An object processing system comprising: an input station comprising at least one programmable motion device for acquiring an object to be processed; a perception system, wherein the at least one programmable motion device is configured to present the object to the perception system for perceiving identifying indicia on the acquired obj ect; a plurality of intermediate containers, each of which is initially unassigned to any destination; a computer processing system configured to: - determine a number of objects expected to arrive at the input station within a given time for the assigned destination and - generate assignment data regarding an assigned intermediate container among the plurality of intermediate containers regarding a destination for the acquired object responsive to the identifying indicia in connection with the acquired object and responsive to the number of objects expected to arrive at the input station within a given time for the assigned destination; and an automated transport system (328, 338) for moving the acquired object to the assigned intermediate container; wherein the system is configured to signal a human worker to come and empty the assigned intermediate container and the computer processing system is configured to subsequently re-assign it to another destination before the container is full in response to the computer processing system determining that another object is not expected to arrive at the input station for the destination of the assigned intermediate container within a given time. an input station comprising at least one programmable motion device for acquiring an object to be processed; a perception system, wherein the at least one programmable motion device is configured to present the object to the perception system for perceiving identifying indicia on the acquired obj ect; a plurality of intermediate containers, each of which is initially unassigned to any destination; a computer processing system configured to: - determine a number of objects expected to arrive at the input station within a given time for the assigned destination and - generate assignment data regarding an assigned intermediate container among the plurality of intermediate containers regarding a destination for the acquired object responsive to the identifying indicia in connection with the acquired object and responsive to the number of objects expected to arrive at the input station within a given time for the assigned destination; and - determine a number of objects expected to arrive at the input station within a given time for the assigned destination and - generate assignment data regarding an assigned intermediate container among the plurality of intermediate containers regarding a destination for the acquired object responsive to the identifying indicia in connection with the acquired object and responsive to the number of objects expected to arrive at the input station within a given time for the assigned destination; and an automated transport system (328, 338) for moving the acquired object to the assigned intermediate container; wherein the system is configured to signal a human worker to come and empty the assigned intermediate container and the computer processing system is configured to subsequently re-assign it to another destination before the container is full in response to the computer processing system determining that another object is not expected to arrive at the input station for the destination of the assigned intermediate container within a given time.