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Document history

Version 0.1. Last compiled on 2023-11-24. Written in Markdown using R-Bookdown. Hosted on the web at for free download.


For my darling wife Cici and our lovely children: Anna, Lucy, and Franklin.


Writing a workbook such as this requires encouragement, help, and advice from many friends, colleagues, and students. It is not possible to mention you all. However, I would like to thank the following people who have particularly inspired me over the last 30 years of my Bullwhip research. If I have missed you out, please forgive me.

The Cardiff University Team. Paul Childerhouse (now in RMIT University, Australia), Barry Evans (formally with Tesco), Irina Harris, Matthias Holweg (now in Oxford University), Carl Philip Hedenstierna (now in Xi’an Jiaotong-Liverpool University), Qinyun Li, Xia Meng (now with Yeo Valley), Moh Naim, Fotios Petropolous (now in Bath Univerity), Borja Ponte (now in the University of Oviedo, Spain), Andrew Potter, Laura Purvis, Bahman Rostami-Tabar, Po-nargm Somkun (née Ratanachote, now at Naresuan University, Thailand), Aris Syntetos, Denis Towill, Xun Wang, and Li Zhou (now in Greenwich University).

The Lexmark Team. Mick Dulany, Lance Hoshiko, Lorin Polley, Mark Watkins, Elizabeth Bartilson Williams, DuWayne Zuehlsdorff, Courtney Yager.

The 3M Team. Jon Noble, Johan Sinke, Ruben Jimenez Gomez.

The Yeo Valley Team. Chris Coles, Gemma Seymour, Jarad Spencer, Ian Calderbank, MariaRoza Toufekoula, Roxane Gorel, Mark Gammon, Tom Jarvie, Jo Reason, Rob Sexton.

Team Europe. Robert Boute (Leuven University), Jeroen Dejonckheere (Ontex International), Gerard Gaalman (Groningen University), Joren Gijsbrechts (Católica Lisbon School of Business and Economics), Robert Grubbström (Linköping Institute of Technology), Jan Holmström (Aalto University), Marc Lambrecht (Leuven University), Peter McCullen (Brighton University), Wim van de Velde (Procter and Gamble).

Team America. Prashant Chintapalli (Ivey Business School, Canada), Nagesh Gavirneni (Cornell University), Arnold Maltz (Arizona State University), David Pyke (University of San Diego), John Saldanha (Ohio State University), Jan Van Mieghem (Northwestern University), Chris Tang (University of California, Los Angeles), Roger Warburton (Boston University).

Team Asia. Youhua (Frank) Chen (City University of Hong Kong), Takamichi Hosoda (Aoyama University, Tokyo), Yasutaka Kainuma (Toyko Metropolitan University).


For the last twenty-five years, I have thought of myself as an industrially inspired supply chain modeler. I have been working with the tools of computer simulation, mathematics, control theory, and stochastic processes. I built up a thorough understanding of how the structure of supply chains, forecasting methods, lead-times, and replenishment algorithms affect the dynamics of supply chains. I have written extensively on the so-called Bullwhip Effect, how it manifests itself, how it causes business inefficiencies, and how to avoid it.

I was an Undergraduate student at Cardiff University. I did my postgraduate degree there, my Ph.D., and worked for twenty-three years for Cardiff University where I was a member of the Logistics Systems Dynamics Group, a research group that I once led at Cardiff Business School. I was the Head of the Logistics and Operations Management Department from 2012-2015. During this time I learned much about the Lean tools of Heijunka, Level Flow, Every Part Every Period, and Single Minute Exchange of Dies, and the like. I came to realize that my Bullwhip research was the key to reducing Mura and Muri waste. Since 2019, I have worked for the University of Exeter Business School. From 2020-2022 I was head of the Science, Innovation, Technology, and Entrepreneurship department; I am currently the Director of the Centre for Simulation, Analytics, and Modelling. I wrote the majority of this workbook while on sabbatical at the University of California, Los Angeles in 2015-2016. As you can see, it has taken me a long time to complete this project. I hope it was worth the wait!

While I have always been an academic, I have spent a lot of my career working with companies. Just after graduating, I spent four years working with CSC and LucasVarity with people such as Jeremy Hammant and John Parnaby. Shortly after I got introduced to Tesco; this became my first implemented instance of the Proportional Order-Up-To replenishment policy. Since then I have worked with many other companies to implement this policy. I have always tried to link my practical research back to the theory, learning from the some of the best theorists in the field; Gerard Gaalman, Takamichi Hosoda, Marc Lambrecht, Moh Naim, Chris Tang, Denis Towill, and Roger Warburton and to name just a few.

While working with these companies, I often found it useful to develop a Value Stream Map so that I could understand the material and information flow–this is essential background information for my Bullwhip reduction methodology. I had started to wonder whether I could extend the technique to capture the dynamics of the supply chain as well. Even more importantly I realised my theoretical work on the Bullwhip Effect was the science and mathematics behind the Pacemaker and the Heijunka Board. Thus, I embarked on a project to create this workbook to translate my Bullwhip research into the language that modern industrialists–logistics professionals, technical experts, and strategic decisions makers–can access and use. That is, I wanted to talk about my research in the language of Lean.

