Bucket brigades: Resources

Who can advise me about bucket brigades?

The idea behind bucket brigades is so simple that most users have been able to implement it themselves. But if you want someone to look over your shoulder, you are welcome to contact us. Meanwhile, here are some immediate resources. (These are mostly for using bucket brigades to coordinate order-pickers in a distribution center; it is harder to generalize about manufacturing because each environment is unique.)

First, see our list of Frequently-Asked Questions. If you have further questions, please contact us: We are very interested in tracking use of bucket brigades and learning from new applications.

We are happy to share videotapes of bucket brigades; or you can see a shorter version here.

For training, you can also run a bucket brigade with real people in a simulated warehouse. Here are instructions and materials for an exercise that our students and clients have found very useful.

Primary references

Most of the following are technical publications and will be of interest primarily to academics. Material of more general interest may be found here.

• A production line that balances itself by J. Bartholdi and D. Eisenstein, in Operations Research 44(1):21-34 (1996), special issue on new directions in operations management. This is the original paper introducing bucket brigades and is the key academic reference. It includes a precise mathematical model of a bucket brigade as a dynamical system, analyzes its asymptotic behavior, and proves that production rate is maximized. Also includes a detailed justification of the appropriateness of the mathematical model.
• Dynamics of 2- and 3-worker `bucket brigade' production lines by J. Bartholdi, L. Bunimovich, and D. Eisenstein, in Operations Research 47(3):488-491 (1999). Primarily for academics: A catalogue of all possible dynamic behavior of small bucket brigade lines plus mention of some open mathematical questions. Among the results: Evidence for the existence of mathematical chaos for some pathologically mis-configured lines.
• Performance of bucket brigades when work is stochastic by J. Bartholdi, D. Eisenstein, and R. Foley (2001), Operations Research 49(5):710-719. Mathematical proof that bucket brigades are expected to perform well even when the work has an element of randomness to it.
• Using Bucket Brigades to Migrate from Craft Manufacturing to Assembly Lines by J. Bartholdi and D. Eisenstein (2005), Manufacturing and Service Operations Management 7(2):121-129. A case study describing how a manufacturer of tractors used bucket brigades to migrate from craft assembly (one person assembles one tractor) to a semi-automated assembly line.
• Bucket brigades on in-tree assembly networks by J. Bartholdi, D. Eisenstein, and Y. F. Lim (2006), The European Journal of Operational Research 168(3):870-879, special issue on balancing assembly and transfer lines. This shows how to use bucket brigades on a "tree" of merging sub-assembly lines so that all the sub-assembly lines are balanced and, moreover, they are all synchronized so that the assembly network produces product at regular, predictable intervals.
• Deterministic Chaos in a Model of Discrete Manufacturing by J. Bartholdi, D. Eisenstein, and Y. F. Lim (2009), Naval Research Logistics Quarterly 56(4):293-299. A mathematical analysis showing that if a special type of bucket brigade is configured pathologically then fully chaotic behavior is possible. One result is that the intercompletion times of product can appear random even though everything about the assembly line is deterministic.

Related publications

• Task partitioning in insect societies: bucket brigades, Insectes Sociaux 49 (2002). In 1999 two Spanish biologists reported a species of ant that carries seeds back to the colony by passing each seed from slower to faster ants--bucket brigades! This paper analyzes how bucket brigades can form spontaneously if each ant simply grabs the first seed it can and carries it back to the nest.
• D. Armbruster and E. Gel of Arizona State University have explored the dynamics of bucket brigades in which worker skills are changing or are multi-dimensional. With J. Murakami, they show that bucket brigades are robustly optimal in the presence of worker learning. In another paper they study a model in which a worker may be faster at one portion of the work but slower at another portion.
• R. Villalobos of Arizona State University and his colleagues have written several papers about how bucket brigades can be especially effective in the presence of high labor turnover. They have also done some nice work implementing a bucket brigade production line at a United Technologies Automotive site.
• Recovering cyclic schedules using dynamic produce up-to policies by D. Eisenstein, Operations Research 53(4):675-688 (2005). This uses the ideas behind bucket brigades to schedule a manufacturing resource amongst competing products. A simple rule tells what to manufacture next and for how long; the result is that the system gravitates to a sustainable and efficient manufacturing schedule.
• A survey of the self-balancing production lines (“bucket brigades”) by A. Bratcu and A. Dolgui, Journal of Intelligent Manufacturing 16 (2005).

Other references, citations, discussions

• A nice summary article in Supply Chain Digest by D. Gilmore (July 2007). (Subsequent to this, a reader wrote in to say that he had set up bucket brigades in his shipping area and “this has helped us considerably”.)
• “The bucket brigade: a new approach to order-picking”, in Warehousing Tips by K. Ackerman, Ackerman Publications (2002).
• Bucket brigades are discussed in the article “Swarm intelligence: A whole new way to think about business” by E. Bonabeau and C. Meyer, which appeard in the Harvard Business Review, May 2001, pp 107-114.
• “Give productivity a boost without any investment in equipment” by S. Estersohn, in Distribution Channels magazine, May 1998, pp 51-54.
• “Self-organization will free employees to act like bosses”, in the weekly column "The Front Line" by Thomas Petzinger, Jr., The Wall Street Journal, January 3, 1997. Petzinger writes "The new model for organizations is the biological world, where uncontrolled actions produce stunningly efficient and robust results, all through adaptation and self-organization."
• The Center of Business Innovations at Ernst and Young LLP has sponsored colloquia on complexity science and business and have published books about each. You can read about bucket brigades in the book describing the second conference.
• “Call out the bucket brigade!”, in The WERCsheet (a publication of the Warehousing Educational and Reseach Council), July/August 1996. A journalist's summary of our presentation on order-picking by bucket brigade, given at the national WERC conference in San Francisco, 1996. It does not quite get the fine points right but is a reasonable summary, with some second opinions.
• Two students at the University of Canterbury in New Zealand have done an excellent honors project predicting how bucket brigades could improve manufacturing at a local company.
• Two graduate students at the University of Lund in Sweden won a prize for their masters thesis, Evaluation of bucket brigades - a next generation order-picking strategy. The work was done with collaboration of Consafe Logistics.
• Here is a lecture by John Bartholdi on self-organizing logistics systems.