Dynamics of Two- and Three-Worker "Bucket Brigade" Production Lines

B ucket b/igade production is a way of organizing workers on a flow line, in which there are fewer workers than stations. Eaeh worker carries a single item from station to station, waiting if necessary for that station to become available (workers are not allowed to pass eaeh other). When the last worker completes an item, he walks back to take over the item of his predecessor, who relinquishes it and walks back to take over the item of his predecessor, and so on until the first worker walks back to start a new item. Bucket brigades are in use in at least two commercial environments: apparel manufacturing (Bartholdi and Eisenstein 1996) and distribution warehousing (Barthoidi et ai. 1999). In both environments, twoand three-worker teams are common. Figure 1 summarizes all asymptotic (stable) behavior of a bucket brigade flow line with three workers. By "stable behavior" we mean qualitative structure that persists, even in the presence of perturbations. This is the behavior that will assert itself in praetice. Most of the behavior we characterize is distinctive and can be easily recognized on the shop floor. This categorization of behavior is based on the model of Theorem 3 of Barthoidi and Eisenstein (1996) in which the work to assemble an item is deterministic and is spread continuously and uniformly over a line (rather than concentrated at work stations). TTiis model has several important properties. • It is simple enough to analyze. • The behavior of this model underlies natural generalizations, such as when the amount of work within an interval of space is random and independent from that within disjoint intervals. In such cases the dynamics due to random work are merely superimposed upon the deterministic dynamics. (See, for example, Barthoidi et al. 1999.) • It is normative: Most implementations of bucket brigades explicitly try to engineer the process to emulate this model because it reduces the chances of blocking.