While I have tried to avoid mathematics as far as possible, and I certainly don’t offer academic style proofs, some mathematics is required. After all, maths is the language of the universe! In the first chapter, we use value stream maps to document and understand the dynamic behaviour of your supply chain. In chapter 2, a strategic review of replenishment decisions is given. Chapter 3 considers forecasting methods. Chapter 4 designs replenishment rules. Chapter 5 finalizes the production plan and discusses how to release it to the shop floor. The final chapter 6 considers how to communicate call-off orders and provide future guidance to suppliers.

I hope this workbook will make a contribution to your Lean journey and that you do indeed find ways to reduce your own Mura and Muri!

Professor Stephen Disney, Ph.D.

About the author

Professor Stephen Disney, Ph.D. works for the University of Exeter Business School as a Professor of Operations Management. He was previously the Head of the Science, Innovation, Technology and Entrepreneurship department within the University of Exeter Business School. He is currently the Director of the Computer Simulation, Analytics and Modelling research centre with the department. His research interests involve the application of control theory and statistical techniques to operations management and supply chain scenarios to investigate their dynamic, stochastic and economic performance. Stephen has a particular interest in the Bullwhip Effect. He has advised several of the world’s largest corporations on the Bullwhip Effect. He has worked with many companies in the UK (including LucasVarity, Tesco, and Yeo Valley), US (including Lexmark) and Europe (including P&G) and on global supply chains.

Previously, Professor Disney led the Logistics Systems Dynamics Group, a research group within Cardiff Business School. He was a previous Head of the Logistics and Operations Management department, also within Cardiff Business School. Professor Disney wrote the majority this workbook while on a research sabbatical at the University of California, Los Angeles in 2015-16. He has also held visiting positions at the Chinese University of Hong Kong (2002 and 2004) and Boston University (2011).

Professor Disney currently lectures Supply Chain Analytics, Operations and Project Management, and Mathematics and Statistics for Business Analytics to Postgraduate students in Exeter Business School. He also teaches Operations Analytics to Undergraduate students. He has also taught Operations Management, Logistics and Transport Modelling, and Operations Analysis, to MBA and Masters students at Cardiff Business School and Supply Chain Modelling to the Mathematics Department of Cardiff University. Previously, he taught Global Supply Chain Management, Project Management, and Decision Making at Boston University. He has extensive experience of teaching in-class, on-line, and on-site to Undergraduate, Postgraduate, and Executive audiences. When Stephen is not working, he enjoys spending time with his family, sailing, skiing, following Formula 1, playing Pokemon Go, and listening to heavy metal and rave music (very loud).

Stephen Disney can be contacted via . Further information about Stephen Disney and his projects can be found at

Key information


Muda Any wasteful activity. There are two types of Muda. 1) waste that can’t be quickly eliminated, and 2) waste that can easily be removed with Kaizen.

Mura Variability in the load placed on production. The waste caused by the variability in the demand and the variability introduced by the production planning and distribution scheduling activities.

Muri The waste of overburden. The waste of overtime that is used to meet the peak loads on our production system or the waste of the excess capacity used to try to avoid the overtime.

Key questions

1 What is your strategic supply chain objective? Are you trying to minimize inventory, production, capacity, overtime, and rush transportation orders or a combination of some/all of these costs?

2 What is your pacemaker process?

3 How often should you create a production plan?

4 What forecasting method should you use?

5 Which replenishment algorithm should you use?

6 What is the optimal sequence of production within the planning cycle?

7 How are you going to place orders on your supplier for raw materials and components?

8 What information should you pass to your suppliers to help them plan their activities?

Key measures of performance


\(NSAmp=\frac{\mathbb{V}[\text{Net Stock}]}{\mathbb{V}[\text{Demand}]}\).

\(Fill\,rate=\frac{\mathbb{E}[\text{Demand fulfiled immediately from stock}]}{\mathbb{E}[\text{Demand}]}\).

\(Availability=\frac{\text{Number of periods ending with inventory on-hand}}{\text{Total number of periods}}\).

Replenishment strategies

Economic order quantity, \(Q^\star=\sqrt{\frac{2Dk}{h}}\).

Economic production quantity, \(Q^\star =\sqrt{\frac{2PDk}{h(P-D)}}\).

Order-up-to (OUT) replenishment policy, \(q_t=\hat{d}_{t,t+T_p+1}+(TNS-ns_t)+\sum^{T_p}_{i=1}(\hat{d}_{t,t+i}-q_{t-i})\).

Proportional OUT replenishment policy, \(q_t=\hat{d}_{t,t+T_p+1}+\frac{1}{T_i}\big((f^\star-f_t)+\sum^{T_p}_{i=1}(\hat{d}_{t,t+i}-q_{t-i})\big)\).

Proportional future guidance, \(q_t=\hat{d}_{t,t+T_p+1}+\frac{1}{T_i}\bigg(\frac{T_i-1}{T_i}\bigg)^j\big((f^\star-f_t)+\sum^{T_p}_{i=1}(\hat{d}_{t,t+i}-q_{t-i})\big)\).