventional radiology unit to the time patients can go home
or return to their hospital unit.

• Finally, the rate at which the process is delivering output (measured in [flow units/unit
of time], e.g., units per day) is called the flow rate or the throughput rate. The maximum
rate with which the process can generate supply is called the capacity of the process. For
December 2, the throughput of the interventional radiology unit was 11 patients per day.

Table 2.2 provides several examples of processes and their corresponding flow rates,
inventory levels, and flow times.

You might be somewhat irritated that we have moved away from the idea of supply
and demand mismatch for a moment. Moreover, we have not talked about profits so far.

FIGURE 2.6 Inputs Process Outputs
Resources: Labor & Capital
The Process View of Flow Units Goods
an Organization (Raw Material, Customers) Services

16 Chapter 2 Flow unit U.S. Immigration Champagne MBA Program Large PC
Industry MBA student Manufacturer
TABLE 2.2 Flow rate/ Application for Computer
Examples of Flow throughput immigration benefit Bottle of 600 students
Rates, Inventories, champagne per year 5,000 units per
and Flow Times Flow time Approved or 260 million bottles day
rejected visa cases: per year 2 years
Inventory 6.3 million per year 10 days
Average time in 1,200 students
Average processing cellar: 3.46 years 50,000 computers
time: 7.6 months 900 million bottles

Pending cases: 4.0
million cases

However, note that increasing the maximum flow rate (capacity) avoids situations where
we have insufficient supply to match demand. From a profit perspective, a higher flow rate
translates directly into more revenues (you can produce a unit faster and thus can produce
more units), assuming your process is currently capacity constrained, that is, there is suf-
ficient demand that you could sell any additional output you make.

Shorter flow times reduce the time delay between the occurrence of demand and its
fulfillment in the form of supply. Shorter flow times therefore also typically help to reduce
demand–supply mismatches. In many industries, shorter flow times also result in addi-
tional unit sales and/or higher prices, which makes them interesting also from a broader
management perspective.

Lower inventory results in lower working capital requirements as well as many quality
advantages that we explore later in this book. A higher inventory also is directly related to
longer flow times (explained below). Thus, a reduction in inventory also yields a reduction
in flow time. As inventory is the most visible indication of a mismatch between supply and
demand, we will now discuss it in greater detail.

2.3 Little’s Law

Accountants view inventory as an asset, but from an operations perspective, inventory
often should be viewed as a liability. This is not a snub on accountants; inventory should
be an asset on a balance sheet, given how accountants define an asset. But in common
speech, the word asset means “desirable thing to have” and the dictionary defines liabil-
ity as “something that works to one’s disadvantage.” In this sense, inventory can clearly
be a liability. This is most visible in a service process such as a hospital unit, where
patients in the waiting room obviously cannot be counted toward the assets of the health
care system.

Let’s take another visit to the interventional radiology unit. Even without much
medical expertise, we can quickly find out which of the patients are currently undergo-
ing care from some resource and which are waiting for a resource to take care of them.
Similarly, if we took a quick walk through a factory, we could identify which parts
of the inventory serve as raw materials, which ones are work-in-process, and which
ones have completed the production process and now take the form of finished goods
inventory.

However, taking a single walk through the process—dishwasher factory or interven-
tional radiology unit—will not leave us with a good understanding of the underlying
operations. All it will give us is a snapshot of what the process looked like at one single

The Process View of the Organization 17

moment in time. Unfortunately, it is this same snapshot approach that underlies most
management (accounting) reports: balance sheets itemize inventory into three catego-
ries (raw materials, WIP, finished goods); hospital administrators typically distinguish
between pre- and postoperative patients. But such snapshots do not tell us why these
inventories exist in the first place! Thus, a static, snapshot approach neither helps us to
analyze business processes (why is there inventory?) nor helps us to improve them (is this
the right amount of inventory?).

Now, imagine that instead of our single visit to the hospital unit, we would be will-
ing to stay for some longer period of time. We arrive early in the morning and make
ourselves comfortable at the entrance of the unit. Knowing that there are no patients
in the interventional radiology unit overnight, we then start recording any arrival or
departure of patients. In other words, we collect data concerning the patient inflow and
outflow.

At the end of our stay, we can plot a graph similar to Figure 2.7. The upper of the two
curves illustrates the cumulative number of patients who have entered the unit. The curve
begins at time zero (7:00) and with zero patients. If we had done the same exercise in a
unit with overnight patients, we would have recorded our initial patient count there. The
lower of the two curves indicates the cumulative number of patients who have left the unit.
Figure 2.7 shows us that by noon, seven patients have arrived, of which five have left the
unit again.

At any given moment in time, the vertical distance between the upper curve and the
lower curve corresponds to the number of patients in the interventional radiology unit,
or—abstractly speaking—the inventory level. Thus, although we have not been inside the
interventional radiology unit this day, we are able to keep track of the inventory level by
comparing the cumulative inflow and outflow. For example, the inventory at noon con-
sisted of two patients.

We also can look at the horizontal distance between the two lines. If the patients leave
the unit in the same order they entered it, the horizontal gap would measure the exact
amount of time each patient spent in the interventional radiology unit. More generally,
given that the length of stay might vary across patients and patients do not necessarily
leave the unit in the exact same sequence in which they entered it, the average gap between
the two lines provides the average length of stay.

