A vehicle operation management system for managing an operation of a vehicle, the vehicle operation management system comprising: an on-vehicle device mounted on the vehicle, the on-vehicle device comprising a digital tachograph configured to collect driving data of the vehicle and an operation button enabling a driver to perform an operation for setting an activity state of the vehicle to one of at least: a start state defined when the driver starts the operation of the vehicle, in which the on-vehicle device can start the collection of driving data of the vehicle; a shutdown state defined when the driver ceases the operation of the vehicle, and a rest state defined when the driver takes a rest, in which the on-vehicle device measures a rest time period; a server installed outside the vehicle, the server being configured to communicate with the on-vehicle device and store the driving data of the vehicle; and a terminal device configured to communicate with the server, the terminal device being capable of being brought outside the vehicle; wherein an operation signal output from the terminal device in response to an operation by the driver operating the terminal device is transmitted to the server, and the on-vehicle device is configured to set the activity state on the basis of the operation signal the server has received from the terminal device and an instruction subsequently transmitted by the server to the on-vehicle device, wherein, when the activity state is set to the shutdown state, the on-vehicle device transmits the driving data and fuel consumption information of the vehicle recorded in the on-vehicle device to the server, wherein the server stores the fuel consumption information of the vehicle, and when a setting of the activity state has been changed to the rest state or the shutdown state, the terminal device is configured to enable confirmation of the fuel consumption information of the vehicle; and wherein, when an ignition switch of the vehicle is turned off without performing the operation for changing a setting of the activity state to the rest state or the shutdown state by operating the operation button of the on-vehicle device, the on-vehicle device issues a notification suggesting a change in the setting of the activity state to the terminal device via the server. an on-vehicle device mounted on the vehicle, the on-vehicle device comprising a digital tachograph configured to collect driving data of the vehicle and an operation button enabling a driver to perform an operation for setting an activity state of the vehicle to one of at least: a start state defined when the driver starts the operation of the vehicle, in which the on-vehicle device can start the collection of driving data of the vehicle; a shutdown state defined when the driver ceases the operation of the vehicle, and a rest state defined when the driver takes a rest, in which the on-vehicle device measures a rest time period; a start state defined when the driver starts the operation of the vehicle, in which the on-vehicle device can start the collection of driving data of the vehicle; a shutdown state defined when the driver ceases the operation of the vehicle, and a rest state defined when the driver takes a rest, in which the on-vehicle device measures a rest time period; a server installed outside the vehicle, the server being configured to communicate with the on-vehicle device and store the driving data of the vehicle; and a terminal device configured to communicate with the server, the terminal device being capable of being brought outside the vehicle; wherein an operation signal output from the terminal device in response to an operation by the driver operating the terminal device is transmitted to the server, and the on-vehicle device is configured to set the activity state on the basis of the operation signal the server has received from the terminal device and an instruction subsequently transmitted by the server to the on-vehicle device, wherein, when the activity state is set to the shutdown state, the on-vehicle device transmits the driving data and fuel consumption information of the vehicle recorded in the on-vehicle device to the server, wherein the server stores the fuel consumption information of the vehicle, and when a setting of the activity state has been changed to the rest state or the shutdown state, the terminal device is configured to enable confirmation of the fuel consumption information of the vehicle; and wherein, when an ignition switch of the vehicle is turned off without performing the operation for changing a setting of the activity state to the rest state or the shutdown state by operating the operation button of the on-vehicle device, the on-vehicle device issues a notification suggesting a change in the setting of the activity state to the terminal device via the server.