Sharing work dynamically on U-lines: System productivity and individual remuneration

Inspired by the concept of cellular bucket brigades, we propose simple rules for workers to share work on U-shaped lines with discrete work stations. For a three-station U-line with a worker-specific velocity setting, we identify the policies that maximize system productivity and the policies that maximize each worker’s remuneration rate. For a team with a faster worker and a slower worker, we find that the faster worker’s preferred policies maximize system productivity for most work-content distributions. When the policies preferred by the system, the faster worker, and the slower worker are all different, we find a way to resolve the tripartite conflict. On the other hand, if both workers prefer the same policy then this policy also maximizes system productivity. For an M-station U-line with a worker- and station-specific velocity setting, we show that the system always converges to a fixed point or a period-2 orbit. We provide a sufficient condition for the fixed point to be a global attractor. We also develop algorithms to determine the fixed point and the corresponding throughput. We find that increasing the number of stations generally improves throughput for certain work-content distributions. However, further dividing the U-line into more stations has diminishing returns.