FIGURE 2.7 Patients Cumulative
11 Inflow
Cumulative Inflow
and Outflow 10

9
Cumulative

8 Outflow

7 Flow Time
6

Inventory
5

4

3

2

1
Inventory = Cumulative Inflow – Cumulative Outflow

0 Time
7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

18 Chapter 2

Thus, Figure 2.7 includes all three of the basic process performance measures we discussed
on the previous page: flow rate (the slope of the two graphs), inventory (the vertical distance
between the two graphs), and flow time (the horizontal distance between the two graphs).

Based on either the graph or the patient log, we can now compute these performance
measures for December 2. We already know that the flow rate was 11 patients/day.

Next, consider inventory. Inventory changes throughout the day, reflecting the differ-
ences between inflow and outflow of patients. A “brute force” approach to compute aver-
age inventory is to count the inventory at every moment in time throughout the day, say
every five minutes, and then take the average. For December 2, this computation yields an
average inventory of 2.076 patients.

Next, consider the flow time, the time a patient spends in the unit. To compute that
information, we need to add to the patient log, Table 2.1, the time each patient left the
interventional radiology unit. The difference between arrival time and departure time
would be the flow time for a given patient, which in turn would allow us to compute the
average flow time across patients. This is shown in Table 2.3 and is in many ways similar
to the two graphs in Figure 2.7. We can easily compute that on December 2, the average
flow time was 2 hours, 4 minutes, and 33 seconds, or 2.076 hours.

At this point, you might ask: “Does the average inventory always come out the same as
the average flow time?” The answer to this question is a resounding no. However, the fact
that the average inventory was 2.076 patients and the average flow time was 2.076 hours
is no coincidence either.

To see how inventory and flow time relate to each other, let us review the three perfor-
mance measures, flow rate, flow time, and inventory:

• Flow rate ϭ 11 patients per day, which is equal to one patient per hour.
• Flow time ϭ 2.076 hours.
• Inventory ϭ 2.076 patients.

Thus, while inventory and flow time do not have to—and, in fact, rarely are—equal,
they are linked in another form. We will now introduce this relationship as Little’s Law
(named after John D. C. Little).

Average inventory Average flow rate Average flow time (Little’s Law)

Many people think of this relationship as trivial. However, it is not. Its proof is rather
complex for the general case (which includes—among other nasty things—variability) and
by mathematical standards is very recent.

TABLE 2.3 Number Patient Name Arrival Time Departure Time Flow Time
Calculation of
Average Flow Time 1 7:35 8:50 1:15
2 7:45 10:05 2:20
3 8:10 10:10 2:00
4 9:30 11:15 1:45
5 10:15 10:30 0:15
6 10:30 13:35 3:05
7 11:05 13:15 2:10
8 12:35 15:05 2:30
9 14:30 18:10 3:40
10 14:35 15:45 1:10
11 14:40 17:20 2:40
Average 2:04:33

The Process View of the Organization 19

Little’s Law is useful in finding the third performance measure when the other two are
known. For example, if you want to find out how long patients in a radiology unit spend
waiting for their chest X-ray, you could do the following:

1. Observe the inventory of patients at a couple of random points during the day, giving
you an average inventory. Let’s say this number is seven patients: four in the waiting
room, two already changed and waiting in front of the procedure room, and one in the
procedure room.

2. Count the procedure slips or any other records showing how many patients were treated
that day. This is the day’s output. Let’s say there were 60 patients over a period of
8 hours; we could say that we have a flow rate of 60/8 ϭ 7.5 patients/hour.

3. Use Little’s Law to compute Flow time ϭ Inventory/Flow rate ϭ 7/7.5 ϭ 0.933
hour ϭ 56 minutes. This tells us that, on average, it takes 56 minutes from the time a
patient enters the radiology unit to the time his or her chest X-ray is completed. Note
that this information would otherwise have to be computed by collecting additional data
(e.g., see Table 2.3).

When does Little’s Law hold? The short answer is always. For example, Little’s Law
does not depend on the sequence in which the flow units (e.g., patients) are served (remem-
ber FIFO and LIFO from your accounting class?). (However, the sequence could influence
the flow time of a particular flow unit, e.g., the patient arriving first in the morning, but not
the average flow time across all flow units.) Furthermore, Little’s Law does not depend on
randomness: it does not matter if there is variability in the number of patients or in how
long treatment takes for each patient; all that matters is the average flow rate of patients
and the average flow time.

In addition to the direct application of Little’s Law, for example, in the computation of
flow time, Little’s Law is also underlying the computation of inventory costs as well as a
concept known as inventory turns. This is discussed in the following section.

2.4 Inventory Turns and Inventory Costs

Using physical units as flow units (and, hence, as the inventory measure) is probably the
most intuitive way to measure inventory. This could be vehicles at an auto retailer, patients
in the hospital, or tons of oil in a refinery.

However, working with physical units is not necessarily the best method for obtaining
an aggregate measure of inventory across different products: there is little value to saying
you have 2,000 units of inventory if 1,000 of them are paper clips and the remaining 1,000
are computers. In such applications, inventory is often measured in some monetary unit,
for example, $5 million worth of inventory.

