Bivariate interval semi‐infinite programming with an application to environmental decision‐making analysis

This paper proposed a bivariate interval semi‐infinite linear programming (BV‐ISIP) method to address a type decision‐making problem where various uncertainties exist in functional relations and parameter uncertainty. The performance of the method is also demonstrated via an illustrative example and an environmental decision‐making problem. As BV‐ISIP guarantees that each of the constraints is satisfied under all possible levels of independent variables, the system‐failure risk can be reduced. The BV‐ISIP solutions can be more robust to the variation of coefficients associated with independent variables than the ILP ones. Other features of BV‐ISIP are as follows: (i) flexible decision‐making schemes can be developed for decision makers in terms of the BV‐ISIP solutions; (ii) BV‐ISIP can conveniently be applied to many large‐scale optimization problems as no significantly‐increased computational costs are required; (iii) the method can easily be improved for addressing functional intervals associated with multiple independent variables.