The dynamics of a bucket brigade line with discrete stations and an analysis of themes throughput of such dynamics are studied. Most of the previous work in bucket brigades assumes that handovers can occur at any point throughout the production line. This research restricts handovers to occur at station endpoints which corresponds to some real-life settings. The adoption of discrete bucket brigades leads to a decrease of throughput in comparison to handovers that occur at any point of the line. Since handovers can only occur at a finite number of points, the dynamics of the production line can be obtained through an adjacency matrix and/or a connectivity graph.;For more than two stations, the reset of the bucket brigade when the last worker has finished his product can be performed in several different ways. Fundamentally there are two distinct handover protocols: synchronous, where workers wait until all of them simultaneously start a new production step; and, asynchronous handover protocols where handovers are staggered. A specific natural asynchronous handover protocol is defined and the dynamics and throughput of a bucket brigade with discrete stations is studied. It is shown that this asynchronous protocol reduces waiting time and hence increases the throughput of the production line in most cases. The dynamics of the line will be studied by generating a finite connectivity graph. With that graph the globally self-balancing bucket brigades can be identified and locally stable periodic self-organizing behavior and its basin of attraction can be determined.;An extension of a bucket brigade system is also proposed to optimize throughput based on the handover point. In this modified policy, called Clever Negotiation policy, every workstation is divided into negotiation and non-negotiation intervals. Such intervals are unique to every configuration of the production line; these intervals determine regions where preemption on an item is allowed with a constant negotiation time, and where workers should wait to handover at station endpoints. Results on the dynamics and throughput of a two-worker m-station system are presented as well as lost production and throughput comparisons against a non-negotiation systems with discrete stations and an always negotiate policy.
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