Measuring inventory in a common monetary unit facilitates the aggregation of inven-
tory across different products. This is why total U.S. inventory is reported in dollars. To
illustrate the notion of monetary flow units, consider Kohl’s Corp, a large U.S. retailer.
Instead of thinking of Kohl’s stores as sodas, toys, clothes, and bathroom tissues (physical
units), we can think of its stores as processes transforming goods valued in monetary units
into sales, which also can be evaluated in the form of monetary units.

As can easily be seen from Kohl’s balance sheet, on January 31, 2011, the company
held an inventory valued at $3.036 billion (see Table 2.4). Given that our flow unit now
is the “individual dollar bill,” we want to measure the flow rate through Kohl’s operation.

The direct approach would be to take “sales” as the resulting flow. Yet, this measure is
inflated by Kohl’s gross profit margin; that is, a dollar of sales is measured in sales dol-

20 Chapter 2

TABLE 2.4 Excerpts from Financial Statements of Kohl’s and Walmart (All Numbers in Millions)

Source: Taken from 10-K filings.

Kohl’s 2011 2010 2009 2008 2007
Revenue
Cost of Goods Sold $ 18,391 $ 17,178 $ 16,389 $ 16,474 $ 15,544
Inventory $ 11,359 $ 10,679 $ 10,332 $ 10,459 $ 9,890
$ 3,036 $ 2,923 $ 2,799 $ 2,856 $ 2,588
Net Income $ 1,114 $ 991 $ 885 $ 1,084 $ 1,109

Walmart $418,952 $ 405,046 $ 401,244 $374,526 $344,992
Revenue $307,646 $2,97,500 $2,99,419 $280,198 $258,693
Cost of Goods Sold $ 36,318 $ 33,160 $ 34,511 $ 35,180 $ 33,685
Inventory $ 16,389 $ 14,335 $ 13,188 $ 12,884 $ 12,036

Net Income

lars, while a dollar of inventory is measured, given the present accounting practice, in a
cost dollar. Thus, the appropriate measure for flow rate is the cost of goods sold, or COGS
for short.

With these two measures—flow rate and inventory—we can apply Little’s Law to
compute what initially might seem a rather artificial measure: how long does the average
flow unit (dollar bill) spend within the Kohl’s system before being turned into sales, at
which point the flow units will trigger a profit intake. This corresponds to the definition
of flow time.

Flow rate ϭ Cost of goods sold ϭ $11, 359 million/year
Inventory ϭ $3,036 million

Hence, we can compute flow time via Little’s Law as

Flow time ϭ Inventory
Flow rate

ϭ $3,036 million/$11, 359 million/year ϭ 0.267 year ϭ 97 days

Thus, we find that it takes Kohl’s—on average—97 days to translate a dollar invest-
ment into a dollar of—hopefully profitable—revenues.

This calculation underlies the definition of another way of measuring inventory, namely
in terms of days of supply. We could say that Kohl’s has 97 days of inventory in their pro-
cess. In other words, the average item we find at Kohl’s spends 97 days in Kohl’s supply
chain.

Alternatively, we could say that Kohl’s turns over its inventory 365 days/year/97
days ϭ 3.74 times per year. This measure is called inventory turns. Inventory turns is a
common benchmark in the retailing environment and other supply chain operations:

Inventory turns ϭ 1
Flow time

The Process View of the Organization 21

TABLE 2.5 Retail Segment Examples Annual Gross
Inventory Turns and Inventory Margin
Margins for Selected Apparel and accessory Ann Taylor, GAP
Retail Segments Catalog, mail-order Spiegel, Lands End Turns 37%
Department stores Sears, JCPenney 39%
Source: Based on Gaur, Fisher, Drug and proprietary stores Rite Aid, CVS 4.57 34%
and Raman 2005. Food stores Albertson’s, Safeway, Walmart 8.60 28%
Hobby, toy/game stores Toys R Us 3.87 26%
Home furniture/equipment Bed Bath & Beyond 5.26 35%
Jewelry Tiffany 10.78 40%
Radio, TV, consumer electronics Best Buy, CompUSA 2.99 42%
Variety stores Kohl’s, Walmart, Target 5.44 31%
1.68 29%
4.10
4.45

To illustrate this application of Little’s Law further, consider Walmart, one of Kohl’s
competitors. Repeating the same calculations as outlined on the previous page, we find the
following data about Walmart:

Cost of goods sold $307, 646 million/year
Inventory $36, 318 million
Flow time $36, 318 million/$307, 646 million/year
0.118 year 43.1 days
Inventory turns 1/43.1 turns/day
365 days/year 1/43.1 turns/day 8.47 turns per year

Thus, we find that Walmart is able to achieve substantially higher inventory turns than
Kohl’s. Table 2.5 summarizes inventory turn data for various segments of the retailing
industry. Table 2.5 also provides information about gross margins in various retail settings
(keep them in mind the next time you haggle for a new sofa or watch!).

