Apparatus and methods for fulfilling orders by a picker utilizing multiple different levels of container-storage devices (tote-storage devices in some embodiments), all interconnected by at least one different type of conveyance device. The use of more than one level of tote-storage device is referred to as multi-level tote storage. The storage is utilized to hold containers and to sequence the containers in a preferred order that enhances the pick rate/performance. The performance and location of the container storage on the conveyance device(s) relative to the picker is determined by the required pick rate/performance of the system. The conveyance devices recirculate the containers between different levels of container storage at specific times based on a multi-level tote storage simulation control algorithm that provides the optimum pick rate/performance until such time the picker completes all the pick requests assigned to the picker.