Abstract
In this contribution, we propose a telescopic decomposition approach for solving scheduling problems from the chemical processing industries online. The general concept is realized for a real-world benchmark process by a two-level algorithm, which comprises a planning step with explicit consideration of uncertainties and a scheduling step where nonlinearities are include in the model. Both steps constitute optimization problems, which are modeled and solved by mathematical programming techniques. Besides conceptual considerations concerning online scheduling, we present the two mathematical models and their problem specific solution algorithms with some numerical results.
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References
F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings, S. J. Wright: Nonlinear predictive control and moving horizon estimation — an introductory overview. In: P. M. Frank (Ed.): Advances in Control (1999) 391–449
G. Applequist, O. Samikoglu, J. Pekny, G. Reklaitis: Issues in the use, design and evolution of process scheduling and planning systems. ISA Transactions (1997)
T. Backx, O. Bosgra, W. Marquardt: Towards intentional dynamics in supply chain concious process operations. In: J. F. Pekny, G. E. Blau, B. Caranham. (Eds.): Proc. Foundations of Computer Aided Process Operations (FOCAP098), CACHE Publications, Michigan, (1998) Suppl.
M. H. Bassett, J. F. Pekny, G. V. Reklaitis: Decomposition techniques for the solution of large-scale scheduling problems. AIChE Journal 42 (1996) 3373–3387
B. Bereanu: Minimum risk criterion in stochastic optimization. Econ. Comput. Econ. Cybern. Stud. Res. 2 (1981) 31–39
J. R. Birge, F. V. Louveaux: Introduction to stochastic programming. Springer, New York (1997)
A. Brooke, D. Kendrick, A. Meeraus, R. Raman: GAMS — A user’s guide. GAMS Development Corporation, Washington (1998)
C. C. Carèe, R. Schultz: A two-stage stochastic program for unit commitment under uncertainty in a hydro-thermal power system. Priority Programme of the Deutsche Forschungsgemeinschaft “Real-Time Optimization of Large Systems”, Preprint 98–132, (1998, revised 1999)
C. C. Carøe, R. Schultz: Dual decomposition in stochastic integer programming. Oper. Res. Lett. 23 (1999)
CPLEX Optimization Inc.: Using the CPLEX callable library. CPLEX Optimization3, (1989–2000)
D. Duffle, J. Pan: An overview of value at risk. Journal of Derivatives 4 (1997) 7–49
G. D. Eppen, R. K. Martin, L. Schräge: A scenario approach to capacity planning. Oper. Res. 37 (1989) 517–527
S. T. Harding, C. A. Floudas: Global optimization in multiproduct and multipurpose batch design under uncertainty. Ind. Eng. Chem. Res. 36 (1997) 1644–1664
R. Hemmecke, R. Schultz: Decomposition in two-stage stochastic integer programs for real-time optimization. This volume.
S. J. Honkomp, S. Lombardo, O. Rosen, J. F. Pekny: The curse of reality — why scheduling problems are so difficult in practice. Comput. Chem. Eng. 24 (2000) 323–328
P. Kall, S. Wallace: Stochastic Programming. Wiley, New York (1994)
K. B. Kanakamedala, G. V. Reklaitis, V. Venkatasubramaniam: Reactive schedule modification in multipurpose batch chemical plants. Ind. Eng. Chem. Res. 33 (1994) 77–90
A. J. King, S. Takriti: Issues in risk modeling for multi-stage systems. IBM Research Report, RC 20993, Illinois (1997)
K. C. Kiwiel: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Programm. 46 (1990) 105–122
K. C. Kiwiel: Exact penalty functions in proximal bundle methods for constraint convex nondifferentiable minimization. Math. Programm. 52 (1991) 285–302
K. C. Kiwiel: User’s guide for NOA 3.0: a fortran package for convex nondifferentiable optimization. System Research Institute, Polish Academy of Sciences, Warsaw (1994)
E. Kondili, C. C. Pantelides, R. W. H. Sargent: A general algorithm for short-term scheduling of batch operations. Part I: MILP formulation. Comput. Chem. Eng. 17 (1993) 211–227