Inventory requires substantial financial investments. Moreover, the inventory holding
cost is substantially higher than the mere financial holding cost for a number of reasons:

• Inventory might become obsolete (think of the annual holding cost of a microprocessor).
• Inventory might physically perish (you don’t want to think of the cost of holding fresh

roses for a year).
• Inventory might disappear (also known as theft or shrink).
• Inventory requires storage space and other overhead cost (insurance, security, real

estate, etc.).
• There are other less tangible costs of inventory that result from increased wait times

(because of Little’s Law, to be discussed in Chapter 8) and lower quality (to be dis-
cussed in Chapter 11).

Given an annual cost of inventory (e.g., 20 percent per year) and the inventory turn
information as computed above, we can compute the per-unit inventory cost that a process
(or a supply chain) incurs. To do this, we take the annual holding cost and divide it by the
number of times the inventory turns in a year:

Per-unit inventory costs ϭ Annual inventory costs
Annual inventory turns

Exhibit 2.1

CALCULATING INVENTORY TURNS AND PER-UNIT INVENTORY COSTS

1. Look up the value of inventory from the balance sheet.
2. Look up the cost of goods sold (COGS) from the earnings statement; do not use sales!
3. Compute inventory turns as

Inventory turns ϭ COGS
Inventory

4. Compute per-unit inventory costs as Annual inventory costs
Per-unit inventory costs Inventory turns

Note: The annual inventory cost needs to account for the cost of financing the inventory, the cost of
depreciation, and other inventory-related costs the firm considers relevant (e.g., storage, theft).

For example, a company that works based on a 20 percent annual inventory cost and
that turns its inventory six times per year incurs per-unit inventory costs of

20% per year ϭ 3.33%
6 turns per year

In the case of Kohl’s (we earlier computed that the inventory turns 3.74 times per year),
and assuming annual holding costs of 20 percent per year, this translates to inventory costs
of about 5.35 percent of the cost of goods sold (20%/3.74 ϭ 5.35). The calculations to
obtain per unit inventory costs are summarized in Exhibit 2.1.

To stay in the retailing context a little longer, consider a retailer of consumer electronics
who has annual inventory costs of 30 percent (driven by financial costs and obsolescence).
Assuming the retailer turns its inventory about four times per year (see Table 2.5.), we obtain
a per-unit inventory cost of 30%/4 ϭ 7.5%. Consider a TV in the retailer’s assortment that
is on the shelf with a price tag of $300 and is procured by the retailer for $200. Based on our
calculation, we know that the retailer incurs a $200 ϫ 7.5% ϭ $15 inventory cost for each
such TV that is sold. To put this number into perspective, consider Figure 2.8.

Figure 2.8 plots the relationship between gross margin and inventory turns for con-
sumer electronics retailers (based on Gaur, Fisher, and Raman 2005). Note that this graph
does not imply causality in this relationship. That is, the model does not imply that if a
firm increases its gross margin, its inventory turns will decline automatically. Instead, the
way to look at Figure 2.8 is to think of gross margin for a given set of products as being
fixed by the competitive environment. We can then make two interesting observations:

• A retailer can decide to specialize in products that turn very slowly to increase its
margins. For example, Radio Shack is known for its high margins, as they carry many products
in their assortment that turn only once or twice a year. In contrast, Best Buy is carrying largely
very popular items, which exposes the company to stiffer competition and lower gross margins.

• For a given gross margin, we observe dramatic differences concerning inventory
turns. For example, inventory turns vary between four and nine times for a 15 percent
gross margin. Consider retailer A and assume that all retailers work with a 30 percent annual
holding cost. Based on the annual inventory turns of 4.5, retailer A faces a 6.66 percent
per-unit inventory cost. Now, compare this to competing retailer B, who turns its inven-
tory eight times per year. Thus, retailer B operates with 3.75 percent per-unit inventory

22

The Process View of the Organization 23

FIGURE 2.8 10 Retailer B
9
Relationship between 8
Inventory Turns and 7
Gross Margin 6
5
Source: Based on Gaur, Fisher, 4
and Raman 2005. 3
2
Inventory Turns 1
0
Retailer A
0%
10% 20% 30% 40% 50%
Gross Margin (%)

costs, almost a 3 percent cost advantage over retailer A. Given that net profits in this industry
segment are around 2 percent of sales, such a cost advantage can make the difference between
profits and bankruptcy.

2.5 Five Reasons to Hold Inventory

While Little’s Law allows us to compute the average inventory in the process (as long as
we know flow time and flow rate), it offers no help in answering the question we raised
previously: Why is there inventory in the process in the first place? To understand the
need for inventory, we can no longer afford to take the black-box perspective and look at
processes from the outside. Instead, we have to look at the process in much more detail.

As we saw from Figure 2.7, inventory reflected a deviation between the inflow into a
process and its outflow. Ideally, from an operations perspective, we would like Figure 2.7
to take the shape of two identical, straight lines, representing process inflow and outflow.
Unfortunately, such straight lines with zero distance between them rarely exist in the real
world. De Groote (1994) discusses five reasons for holding inventory, that is, for having
the inflow line differ from the outflow line: (1) the time a flow unit spends in the process,
(2) seasonal demand, (3) economies of scale, (4) separation of steps in a process, and
(5) stochastic demand. Depending on the reason for holding inventory, inventories are
given different names: pipeline inventory, seasonal inventory, cycle inventory, decoupling
inventory/ buffers, and safety inventory. It should be noted that these five reasons are not
necessarily mutually exclusive and that, in practice, there typically exist more than one
reason for holding inventory.

