Modeling conveyor merges in zone picking systems

In many order picking and sorting systems conveyors are used to transport products through the system and to merge multiple flows of products into one single flow. In practice, conveyor merges are potential points of congestion, and consequently can lead to a reduced throughput. In this paper, we study merges in a zone picking system. The performance of a zone picking system is, for a large part, determined by the performance of the merge locations. We model the system as a closed queueing network that describes the conveyor, the pick zones, and the merge locations. The resulting model does not have a product-form stationary queue-length distribution. This makes exact analysis practically infeasible. Therefore, we approximate the behavior of the model using the aggregation technique, where the resulting subnetworks are solved using matrix-geometric methods. We show that the approximation model allows us to determine very accurate estimates of the throughput when compared with simulation. Furthermore, our model is in particular well suited to evaluate many design alternatives, in terms of number of zones, zone buffer lengths, and maximum number of totes in the systems. It also can be used to determine the maximum throughput capability of the system and, if needed, modify the system in order to meet target performance levels.