Managing Stochastic Bucket Brigades on Discrete Work Stations

Abstract

Bucket brigades are notably used to coordinate workers in production systems. We study a J‐station, I‐worker bucket brigade system. The time duration for each worker to serve a job at a station is exponentially distributed with a rate that depends on the station's expected work content and the worker's work speed. Our goal is to maximize the system's productivity or to minimize its inter‐completion time variability. We analytically derive the throughput and the coefficient of variation (CV) of the inter‐completion time. We study the system under two cases. (i) If the work speeds depend only on the workers, the throughput gap between the stochastic and the deterministic systems can be up to $47\%$ when the number of stations is small. Either maximizing the throughput or minimizing the CV of the inter‐completion time, the slowest‐to‐fastest worker sequence always outperforms the reverse sequence for the stochastic bucket brigade. To maximize the throughput, more work content should be assigned to the stations near the faster workers. In contrast, to minimize the CV of the inter‐completion time, more work content should be allocated to the stations near the slower workers. (ii) If the work speeds depend on the workers and the stations such that the workers may not dominate each other at every station, the asymptotic throughput can be expressed as a function of the average work speeds and the asymptotic expected blocked times of the workers, and can be interpreted as the sum of the effective production rates of all the workers.