Pipeline Inventory

This first reason for inventory reflects the time a flow unit has to spend in the process
in order to be transformed from input to output. Even with unlimited resources, patients
still need to spend time in the interventional radiology unit; their flow time would be the
length of the critical path. We refer to this basic inventory on which the process operates
as pipeline inventory.

24 Chapter 2 For the sake of simplicity, let’s assume that every patient would have to spend exactly
1.5 hours in the interventional radiology unit, as opposed to waiting for a resource to
FIGURE 2.9 become available, and that we have one patient arrive every hour. How do we find the
pipeline inventory in this case?
Pipeline Inventory
The answer is obtained through an application of Little’s Law. Because we know two
of the three performance measures, flow time and flow rate, we can figure out the third, in
this case inventory: with a flow rate of one patient per hour and a flow time of 1.5 hours,
the average inventory is

Inventory 1[patient/hour] 1.5[hours] 1.5 patients

which is the number of patients undergoing some value-adding activity. This is illustrated
by Figure 2.9.

In certain environments, you might hear managers make statements of the type “we need
to achieve zero inventory in our process.” If we substitute Inventory ϭ 0 into Little’s Law,
the immediate result is that a process with zero inventory is also a process with zero flow
rate (unless we have zero flow time, which means that the process does not do anything to
the flow unit). Thus, as long as it takes an operation even a minimum amount of time to
work on a flow unit, the process will always exhibit pipeline inventory. There can be no
hospital without patients and no factory can operate without some work in process!

Little’s Law also points us toward the best way to reduce pipeline inventory. As
reducing flow rate (and with it demand and profit) is typically not a desirable option, the
only other way to reduce pipeline inventory is by reducing flow time.

Seasonal Inventory

Seasonal inventory occurs when capacity is rigid and demand is variable. Two examples
illustrate this second reason for inventory. Campbell’s Soup sells more chicken noodle
soup in January than in any other month of the year (see Chapter 17)—not primarily
because of cold weather, but because Campbell’s discounts chicken noodle soup in Janu-
ary. June is the next biggest sales month, because Campbell’s increases its price in July.

So much soup is sold in January that Campbell’s starts production several months in
advance and builds inventory in anticipation of January sales. Campbell’s could wait longer
to start production and thereby not build as much inventory, but it would be too costly to
assemble the needed capacity (equipment and labor) in the winter only to dismantle that
capacity at the end of January when it is no longer needed.

In other words, as long as it is costly to add and subtract capacity, firms will desire to
smooth production relative to sales, thereby creating the need for seasonal inventory.

Cumulative 1.5 Patients
Number of 7
Patients 1.5 Hours

6 Time

5 8:00 9:00 10:00 11:00 12:00

4

3

2

1

0
7:00

The Process View of the Organization 25

FIGURE 2.10 Tons of 1,400 Total Beets Received
Beets 1,200 Inventory
Seasonal Inventory— (in 000s)
Sugar
1,000
Total Beets
800 Processed

600 Time

400

200

0

End of Harvest

An extreme case of seasonal inventory can be found in the agricultural and food pro-
cessing sector. Due to the nature of the harvesting season, Monitor Sugar, a large sugar
cooperative in the U.S. Midwest, collects all raw material for their sugar production over
a period of six weeks. At the end of the harvesting season, they have accumulated—in the
very meaning of the word—a pile of sugar beets, about 1 million tons, taking the form of
a 67-acre sugar beets pile.

Given that food processing is a very capital-intense operation, the process is sized such
that the 1.325 million tons of beets received and the almost 1 million tons of inventory
that is built allow for a nonstop operation of the production plant until the beginning of
the next harvesting season. Thus, as illustrated by Figure 2.10, the production, and hence
the product outflow, is close to constant, while the product inflow is zero except for the
harvesting season.

Cycle Inventory

Throughout this book, we will encounter many situations in which it is economical to pro-
cess several flow units collectively at a given moment in time to take advantage of scale
economies in operations.

The scale economics in transportation processes provide a good example for the third
reason for inventory. Whether a truck is dispatched empty or full, the driver is paid a fixed
amount and a sizeable portion of the wear and tear on the truck depends on the mileage
driven, not on the load carried. In other words, each truck shipment incurs a fixed cost that
is independent of the amount shipped. To mitigate the sting of that fixed cost, it is tempt-
ing to load the truck completely, thereby dividing the fixed cost across the largest number
of units.

In many cases, this indeed may be a wise decision. But a truck often carries more prod-
uct than can be immediately sold. Hence, it takes some time to sell off the entire truck
delivery. During that interval of time, there will be inventory. This inventory is labeled
cycle inventory as it reflects that the transportation process follows a certain shipment
cycle (e.g., a shipment every week).

Figure 2.11 plots the inventory level of a simple tray that is required during the opera-
tion in the interventional radiology unit. As we can see, there exists a “lumpy” inflow of
units, while the outflow is relatively smooth. The reason for this is that—due to the admin-
istrative efforts related to placing orders for the trays—the hospital only places one order
per week.

