Bucket Brigade with Stochastic Worker Pace

We study Bucket Brigade (BB) production systems under the assumption of stochastic worker speeds. Our analysis provides interesting and counter-intuitive insights into realistic production environments. We analyze the following three systems: the traditional BB of Bartholdi & Eisenstein (1996), BB with overtaking allowed (BBO), and a benchmark system of parallel workers. After formulating the dynamic equations for all systems, we solve them analytically when possible and numerically in general. We identify settings in which conclusions that emerge from deterministic analysis fail to hold when speeds are stochastic, in particular relating to worker order assignment. Specifically, a fastest to slowest order with respect to expected speeds may be optimal as long as the standard deviation of the fastest worker is large enough. Significantly, in a stochastic environment the BB can improve the throughput rate compared to parallel workers, despite the fact that no blockage or starvation may occur in the latter. The BBO setting, which is relevant in a stochastic environment, and can be sometimes implemented in practice, provides an upper bound on the throughput rate of parallel workers, and is shown numerically to significantly improve upon BB.