T. Löhl, C. Schulz, S. Engell: Sequencing of batch operations for a highly coupled production process: genetic algorithms vs. mathematical programming. Comput. Chem. Eng. 22 (1998) 579–585
J. F. Pekny, G. V. Reklaitis: Towqards the convergence of theory an practice: a technology guide for scheduling/ planning methodology. In: J. F. Pekny, G. E. Blau, B. Caranham. (Eds.): Proc. Foundations of Computer Aided Process Operations (FOCAP098), CACHE Publications, Michigan (1998) 91–111
J. M. Pinto, I. E. Grossmann: A continuous time MILP model for short term scheduling of batch plants with pre-ordering constraints. Proc. Sixth European Symposium on Computer Aided Process Engineering (ESCAPE-6) (1996) 1197–1202
H. M. Markowitz: Portfolio selections: efficient diversification of investments. Wiley, New York (1959)
D. J. Mignon, S. J. Honkomp, G. V. Reklaitis: A framework for investigation schedule robustness under uncertainty. Comput. Chem. Eng. S19 (1995) 615–620
G. L. Nemhauser, L. A. Wolsey: Integer and combinatorial optimization. Wiley, New York (1988)
A. Prekopa: Stochastic programming. Kluwer, Dordrecht (1995)
J. Rauch (Ed.): Mehrproduktanlagen. Wiley, Weinheim (1998)
G. V. Reklaitis: Scheduling approaches for the batch process industries. ISA Transactions 34 (1995) 349–358
G. Sand: Planning model for real-time optimization of multiproduct batch plants under uncertainty (in German). Priority Programme of the Deutsche Forschungsgemeinschaft “Real-Time Optimization of Large System”, Preprint 98–284, (1998)
G. Sand, S. Engell, A. Märkert, R. Schultz, C. Schulz: A hierarchical approach to realtime scheduling of a multiproduct batch plant with uncertainties. In: S. Pierucci (Ed.): Computer-Aided Chemical Engineering, Vol. 8: European Symposium on Computer-Aided Process Engineering-10 (2000) 1075–1080
G. Sand, S. Engell, A. Märkert, R. Schultz, C. Schulz: Approximation of an ideal online scheduler for a multiproduct batch plant. Comput. Chem. Eng. 24 (2000) 361–367
G. Schilling, C. C. Pantelides: A simple continuous-time process scheduling formulation and a novel solution algorithm. Proc. Sixth European Symposium on Computer Aided Process Engineering (ESCAPE-6) (1996) 1221–1226
C. Schulz, S. Engell, R. Rudolf: Scheduling of a multiproduct polymer batch plant. In: J. F. Pekny, G. E. Blau, B. Caranham (Eds.): Proc. Foundations of Computer Aided Process Operations (FOCAP098), CACHE Publications, Michigan (1998) 224–230
C. Schulz: PhD thesis: Modeling and optimization of a multiproduct batch plant (in German). University of Dortmund, Dortmund (2001) (in preparation)
N. Shah: Single- and multisite planning and scheduling: current status and future challenges. In: J. F. Pekny, G. E. Blau, B. Caranham. (Eds.): Proc. Foundations of Computer Aided Process Operations (FOCAP098), CACHE Publications, Michigan (1998) 75–90
D. E. Shobrys, D. C. White: Planning, scheduling and control systems: why can they not work together. Comput. Chem. Eng. 24 (2000) 163–173
J. Viswanathan, I. E. Grossmann: A combined penalty function and outer approximation for MINLP optimization. Comput. Chem. Eng. 14 (1990) 769–782
S. J. Wilkinson, N. Shah, C. C. Pantelides: Aggregate modelling of multipurpose plant operation. Comput. Chem. Eng. 19 (1995) S583-S588
H. P. Williams: Model building in mathematical programming. John Wiley & Sons, New York (1994)
X. Zhang: PhD thesis: Algorithms for optimal process scheduling using nonlinear models. University of London, London (1995)
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Engell, S., Märkert, A., Sand, G., Schultz, R., Schulz, C. (2001). Online Scheduling of Multiproduct Batch Plants under Uncertainty. In: Grötschel, M., Krumke, S.O., Rambau, J. (eds) Online Optimization of Large Scale Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04331-8_32
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DOI: https://doi.org/10.1007/978-3-662-04331-8_32
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