Open Access

In designing energy supply systems, it is important to consider the uncertainty in energy demands, evaluate the robustness in some performance criteria, and heighten the robustness. A robust optimal design method has been previously proposed to maximize the robustness in a single performance criterion against the uncertainty in energy demands based on a mixed-integer linear model. In this paper, as a preliminary step toward multiobjective robust optimal design, a method of evaluating robustness in multiple performance criteria against the uncertainty in energy demands is proposed based on a mixed-integer linear model. The problems of evaluating the robustness in the performance criteria are formulated as bilevel mixed-integer linear programming (MILP) ones. They are solved by evaluating lower and upper bounds for the maximum regrets in the performance criteria alternately and repeatedly with the aid of a solution method based on reformulation and decomposition. In addition, for the purpose of applying the proposed method to practical problems, a hierarchical MILP method is used to efficiently solve some MILP problems in the solution process. Through a case study on a cogeneration system, the robustness in the annual total cost and primary energy consumption is evaluated and its trade-off relationship is clarified. As a result, it turns out how the values of these performance criteria are close to the optimal ones in relation to the uncertainty in energy demands. This work will be an important step toward developing a multiobjective robust optimal design method.