Some optimal operation methods based on the mixed-integer linear programming (MILP) have been proposed to operate energy supply plants properly from the viewpoints o f eco nomics, energy saving, and CO2 emission reduction. However, most o f the methods are effective only under certain energy demands. In operating an energy supply plant actually, it is necessary to determine the operational strategy properly based on pre dicted energy demands. In this case, realized energy demands may differ from the pre dicted ones. Therefore, it is necessary to determine the operational strategy so that it is robust against the uncertainty in energy demands. In this paper, an optimization method based on the MILP is proposed to conduct the robust optimal operation o f energy supply plants under uncertain energy demands. The uncertainty in energy demands is expressed by their intervals. The operational strategy is determined to minimize the maximum regret in the operational cost under the uncertainty. In addition, a hierarchical relationship among operation modes and on!off states o f equipment, energy demands, and energy flow rates o f equipment is taken into account. First, a general formulation o f a robust optimal operation problem is presented, which is followed by a general solution procedure. Then, in a numerical study, the proposed method is applied to a gas turbine cogeneration plant fo r district energy supply. Through the study, some features o f the robust optimal opera tion are clarified, and the validity and effectiveness o f the proposed method are ascer tained.