A system according to the present invention includes a server and a plurality of apparatuses each incorporating a device. The apparatuses control power supply ON and OFF states of the devices in accordance with an instruction from the server. The server collects pieces of operation state information indicating operation states of the apparatuses from the apparatuses, and groups, based on the collected information, the apparatuses into groups which respectively correspond to different operation states and respectively have different priorities. The server further sends an allowance notification indicating a device power supply allowance to apparatuses which belong to respective groups in descending order of priority taking into consideration a parameter associated with power consumption values of apparatuses to which the device power supply allowance is given. Each apparatus sets the device in a power supply ON state when the allowance notification is received from the server.