A delivery processing apparatus includes: a plurality of stackers configured to stack delivery objects; a conveyer configured to transport the delivery objects to a designated stacker out of the plurality of stackers; a first detector configured to detect that a monitored stacker out of the plurality of stackers is in an overflow state in which more than a predetermined amount of delivery objects have accumulated; a second detector configured to detect that a monitored stacker out of the plurality of stackers is in an empty state in which all delivery objects have been retrieved from the stacker; and a main controller configured to specify a regular stacker that is a stacker out of the plurality of stackers and serving as a sort destination of the delivery object.