The major difference between cycle inventory and seasonal inventory is that seasonal
inventory is due to temporary imbalances in supply and demand due to variable demand
(soup) or variable supply (beets) while cycle inventory is created due to a cost motivation.

26 Chapter 2 Inventory New Shipment Arrives
20
FIGURE 2.11 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
16 Days
Cycle Inventory 14
12
10
8
6
4
2
0

Decoupling Inventory/Buffers

Inventory between process steps can serve as buffers. An inventory buffer allows manage-
ment to operate steps independently from each other. For example, consider two workers
in a garment factory. Suppose the first worker sews the collar onto a shirt and the second
sews the buttons. A buffer between them is a pile of shirts with collars but no buttons.
Because of that buffer, the first worker can stop working (e.g., to take a break, repair the
sewing machine, or change thread color) while the second worker keeps working. In other
words, buffers can absorb variations in flow rates by acting as a source of supply for a
downstream process step, even if the previous operation itself might not be able to create
this supply at the given moment in time.

An automotive assembly line is another example of a production process that uses buf-
fers to decouple the various stations involved with producing the vehicle. In the absence
of such buffers, a disruption at any one station would lead to a disruption of all the other
stations, upstream and downstream. Think of a bucket brigade to fight a fire: There are no
buffers between firefighters in a bucket brigade, so nobody can take a break without stop-
ping the entire process.

Safety Inventory

The final reason for inventory is probably the most obvious, but also the most challeng-
ing: stochastic demand. Stochastic demand refers to the fact that we need to distinguish
between the predicted demand and the actually realized demand. In other words, we typi-
cally face variation in demand relative to our demand prediction. Note that this is different
from variations in predictable demand, which is called seasonality, like a sales spike of
Campbell’s chicken noodle soup in January. Furthermore, stochastic demand can be pres-
ent along with seasonal demand: January sales can be known to be higher than those for
other months (seasonal demand) and there can be variation around that known forecast
(stochastic demand).

Stochastic demand is an especially significant problem in retailing environments or at
the finished goods level of manufacturers. Take a book retailer that must decide how many
books to order of a given title. The book retailer has a forecast for demand, but forecasts
are (at best) correct on average. Order too many books and the retailer is faced with left-
over inventory. Order too few and valuable sales are lost. This trade-off can be managed,
as we will discover in Chapter 12, but not eliminated (unless there are zero forecast errors).

The Process View of the Organization 27

FIGURE 2.12 Cumulative 1,200
Inflow and
Safety Inventory at Outflow 1,000
a Blood Bank
800
Cumulative
Inflow

600 Safety Cumulative
Inventory Outflow

400

200

0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Days of the Month

The resulting inventory thereby can be seen as a way to hedge against the underlying
demand uncertainty. It might reflect a one-shot decision, for example, in the case of a book
retailer selling short-life-cycle products such as newspapers or magazines. If we consider a
title with a longer product life cycle (e.g., children’s books), the book retailer will be able
to replenish books more or less continuously over time.

Figure 2.12 shows the example of the blood bank in the Presbyterian Hospital in Philadelphia.
While the detailed inflow and consumption of blood units vary over the course of the month, the
hospital always has a couple of days of blood in inventory. Given that blood perishes quickly, the
hospital wants to keep only a small inventory at its facility, which it replenishes from the regional
blood bank operated by the Red Cross.

2.6 The Product–Process Matrix

Processes leading to the supply of goods or services can take many different forms. Some
processes are highly automated, while others are largely manual. Some processes resemble
the legendary Ford assembly line, while others resemble more the workshop in your local
bike store. Empirical research in operations management, which has looked at thousands
of processes, has identified five “clusters” or types of processes. Within each of the five
clusters, processes are very similar concerning variables such as the number of different
product variants they offer or the production volume they provide. Table 2.6 describes
these different types of processes.

By looking at the evolution of a number of industries, Hayes and Wheelwright (1979)
observed an interesting pattern, which they referred to as the product–process matrix (see
Figure 2.13). The product–process matrix stipulates that over its life cycle, a product typi-
cally is initially produced in a job shop process. As the production volume of the product
increases, the production process for the product moves from the upper left of the matrix
to the lower right.

For example, the first automobiles were produced using job shops, typically creating
one product at a time. Most automobiles were unique; not only did they have different
colors or add-ons, but they differed in size, geometry of the body, and many other aspects.
Henry Ford’s introduction of the assembly line corresponded to a major shift along the
diagonal of the product–process matrix. Rather than producing a couple of products in a
job shop, Ford produced thousands of vehicles on an assembly line.

28 Chapter 2 Examples Number of Product Volume
Different (Units/Year)
TABLE 2.6 • Design company Product Variants Low
Process Types and • Commercial printer (1–100)
Their Characteristics • Formula 1 race car High
• Apparel sewing (100ϩ) Medium
Job shop • Bakery (100–100k)
• Semiconductor wafers Medium
Batch process • Auto assembly (10–100) High
• Computer assembly (10k–1M)
Worker-paced • Large auto assembly Medium High
line flow (1–50) (10k–1M)
Machine-paced • Paper mill Low Very high
line flow • Oil refinery (1–10)
Continuous process • Food processing Low
(1–10)

Note that the “off-diagonals” in the product–process matrix (the lower left and the
upper right) are empty. This reflects that it is neither economical to produce very high
volumes in a job shop (imagine if all of the millions of new vehicles sold in the United
States every year were handcrafted in the same manner as Gottlieb Daimler created the
first automobile) nor does it make sense to use an assembly line in order to produce only a
handful of products a year.

