Back-of-the-envelope miniload throughput bounds and approximations

We derive simple formulas bounding and approximating the throughput of an end-of-aisle miniload system with exponentially distributed pick times and either uniform or turnover-based storage. For typical configurations, the worst-case relative error for the bounds is less than 4%. We use our bounds to show that, for all practical purposes, regardless of the configuration, the picker utilization determines the storage/retrieval machine utilization, and vice versa. Thus, a system designer cannot hope to independently achieve separate goals for the utilization rates.