Process scheduling under uncertainty using multiparametric programming

In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed intege...

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Veröffentlicht in:	AIChE journal Jg. 53; H. 12; S. 3183 - 3203
Hauptverfasser:	Li, Zukui, Ierapetritou, Marianthi G
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.12.2007 Wiley Subscription Services American Institute of Chemical Engineers
Schlagworte:	Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences Chemical engineering Economics. Management. Design assessment Exact sciences and technology Linear programming multiparametric programming Nonlinear programming Objective function process scheduling Scheduling Uncertainty Uncertainty multiparametric programming process scheduling Linear programming Mixed integer programming Scheduling Non linear programming Objective function Modeling Mathematical programming
ISSN:	0001-1541, 1547-5905
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Abstract	In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed integer linear (mpMILP), quadratic (mpMIQP), and general nonlinear programming (mpMINLP) problem. This article analyzes the solution characteristics and proposes a novel solution framework for specific mpMILP/mpMIQP problems addressing a wide variety of scheduling problems under different types of uncertainty, which are modeled as coefficient in objective function, as coefficient of integer variable and right hand side vector of the constraints. The main idea of the proposed framework is to decompose the problem into a series of smaller subproblems, each of them producing the parametric information around a given parameter value. The parametric solution of every subproblem is retrieved by solving a series of multiparametric linear programming (mpLP) and mixed integer linear/nonlinear programming problems (MILP/MINLP). Several examples were solved to analyze the complexity and the effectiveness of the proposed method. © 2007 American Institute of Chemical Engineers AIChE J, 2007
AbstractList	In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed integer linear (mpMILP), quadratic (mpMIQP), and general nonlinear programming (mpMINLP) problem. This article analyzes the solution characteristics and proposes a novel solution framework for specific mpMILP/mpMIQP problems addressing a wide variety of scheduling problems under different types of uncertainty, which are modeled as coefficient in objective function, as coefficient of integer variable and right hand side vector of the constraints. The main idea of the proposed framework is to decompose the problem into a series of smaller subproblems, each of them producing the parametric information around a given parameter value. The parametric solution of every subproblem is retrieved by solving a series of multiparametric linear programming (mpLP) and mixed integer linear/nonlinear programming problems (MILP/MINLP). Several examples were solved to analyze the complexity and the effectiveness of the proposed method. In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed integer linear (mpMILP), quadratic (mpMIQP), and general nonlinear programming (mpMINLP) problem. This article analyzes the solution characteristics and proposes a novel solution framework for specific mpMILP/mpMIQP problems addressing a wide variety of scheduling problems under different types of uncertainty, which are modeled as coefficient in objective function, as coefficient of integer variable and right hand side vector of the constraints. The main idea of the proposed framework is to decompose the problem into a series of smaller subproblems, each of them producing the parametric information around a given parameter value. The parametric solution of every subproblem is retrieved by solving a series of multiparametric linear programming (mpLP) and mixed integer linear/nonlinear programming problems (MILP/MINLP). Several examples were solved to analyze the complexity and the effectiveness of the proposed method. [PUBLICATION ABSTRACT] In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type (prices, demands, and processing times), the scheduling formulation results in different parametric problems including multiparametric mixed integer linear (mpMILP), quadratic (mpMIQP), and general nonlinear programming (mpMINLP) problem. This article analyzes the solution characteristics and proposes a novel solution framework for specific mpMILP/mpMIQP problems addressing a wide variety of scheduling problems under different types of uncertainty, which are modeled as coefficient in objective function, as coefficient of integer variable and right hand side vector of the constraints. The main idea of the proposed framework is to decompose the problem into a series of smaller subproblems, each of them producing the parametric information around a given parameter value. The parametric solution of every subproblem is retrieved by solving a series of multiparametric linear programming (mpLP) and mixed integer linear/nonlinear programming problems (MILP/MINLP). Several examples were solved to analyze the complexity and the effectiveness of the proposed method. © 2007 American Institute of Chemical Engineers AIChE J, 2007
Author	Ierapetritou, Marianthi G. Li, Zukui
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References_xml	– reference: Kondili E,Pantelides CC,Sargent RWH. A general algorithm for short-term scheduling of batch operations. I. MILP Formulation. Comput Chem Eng. 1993; 17: 211-227. – reference: Honkomp SJ,Mockus L,Reklaitis GV. A framework for schedule evaluation with processing uncertainty. Comput Chem Eng. 1999; 23: 595-609. – reference: Ruiz D,Cantón J,Nougués JM,Espuña A,Puigjaner L. On-line fault diagnosis system support for reactive scheduling in multipurpose batch chemical plants. Comput Chem Eng. 2001; 25: 829-837. – reference: Lin X,Janak SL,Floudas CA. A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty. Comput Chem Eng. 2004; 28: 1069-1085. – reference: Mendez CA,Cerdá J. An MILP framework for batch reactive scheduling with limited discrete resources. Comput Chem Eng. 2004; 28: 1059-1068. – reference: Hugo A,Pistikopoulos S. Long-range process planning under uncertainty via parametric programming. 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Snippet	In this article, the problem of process scheduling under uncertainty was studied using multiparametric programming method. Based on the uncertainty type...
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SubjectTerms	Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences Chemical engineering Economics. Management. Design assessment Exact sciences and technology Linear programming multiparametric programming Nonlinear programming Objective function process scheduling Scheduling Uncertainty
Title	Process scheduling under uncertainty using multiparametric programming
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