We have to admit that few companies—if any—would be foolish enough to produce
a high-volume product in a job shop. However, identifying a process type and looking at
the product–process matrix is more than an academic exercise in industrial history. The
usefulness of the product–process matrix lies in two different points:

1. Similar process types tend to have similar problems. For example, as we will dis-
cuss in Chapter 4, assembly lines tend to have the problem of line balancing (some work-
ers working harder than others). Batch-flow processes tend to be slow in responding to

FIGURE 2.13 Low Volume Medium Volume High Volume Very High Volume

Product–Process (Unique) (High Variety) (Lower Variety) (Standardized)
Matrix
Job Shop Commercial Unit Variable Costs
Source: Hayes and Printer Generally Too High
Wheelwright (1979).

Batch Process Apparel Production

Worker-Paced Line Low-Volume
Auto Assembly

Machine-Paced Line High-Volume
Auto Assembly
Utilization of Fixed
Continuous Process Capital Generally Too Low Oil Refinery

2.7 The Process View of the Organization 29
Summary
customer demand (see Chapter 7). Thus, once you know a process type, you can quickly
determine what type of problems the process is likely to face and what solution methods
are most appropriate.

2. The “natural drift” of industries toward the lower right of Figure 2.13 enables you to
predict how processes are likely to evolve in a particular industry. Consider, for example,
the case of eye surgery. Up until the 1980s, corrective eye surgery was done in large hos-
pitals. There, doctors would perform a large variety of very different eye-related cases.
Fifteen years later, this situation had changed dramatically. Many highly specialized eye
clinics have opened, most of them focusing on a limited set of procedures. These clinics
achieve high volume and, because of the high volume and the lower variety of cases, can
operate at much higher levels of efficiency. Similarly, semiconductor production equip-
ment used to be assembled on a one-by-one basis, while now companies such as Applied
Materials and Kulicke & Soffa operate worker-paced lines.

In this chapter, we emphasized the importance of looking at the operations of a firm not
just in terms of the products that the firm supplies, but also at the processes that generate
the supply. Looking at processes is especially important with respect to demand–supply
mismatches. From the perspective of the product, such mismatches take the form of wait-
ing times; from the perspective of the process, they take the form of inventory.

For any process, we can define three fundamental performance measures: inventory,
flow time, and flow rate. The three measures are related by Little’s Law, which states that
the average inventory is equal to the average flow time multiplied by the average flow rate.

Little’s Law can be used to find any of the three performance measures, as long as the
other two measures are known. This is specifically important with respect to flow time,
which is in practice frequently difficult to observe directly.

A measure related to flow time is inventory turns. Inventory turns, measured by 1/(flow
time), captures how fast the flow units are transformed from input to output. It is an impor-
tant benchmark in many industries, especially retailing. Inventory turns are also the basis
of computing the inventory costs associated with one unit of supply.

2.8 De Groote (1994) is a very elegant note describing the basic roles of inventory. This note, as well as
Further many other notes and articles by de Groote, takes a very “lean” perspective to operations manage-
Reading ment, resembling much more the tradition of economics as opposed to engineering.

2.9 Gaur, Fisher, and Raman (2005) provide an extensive study of retailing performance. They pres-
Practice ent various operational measures, including inventory turns, and show how they relate to financial
Problems performance measures.

The Hayes and Wheelwright (1979) reference is widely recognized as a pioneering article linking
operations aspects to business strategy. Subsequent work by Hayes, Wheelwright, and Clark (1988)
established operations as a key source for a firm’s competitive advantage.

Q2.1* (Dell) What percentage of cost of a Dell computer reflects inventory costs? Assume Dell’s
Q2.2 yearly inventory cost is 40 percent to account for the cost of capital for financing the
inventory, the warehouse space, and the cost of obsolescence. In other words, Dell incurs
a cost of $40 for a $100 component that is in the company’s inventory for one entire year.
In 2001, Dell’s 10-k reports showed that the company had $400 million in inventory and
COGS of $26,442 million.

(Airline) Consider the baggage check-in of a small airline. Check-in data indicate that from
9 a.m. to 10 a.m., 255 passengers checked in. Moreover, based on counting the number of

(* indicates that the solution is at the end of the book)

30 Chapter 2

Q2.3 passengers waiting in line, airport management found that the average number of passengers
Q2.4** waiting for check-in was 35. How long did the average passenger have to wait in line?
Q2.5
(Inventory Cost) A manufacturing company producing medical devices reported
Q2.6 $60,000,000 in sales over the last year. At the end of the same year, the company had
Q2.7 $20,000,000 worth of inventory of ready-to-ship devices.
Q2.8**
a. Assuming that units in inventory are valued (based on COGS) at $1,000 per unit and
are sold for $2,000 per unit, how fast does the company turn its inventory? The com-
pany uses a 25 percent per year cost of inventory. That is, for the hypothetical case that
one unit of $1,000 would sit exactly one year in inventory, the company charges its
operations division a $250 inventory cost.

b. What—in absolute terms—is the per unit inventory cost for a product that costs $1,000?

