Analytical models for estimating sortation time in discrete, partially filled, and multiple-lane conveyor systems

When items such as cartons or packages must be sorted into distinct groups, they are often separated using a recirculating conveyor system. Expressions exist to estimate the expected sortation time under different sorting strategies when the items fill the conveyor and the order is preassigned to an output lane. However, none was previously available for a conveyor that is only partially filled or a system in which an order can be sorted in any of multiple lanes. This paper demonstrates that this expression also applies to a conveyor with discrete carriers and develops an expression to estimate the expected sortation time for a partially full conveyor. The methodology is adapted for a multiple lane system. The results produced by this formula are compared with the results obtained from a computer simulation of a sortation system and the comparison shows the new method to be a good predictor of the average sortation time, especially with large orders or a large number of orders per lane.