A Two-Stage Method for the Approximate Solution of General Multiparametric Mixed-Integer Linear Programming Problems

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• 作者：Martina Wittmann-Hohlbein ; Efstratios N. Pistikopoulos
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2012
• 出版时间：June 13, 2012
• 年：2012
• 卷：51
• 期：23
• 页码：8095-8107
• 全文大小：641K
• 年卷期：v.51,no.23(June 13, 2012)
• ISSN：1520-5045

文摘

In this work, we focus on the approximate solution of multiparametric mixed-integer linear programming (mp-MILP) problems involving uncertainty in the objective function coefficients and in the entries of the constraint matrices and vectors. A two-stage algorithmic procedure is proposed. In the first stage, the model is partially immunized against uncertainty using the worst-case oriented approach which leads to a partially robust mp-MILP model, whereas in the second stage explicit solutions of the robust model are derived by applying a suitable multiparametric programming algorithm for mp-MILP problems. Computational studies are presented, demonstrating that the proposed two-stage robust optimization/multiparametric programming procedure is computationally efficient and that it provides an upper bound on the overall solution of the general mp-MILP problem.