Abstract
In recent years the flexibility analysis of chemical processes has attracted a significant amount of attention among researchers in the chemical engineering community. Flexibility analysis permits to identify/create chemical processes, which can satisfy all design specifications in spite of process and parametric uncertainty (from several sources) at the operation stage. All formulations of the flexibility problem are based on the supposition that during the operation stage there is enough experimental data from which exact values of the uncertain parameters can be obtained. However, in practice this assumption is often not met. Here in this paper, we consider the case when the uncertain parameters can be divided into two sets, namely a set that can be estimated with sufficient accuracy (at the operation stage) and a set that cannot be. Based on this view, we have developed extensions of the feasibility test and two-stage optimization problem to handle the two sets of uncertainty. We have developed the relevant split and bound algorithm for solving the new two-step optimization problem.
Similar content being viewed by others
References
Ahmad, S., N.V. Sahinidis, and E.N. Pistikopoulos. (2000). “An Improved Algorithm for Optimization under Uncertainty”, Comp. Chem. Eng. 23, 1589–1604.
Andreatti, G.B., G. Sainetti, and R.J.-B. Wets. (eds.). (1995). Ann. Oper. Res. 56. Special Issue on Stochastic Programming.
Bahri, P.A., J.A. Bandoni, and J.A. Romagnoli. (1996). “Effect of Disturbances in Optimizing Control: Steady-State Open-Loop Back off Problem.” AIChE J. 42, 983–994.
Bernardo, F.P., E.N. Pistikopoulos, and P.M. Saraiva. (1999). “Integration and Computational Issues in Stochastic Design and Planning Optimization Problems.” Ind. Engrg. Chem. Res. 38, 3056.
Biegler, L.T., I.E. Grossmann, and A.W. Westerberg. (1997). Systematic Methods of Chemical Process Design. New Jersey: Prentice Hall.
Carnahan, B., H.A. Luther, and J.O. Wilkes. (1969). Applied Numerical Methods. New York: Wiley.
Grossmann, I.E. and C.A. Floudas. (1987). “Active Constraints Strategy for Flexibility Analysis in Chemical Processes.” Comput. Chem. Engrg. 11, 675–693.
Halemane, K.P. and I.E. Grossmann. (1983). “Optimal Process Design under Uncertainty.” AIChE J. 29, 425–433.
Ierapetritou, M.G. and E.N. Pistikopoulos. (1995). “Novel Approach for Optimal Process Design under Uncertainty.” Comput. Chem. Engrg. 19, 1089–1110.
Kocis, G.R. and I.E. Grossmann. (1989). “A Modeling and Decomposition Strategy for MINLP Optimization of Process Flowsheets.” Comput. Chem. Engrg. 13, 797–819.
McKinsey, J.C.C. (1952). Introduction to the Theory of Games.New York: McGraw-Hill.
Nishida, N., Y.A. Liu, and L. Lapidus. (1977). “Studies in Chemical Process Design and Synthesis.” AIChE J. 23, 77–93.
Ostrovsky, G.M., L.E.K. Achenie, I. Datskov, and Y.M. Volin. “Consideration of Parametric Uncertainty at Both the Design and Operation Stages of Chemical Processes.” Chem. Engrg. Comm. (in print, 2003).
Ostrovsky, G., L.E.K. Achenie, I. Datskov, and Y. Volin. (2004). “Uncertainty at Both Design and Operation Stages.” Chem. Engrg. Commun. 191, 105–124.
Ostrovsky, G.M., Y.M. Volin, and M.M. Senyavin. (1997). “An Approach to Solving a Two-Stage Optimization Problem under Uncertainty.” Comput. Chem. Engrg. 21, 311–325.
Paules, G.E. and C.A. Floudas. (1992). “Stochastic Programming in Process Synthesis: A Two-Stage Model with MINLP Recourse for Multiperiod Heat-Integrated Distillation Sequences.” Comput. Chem. Engrg. 16, 189–210.
Pistikopoulos, E.N. and I.E. Grossmann. (1989). “Optimal Retrofit Design for Improving Process Flexibility in Nonlinear Systems-1. Fixed Degree of Flexibility.” Comput. Chem. Engrg. 12, 1003–1016.
Polak, E. (1982). “An Implemented Algorithm for the Optimal Design Centering, Tolerancing and Tuning.” J. Optim. Theory Appl. 37, 45–67.
Raspanti, C.G., J.A. Bandoni, and L.T. Biegler. (2000). “New Strategies for Flexibility Analysis and Design under Uncertainty.” Comput. Chem. Engrg.24, 2193–2209.
Rooney, W.C. and L.T. Biegler. (2003). “Optimal Process Design with Model Parameter Uncertainty and Process Variability.” AIChE J. 49, 438–449.
Ruszczynski, A. (1997). “Decomposition Methods in Stochastic Programming.” Math. Programming 79, 333–353.
Shapiro, A. and T.H. de-Mello. (1998). “A Simulation-Based Approach to Two-Step Stochastic Programming with Recourse.” Math. Programming 81, 301–305.
Straub, D.A. and I.E. Grossmann. (1993). “Design Optimization of Stochastic Flexibility.” Comput. Chem. Engrg. 17, 339–354.
Swaney, R.E. and I.E. Grossmann. (1985). “An Index for Operational Flexibility in Chemical Process Design.” AIChE J. 31(4), 621.
Walsh, S. and J. Perkins. (1996). “Operability and Control in Process Synthesis and Design.” In: J.L. Anderson (ed.), Process Synthesis, pp. 301–341. New York: Academic Press.
Waltz, R.A. and J. Nocedal. (2002). “Knitro 2.0 User's Guide.” Northwestern University.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ostrovsky, G., Achenie, L., Datskov, I. et al. Flexibility Analysis in the Case of Incomplete Information about Uncertain Parameters. Ann Oper Res 132, 257–275 (2004). https://doi.org/10.1023/B:ANOR.0000045286.85889.db
Issue Date:
DOI: https://doi.org/10.1023/B:ANOR.0000045286.85889.db