An air-conditioning management apparatus for controlling an air-conditioning apparatus that comprises: a heat source unit; one or more indoor units; and a refrigerant-heat-medium heat exchanger configured to cause heat exchange to be performed between refrigerant that flows in the heat source unit and a heat medium that flows in the one or more indoor units to heat or cool the heat medium and heat or cool an indoor space, the air-conditioning management apparatus comprising: a storage unit configured to store a schedule including a set time and a set temperature; a communication processing unit configured to communicate with the air-conditioning apparatus and receive operation status information including a heat medium temperature that is a temperature of the heat medium; and a controller configured to perform a schedule control to control the air-conditioning apparatus according to the schedule, characterized in that the schedule control includes an optimal start-up control to control the air-conditioning apparatus such that an indoor space temperature that is a temperature of the indoor space reaches the set temperature at the set time, by starting an operation of the air-conditioning apparatus before the set time, wherein the controller is configured to perform a preheating control or a precooling control to control the heat source unit such that before the optimal start-up control is started, the heat medium temperature included in the operation status information obtained from the air-conditioning apparatus falls within a target range including a target heat medium temperature set in advance, wherein the storage unit stores a calculation formula or a table prepared to calculate a required time required for the preheating control or the precooling control based on the heat medium temperature, a heat medium flow rate that is a flow rate of the heat medium, the target heat medium temperature, and an outside air temperature, wherein the operation status information includes the heat medium flow rate and the outside air temperature, and wherein the controller is configured to perform the preheating control or the precooling control for the required time calculated based on the operation status information received by the communication processing unit and the calculation formula or the table stored in the storage unit. a storage unit configured to store a schedule including a set time and a set temperature; a communication processing unit configured to communicate with the air-conditioning apparatus and receive operation status information including a heat medium temperature that is a temperature of the heat medium; and a controller configured to perform a schedule control to control the air-conditioning apparatus according to the schedule, characterized in that the schedule control includes an optimal start-up control to control the air-conditioning apparatus such that an indoor space temperature that is a temperature of the indoor space reaches the set temperature at the set time, by starting an operation of the air-conditioning apparatus before the set time, wherein the controller is configured to perform a preheating control or a precooling control to control the heat source unit such that before the optimal start-up control is started, the heat medium temperature included in the operation status information obtained from the air-conditioning apparatus falls within a target range including a target heat medium temperature set in advance, wherein the storage unit stores a calculation formula or a table prepared to calculate a required time required for the preheating control or the precooling control based on the heat medium temperature, a heat medium flow rate that is a flow rate of the heat medium, the target heat medium temperature, and an outside air temperature, wherein the operation status information includes the heat medium flow rate and the outside air temperature, and wherein the controller is configured to perform the preheating control or the precooling control for the required time calculated based on the operation status information received by the communication processing unit and the calculation formula or the table stored in the storage unit.