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Global Optimization for Stochastic Planning, Scheduling and Design Problems

  • M. G. Ierapetritou
  • E. N. Pistikopoulos
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 9)

Abstract

The work addresses the problem of including aspects of uncertainty in process parameters and product demands at the planning, scheduling and design of multiproduct/multipurpose plants operating in either continuous or batch mode. For stochastic linear planning models, it is shown that based on a two-stage stochastic programming formulation, a decomposition based global optimization approach can be developed to obtain the plan with the maximum expected profit by simultaneously considering future feasibility. An equivalent representation is also presented based on the relaxation of demand requirements enabling the consideration of partial order fulfilment while properly penalizing unfilled orders in the objective function. A similar relaxation is shown for the problem of scheduling of continuous multiproduct plants enabling the determination of a robust schedule capable of meeting stochastic demands. In both cases, it is shown that such relaxed reformulations can be solved to global optimality, since despite the presence of stochastic parameters the convexity properties of the original deterministic (i.e. without uncertainty) models are fully preserved. Finally, for the case of batch processes, global solution procedures are derived for the cases of continuous and discrete equipment sizes by exploiting the special structure of the resulting stochastic models. Examples are presented to illustrate the applicability of the proposed techniques.

Keywords

Global Optimization Feasible Region Stochastic Program Uncertain Parameter Master Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Acevedo J. and E. N. Pistikopoulos (1995). Computational Studies of Stochastic Optimization Techniques for Process Synthesis under Uncertainty. Manuscript in preparation.Google Scholar
  2. 2.
    Beale, E.M., J.J.H. Forrest and C.J. Taylor. Multi-time-period Stochastic Programming, Stochastic Programming; Academic Press: New York, 1980.Google Scholar
  3. 3.
    Bienstock, D. and J.F. Shapiro (1988). Optimizing Resource Acquisition Decisions by Stochastic Programming. Mang. Sci., 34, 215.CrossRefGoogle Scholar
  4. 4.
    Birge, J. R. (1982). The Value of the Stochastic Solution in Stochastic Linear Programs with Fixed Recourse. Math. Prog., 24, 314.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Birge, J. R. (1985). Aggregation Bounds in Stochastic Linear Programming. Math. Prog., 25, 31.MathSciNetGoogle Scholar
  6. 6.
    Birge, J. R., R. Wets (1989). Sublinear Upper Bounds for Stochastic Programs with Recourse. Math. Prog., 43, 131.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bloom, J. A. (1983). Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders Decomposition. Oper. Res., 31, 84.zbMATHCrossRefGoogle Scholar
  8. 8.
    Borison, A. B.. P.A. Morris and S.S. Oren (1984). A State-of-the World Decomposition Approach to Dynamics and Uncertainty in Electric Utility Generation Expansion Planning. Oper. Res., 32, 1052.zbMATHCrossRefGoogle Scholar
  9. 9.
    Brauers, J. and M.A. Weber (1988). New Method of Scenario Analysis for Strategic Planning. Jl. of Forecasting, 7, 31–47.CrossRefGoogle Scholar
  10. 10.
    Clay R.L. and I.E. Grossmann (1994a). Optimization of Stochastic Planning Models I. Concepts and Theory. Submitted for publication.Google Scholar
  11. 11.
    Clay R.L. and I.E. Grossmann (1994b). Optimization of Stochastic Planning Models I I. Two-Stage Successive Disaggregation Algorithm. Submitted for publication.Google Scholar
  12. 12. Dantzig, G. B. (1989). Decomposition Techniques for Large-Scale Electric Power Systems Planning Under Uncertainty. Annals of Operations Research. Google Scholar
  13. 13.
    Edgar, T.F. and D.M. Himmelblau Optimization of Chemical Processes; McGraw Hill: New York, 1988.Google Scholar
  14. 14.
    Fichtner, G., H.J. Reinhart and D.W.T. Rippin (1990). The Design of Flexible Chemical Plants by the Application of Interval Mathematics. Comp. Chem. Engng., 14, 1311.CrossRefGoogle Scholar
  15. 15.
    Floudas, C.A. and V. Visweswaran, (1990). A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs-I. Theory, Comp. Chem. Engng., 14, 1397.CrossRefGoogle Scholar
  16. 16.
    Floudas, C.A. and V. Visweswaran, (1993). Primal-Relaxed Dual Global Optimization Approach, JOTA, 78, 187.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Friedman, Y. and G.V. Reklaitis (1975). Flexible Solutions to Linear Programs under Uncertainty: Inequality Constraints. AIChE Jl,21. 77–83.Google Scholar
  18. 18.
    Grossmann, I.E., K.P. Halemane K.P. and R.E. Swaney (1983). Optimization Strategies for Flexible Chemical Processes. Comput. them. Engng., 7, 439–462.CrossRefGoogle Scholar
  19. 19.
    Horst, R. (1990). Deterministic methods in Constrained Global Optimization: Some Recent Advances and New Fields of Application. Nan. Res. Log., 37, 433–471.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Ierapetritou, M.G. (1995). Optimization Approaches for Process Engineering Problems Under Uncertainty. PhD Thesis University of London.Google Scholar
