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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Vydáno v:AIChE journal Ročník 53; číslo 12; s. 3183 - 3203
Hlavní autoři: Li, Zukui, Ierapetritou, Marianthi G
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.12.2007
Wiley Subscription Services
American Institute of Chemical Engineers
Témata:
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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Shrnutí: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
Bibliografie:http://dx.doi.org/10.1002/aic.11351
National Science Foundation - No. CTS 0625515; No. 0224745
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ArticleID:AIC11351
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ISSN:0001-1541
1547-5905
DOI:10.1002/aic.11351