The bottom-up model of the industrial energy system has hitherto been analyzed using linear programming. However, it has limitations in describing practical technology selection and reproducing base-year technology selection. Positive mathematical programming, which provides an interior solution without any subjective constraints, can be considered as an alternative method that overcomes the limitations of linear programming when constructing a bottom-up model of the industry sector. The purpose of this study is to apply positive mathematical programming and identify the plausibility of using it in a forward-looking optimization model of the industry sector. A bottom-up model based on positive mathematical programming has the advantages of avoiding impractical technology selection in the industry sector, describing more flexible reactions to external changes, and calibrating base-year technology selection without subjective constraints. Although optimal solutions and simulation responses are dependent on parameter identification, the dependence of positive mathematical programming on the identification method can be lower than that of linear programming on the subjective constraints.