The Beer Game and the Bullwhip
Astonishing Results When Carlos Daganzo Applies Traffic Flow Theory to Supply Chains
Ordinarily, serendipity and supply chains are not compatible; supply chains at their best are idealized expressions of order and predictability; serendipity is just the opposite. However, a moment of serendipity has led to a revolution in understanding how supply chains work. The serendipitous moment occurred when Carlos Daganzo, ITS Berkeley traffic flow theorist and professor of civil engineering, analyzed supply chain behavior using traffic flow theory and found a solution to the vexing phenomenon known as "the Bullwhip Effect," first described in the early 1960s. But because the breakthrough came from someone outside the specialized world of supply chains, it has created little more than a ripple.
The story starts with the Beer Game, a well-known simulation tool used to teach how supply chain theory works in the real world. A professor places orders for beer, and a chain of suppliers—the students in his class—place orders with one another to fill his requests, from the hops grower down to the bottling plant and wholesaler. Because the suppliers don't know when or how much the professor will order, they have to order enough supplies from each other to cover the highest demands, which "costs" them money for extra storage, extra employees and the like.
Having taught logistics and having written a textbook on it, Daganzo was familiar with the Beer Game, but had never run it in a class. One of Daganzo's former students, Al Erera (Berkeley Ph.D. 2000), had just started teaching a course in supply chains at Georgia Tech, where he is an assistant professor. Because his class was more applied, he was using the Beer Game to illustrate the Bullwhip Effect in a concrete manner.
"When the Bullwhip Effect arises," Daganzo explains, "the farther away a supplier is from the consumer, the more variable the orders that that supplier receives become. Even if I order very regularly, and the person on the supply chain next to me is very happy, the last person in the supply chain won't be happy because things will fluctuate for that person tremendously."
The Bullwhip Effect is so prevalent, so costly to society, that some people think it could be a contributor to business cycles...
The phenomenon was named the Bullwhip Effect because the wide fluctuations experienced by the supplier who is farthest away, e.g., the person supplying hops for the beer, are similar to the wide fluctuations at the end of a long whip. (To complete the analogy, the retail customer would be the equivalent of the handle.) "The thing is so prevalent, so costly to society, that some people think it could be a contributor to business cycles," Daganzo explains.
As Erera described the outcome of the Beer Game in his class, Daganzo realized that "the Bullwhip Effect happened even when the students were not given any directions or rules to follow. Al let them act according to their own devices. That sounded like traffic to me, because in traffic we can't tell drivers how to drive. They drive pretty much the way they want, within the parameters of what is safe."
Furthering the traffic analogy, the oscillations in the supply chain sounded to Daganzo like the oscillations that happen to traffic upstream of a bottleneck. The drivers upstream of a bottleneck typically experience much wider oscillations in traffic speeds, more stop-and-go driving, than those who are passing through.
"It sounded just like traffic entering and leaving a bottleneck. You have cars going down toward the bottleneck, and they're discharging out of the bottleneck at a pretty steady rate. But if you look at traffic data upstream of the bottleneck, you see it is more variable. The farther away from the bottleneck you are, the more variable it is." Daganzo saw the customer at the end of the supply chain as the bottleneck, dictating how many orders will have to pass through. "Upstream of the customer, among your suppliers, it's getting crazier and crazier, just like traffic. I wondered if people in supply chains understood things in the same way."
There is a large body of literature on the Bullwhip Effect, and Daganzo undertook to review it (enlisting the aid of a number of Ph.D. students). "The typical paper would say, 'Let's assume that the customer places these orders with these properties, seasonal, whatever,' and they would give some mathematical properties to the customer orders. Then they would assume that the suppliers replenish their inventories according to some rule, for example, when an inventory is down to a certain level. All the papers assumed that the Bullwhip Effect was a combination of something the customer did and something the suppliers did."
Using that assumption, any method for smoothing out the flow of goods and eliminating the Bullwhip Effect would have to be able to anticipate the customer's behavior all of the time, but that is not possible. Daganzo sought to develop methods that do not require knowing what the customer is going to do. Surprisingly, this line of reasoning had never been pursued, he found.
He used traffic flow theory to analyze the Bullwhip Effect and started by searching for conditions under which the Bullwhip Effect would always arise, no matter what the customer does. He found that when suppliers tended to keep higher inventories during periods of higher demand, the Bullwhip Effect resulted. "Always. No matter what the customer does. That is a powerful result. Now we know something that is very generic, a root cause, and we can attack it."
Removing Uncertainty and Spreading the Gains
The key he found to smoothing out the flow of goods and eliminating the Bullwhip Effect's oscillations is to introduce commitments into the process, "information from the future," as Daganzo describes them. "They are used all the time, by the way," he says. "Just-in-time inventory that automobile companies use is a type of commitment. The automaker knows what he is going to produce, and he tells the seller upstream to begin producing this now because he's going to need it next month. The only way they'll do that is if the car maker commits to taking that order."
And why aren't all supply chains run that way? Because of how the rewards and risks of the current system are distributed, Daganzo explains.
And why aren't all supply chains run that way? Because of how the rewards and risks of the current system are distributed, Daganzo explains. "The people who are suffering are the people way upstream. If you introduce commitments, who suffers? The customer. He has to commit. Who gets the benefits? The people higher up." To induce the customer to change, a mechanism needs to give each occupant on the chain some of the value gained by eliminating the Bullwhip Effect, "so that every supplier wins, and the customer wins, and society wins."
While the analysis is revolutionary, it is an orphan academically, Daganzo notes, possibly because he is a newcomer to the supply chain world, but also for other reasons. After getting his work published as an ITS Research Report (A Theory of Supply Chains, 2001), he went public with his theory, starting with four lectures at UC Berkeley in the fall of 2001. He also went on a tour of other universities in the U.S. and Europe. "When I talked to them, many of them could see the value," he recalls, noting that his audiences were more diverse and included people from other fields outside of supply chains.
One of his hosts, Paul Zipkin, a leading authority in inventory theory at Duke University, saw the value of it. But Daganzo suspects that general acceptance will be slow to come in large part because of a natural inertia and resistance to what is in essence a paradigm change in thinking about supply chains.
A monograph outlining his theory, A Theory of Supply Chains, was published in 2003 by Springer-Verlag, where Daganzo has also published his logistics textbook, Logistics Systems Analysis (link to preface 90K PDF). He also published a shorter version in Operations Research, the flagship of the field (Volume 52, No. 6, Nov.-Dec. 2004).
Daganzo figures it will take a generation of students to effect a broader impact, but he may be proven to be too pessimistic. The seeds for change have already been sown, with Daganzo having enlisted current or recently graduated Ph.D. students Alejandro Lago, Anne Goodchild, Jorge Laval, Juan Carlos Munoz, Yuwei Li and Yanfeng Ouyang in his work. (He thanks them in the preface to his supply chains book.) To date, two of them, Lago and Ouyang (both of who now hold faculty positions) are working on refinements of the theory.
Carlos Daganzo's ITS Berkeley Publications Related to Supply Chains:
A Theory of Supply Chains, UCB-ITS-RR-2001-07 (link to catalog results page).
On the Stability of Supply Chains, Daganzo, UCB-ITS-RR-2002-02 (684 K PDF).
Some Properties of Decentralized Supply Chains, Yanfeng Ouyang and Carlos Daganzo, UCB-ITS-RR-2005-3 (454 K PDF).
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Last Updated April 4, 2006