(Apparel Retailing) A large catalog retailer of fashion apparel reported $100,000,000 in
revenues over the last year. On average, over the same year, the company had $5,000,000
worth of inventory in their warehouses. Assume that units in inventory are valued based on
cost of goods sold (COGS) and that the retailer has a 100 percent markup on all products.

a. How many times each year does the retailer turn its inventory?

b. The company uses a 40 percent per year cost of inventory. That is, for the hypothetical
case that one item of $100 COGS would sit exactly one year in inventory, the company
charges itself a $40 inventory cost. What is the inventory cost for a $30 (COGS) item?
You may assume that inventory turns are independent of the price.

(LaVilla) LaVilla is a village in the Italian Alps. Given its enormous popularity among
Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter
season and there are, on average, 1,200 skiers in the village. On average, skiers stay in
LaVilla for 10 days.

a. How many new skiers are arriving—on average—in LaVilla every day?

b. A study done by the largest hotel in the village has shown that skiers spend on aver-
age $50 per person on the first day and $30 per person on each additional day in local
restaurants. The study also forecasts that—due to increased hotel prices—the average
length of stay for the 2003/2004 season will be reduced to five days. What will be the
percentage change in revenues of local restaurants compared to last year (when skiers
still stayed for 10 days)? Assume that hotels continue to be fully booked!

(Highway) While driving home for the holidays, you can’t seem to get Little’s Law out of
your mind. You note that your average speed of travel is about 60 miles per hour. Moreover,
the traffic report from the WXPN traffic chopper states that there is an average of 24 cars
going in your direction on a one-quarter mile part of the highway. What is the flow rate of
the highway (going in your direction) in cars per hour?

(Industrial Baking Process) Strohrmann, a large-scale bakery in Pennsylvania, is laying
out a new production process for their packaged bread, which they sell to several grocery
chains. It takes 12 minutes to bake the bread. How large an oven is required so that the
company is able to produce 4,000 units of bread per hour (measured in the number of units
that can be baked simultaneously)?

(Mt. Kinley Consulting) Mt. Kinley is a strategy consulting firm that divides its consul-
tants into three classes: associates, managers, and partners. The firm has been stable in
size for the last 20 years, ignoring growth opportunities in the 90s, but also not suffering
from a need to downsize in the recession at the beginning of the 21st century. Specifi-
cally, there have been—and are expected to be—200 associates, 60 managers, and
20 partners.

The work environment at Mt. Kinley is rather competitive. After four years of working
as an associate, a consultant goes “either up or out”; that is, becomes a manager or is dis-
missed from the company. Similarly, after six years, a manager either becomes a partner
or is dismissed. The company recruits MBAs as associate consultants; no hires are made at
the manager or partner level. A partner stays with the company for another 10 years (a total
of 20 years with the company).

The Process View of the Organization 31

a. How many new MBA graduates does Mt. Kinley have to hire every year?

b. What are the odds that a new hire at Mt. Kinley will become partner (as opposed to
being dismissed after 4 years or 10 years)?

Q2.9 (Major U.S. Retailers) The following table shows financial data (year 2004) for Costco
Wholesale and Walmart, two major U.S. retailers.

Inventories Costco Walmart
Sales (net)
COGS ($ Millions) ($ Millions)

Source: Compustat, WRDS. $ 3,643 $ 29,447
$48,106 $286,103
$41,651 $215,493

Q2.10 Assume that both companies have an average annual holding cost rate of 30 percent (i.e., it
costs both retailers $3 to hold an item that they procured for $10 for one entire year).

a. How many days, on average, does a product stay in Costco’s inventory before it is
sold? Assume that stores are operated 365 days a year.

b. How much lower is, on average, the inventory cost for Costco compared to Walmart
of a household cleaner valued at $5 COGS? Assume that the unit cost of the household
cleaner is the same for both companies and that the price and the inventory turns of an
item are independent.

(McDonald’s) The following figures are taken from the 2003 financial statements of
McDonald’s and Wendy’s.1 Figures are in million dollars.

Inventory McDonald’s Wendy’s
Revenue
Cost of goods sold $ 129.4 $ 54.4
Gross profit 17,140.5 3,148.9
11,943.7 1,634.6
5,196.8 1,514.4

a. In 2003, what were McDonald’s inventory turns? What were Wendy’s inventory turns?
b. Suppose it costs both McDonald’s and Wendy’s $3 (COGS) per their value meal offer-

ings, each sold at the same price of $4. Assume that the cost of inventory for both
companies is 30 percent a year. Approximately how much does McDonald’s save in
inventory cost per value meal compared to that of Wendy’s? You may assume the
inventory turns are independent of the price.

1 Example adopted from an About.com article (http://beginnersinvest.about.com/cs/investinglessons/1/
blles3mcwen.htm). Financial figures taken from Morningstar.com.

You can view a video of how problems marked with a ** are solved by going on www.
cachon-terwiesch.net and follow the links under ‘Solved Practice Problems’