  21. 21.
    Ierapetritou, M.G. and E.N. Pistikopoulos (1994). Novel Optimization Approach of Stochastic Planning Models. Ind. Eng. Chem. Res., 33, 1930.CrossRefGoogle Scholar
  22. 22.
    Ierapetritou, M.G. and E.N. Pistikopoulos (1995). Batch Plant design and operations under Uncertainty. Accepted for publication in Ind. Eng. Chem. Res..Google Scholar
  23. 23.
    Ierapetritou, M.G., J. Acevedo and E.N. Pistikopoulos (1995). An Optimization Approach for Process Engineering Problems Under Uncertainty. Accepted for publication in Comput. chem. Engng..Google Scholar
  24. 24.
    Inuiguchi, M. M. Sakawa and Y. Kume (1994). The usefulness of Possibilistic Programming in Production Planning Problems. Inter. J. Prod. Econ., 33, 42.Google Scholar
  25. 25.
    Kocis, G.R. and I.E. Grossmann (1988). Global Optimization of Nonconvex MINLP Problems in Process Synthesis. Ind. Eng. Chem. Res., 27, 1407.CrossRefGoogle Scholar
  26. 26.
    Liu, M.L. and N.V. Sahinidis (1995). Process Planning in a Fuzzy Environment. Submitted for publication in Eger. J. Oper. Res.Google Scholar
  27. 27.
    Modiano, E.M. (1987). Derived Demand and Capacity Planning Under Uncertainty. Oper. Res.. 35, 185–197.CrossRefGoogle Scholar
  28. 28.
    Pinto J. and I.E. Grossmann (1994). Optimal Cyclic Scheduling of Multistage Continuous Multiproduct Plants. Submitted for publication.Google Scholar
  29. 29.
    Pistikopoulos, E.N. and I.E. Grossmann (1989a). Optimal Retrofit Design for Improving Process Flexibility in nonlinear Systems: -I. Fixed degree of Flexibility. Comput. chem. Engng., 13, 1003–1016.CrossRefGoogle Scholar
  30. 30.
    Pistikopoulos, E.N. and I.E. Grossmann (1989b). Optimal Retrofit Design for Improving Process Flexibility in nonlinear Systems: -II. Optimal Level of Flexibility. Comput. chem. Engng. 13, 1087.CrossRefGoogle Scholar
  31. 31.
    Pistikopoulos, E.N. and M.G. Ierapetritou (1995). A Novel Approach for Optimal Process Design Under Uncertainty. Comput. chem. Engng., 19, 1089.CrossRefGoogle Scholar
  32. 32.
    Reinhart, H.J. and D.W.T. Rippin, (1986). Design of flexible batch chemical plants. AIChE Spring National Mtg, New Orleans, Paper No 50e.Google Scholar
  33. 33.
    Reinhart, H.J. and D.W.T. Rippin, (1987). Design of flexible batch chemical plants. AIChE Annual Mtg, New York, Paper No 92f.Google Scholar
  34. 34.
    Rotstein, G.E., R. Lavie and D.R. Lewin (1994). Synthesis of Flexible and Reliable Short-Term batch production Plans. Submitted for publication.Google Scholar
  35. 35.
    Sahinidis, N.V., I.E. Grossmann and R.E. Fornari (1989). Chathrathi, M. Optimization Model for Long-Range Planning in Chemical Industry. Comput. Chem. Engng., 9, 1049.CrossRefGoogle Scholar
  36. 36.
    Sahinidis, N.V. and I.E. Grossmann (1991). MINLP model for Cyclic Multiproduct Scheduling on Continuous parallel lines. Comput. Chem. Engng., 15, 85.CrossRefGoogle Scholar
  37. 37.
    Schilling, G., Y.-E. Pineau, C.C. Pantelides and N. Shah. Optimal Scheduling of Multipurpose Continuous Plants AIChE 1994 Annual Meeting San Francisco.Google Scholar
  38. 38.
    Shah, N. and C.C.Pantelides (1992). Design of Multipurpose batch Plants with Uncertain Production Requirements. Ind. Eng. Chem. Res. 31, 1325.CrossRefGoogle Scholar
  39. 39.
    Shimizu, Y. (1989). Application of flexibility analysis for compromise solution in large-scale linear systems. Jl of Chem. Engng of Japan, 22, 189–193.CrossRefGoogle Scholar
  40. 40.
    Straub, D.A. and I.E. Grossmann (1992). Evaluation and optimization of stochastic flexibility in multiproduct batch plants. Comput. chem. Engng., 16. 69.CrossRefGoogle Scholar
  41. 41.
    Straub, D.A. and I.E. Grossmann (1993). Design Optimization of Stochastic Flexibility (1993). Comput. Chem. Engng., 17, 339.CrossRefGoogle Scholar
  42. 42.
    Subrahmanyam, S., J.F. Pekny and G.V. Reklaitis (1994). Design of Batch Chemical Plants under Market Uncertainty. Ind. Eng. Chem. Res., 33, 2688.Google Scholar
  43. 43.
    Van Slyke, R.M. and R. Wets, (1969). L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming. SIAM J. Appl. Math., 17, 573.Google Scholar
  44. 44.
    Voudouris, V.T. and I.E. Grossmann, (1992). Mixed-Integer Linear Programming Reformulation for Batch Process Design with Discrete Equipment Sizes, Ind. Eng. Chem. Res., 31, 1315.CrossRefGoogle Scholar
  45. 45.
    Wallace, S. W. (1987). A piecewise linear upper bound on the network recourse function. Math. Prog., 38, 133.zbMATHCrossRefGoogle Scholar
  46. 46.
    Wellons, H.S. and G.V. Reklaitis (1989). The design of multiproduct batch plants under uncertainty with staged expansion. Comput. Chem. Engng., 13, 115–126.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • M. G. Ierapetritou
    • 1
  • E. N. Pistikopoulos
    • 1
  1. 1.Centre for Process Systems Engineering, Department of Chemical EngineeringImperial CollegeLondonUK

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