Abstract
In this paper, a general algorithm is developed to address the multiparametric mixed-integer linear programming (mpMILP) problem with uncertain parameters in the left-hand side (LHS), right-hand side (RHS), and objective function coefficients simultaneously. The algorithm is based on a general multiparametric linear programming (mpLP) algorithm, which is derived using the optimality conditions of standard linear programming (LP) problem. The intent of the proposed framework is to propose a general framework to address different uncertainties in the process engineering problems. In addition, the paper also discusses the solution of the special problem where LHS uncertainty is included in the optimization model as a coefficient of continuous variable, and it notes the high computational complexity needed to retrieve the rigorous solution of large-scale problems, because of the nonlinearities of the objective function and nonconvex critical regions. Several numerical examples are presented to illustrate the effectiveness and applicability of the proposed method.
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