Vertical sequencer for product order fulfillment

A product order fulfillment system including a multi-level transport system and a lifting transport system. Each level of the multi-level transport system having a corresponding independent asynchronous level transport system separate and distinct from the asynchronous level transport system corresponding to each other level of the multi-level transport system. Each independent lift axis of the lifting transport system being configured to independently hold at least one case and being communicably coupled to each asynchronous level transport system so as to provide for exchange of the at least one case between each asynchronous level transport system and each independent lift axis. Each independent lift axis is communicably coupled to each other independent lift axis of the more than one lift axis and forms a common output of mixed cases so as to create an ordered sequence of mixed cases in accordance to a predetermined case out ordered sequence.