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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Acevedo J. and E. N. Pistikopoulos (1995). Computational Studies of Stochastic Optimization Techniques for Process Synthesis under Uncertainty. Manuscript in preparation.
Beale, E.M., J.J.H. Forrest and C.J. Taylor. Multi-time-period Stochastic Programming, Stochastic Programming; Academic Press: New York, 1980.
Bienstock, D. and J.F. Shapiro (1988). Optimizing Resource Acquisition Decisions by Stochastic Programming. Mang. Sci., 34, 215.
Birge, J. R. (1982). The Value of the Stochastic Solution in Stochastic Linear Programs with Fixed Recourse. Math. Prog., 24, 314.
Birge, J. R. (1985). Aggregation Bounds in Stochastic Linear Programming. Math. Prog., 25, 31.
Birge, J. R., R. Wets (1989). Sublinear Upper Bounds for Stochastic Programs with Recourse. Math. Prog., 43, 131.
Bloom, J. A. (1983). Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders Decomposition. Oper. Res., 31, 84.
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.
Brauers, J. and M.A. Weber (1988). New Method of Scenario Analysis for Strategic Planning. Jl. of Forecasting, 7, 31–47.
Clay R.L. and I.E. Grossmann (1994a). Optimization of Stochastic Planning Models I. Concepts and Theory. Submitted for publication.
Clay R.L. and I.E. Grossmann (1994b). Optimization of Stochastic Planning Models I I. Two-Stage Successive Disaggregation Algorithm. Submitted for publication.
12. Dantzig, G. B. (1989). Decomposition Techniques for Large-Scale Electric Power Systems Planning Under Uncertainty. Annals of Operations Research.
Edgar, T.F. and D.M. Himmelblau Optimization of Chemical Processes; McGraw Hill: New York, 1988.
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.
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.
Floudas, C.A. and V. Visweswaran, (1993). Primal-Relaxed Dual Global Optimization Approach, JOTA, 78, 187.
Friedman, Y. and G.V. Reklaitis (1975). Flexible Solutions to Linear Programs under Uncertainty: Inequality Constraints. AIChE Jl,21. 77–83.
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.
Horst, R. (1990). Deterministic methods in Constrained Global Optimization: Some Recent Advances and New Fields of Application. Nan. Res. Log., 37, 433–471.
Ierapetritou, M.G. (1995). Optimization Approaches for Process Engineering Problems Under Uncertainty. PhD Thesis University of London.
Ierapetritou, M.G. and E.N. Pistikopoulos (1994). Novel Optimization Approach of Stochastic Planning Models. Ind. Eng. Chem. Res., 33, 1930.
Ierapetritou, M.G. and E.N. Pistikopoulos (1995). Batch Plant design and operations under Uncertainty. Accepted for publication in Ind. Eng. Chem. Res..
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..
Inuiguchi, M. M. Sakawa and Y. Kume (1994). The usefulness of Possibilistic Programming in Production Planning Problems. Inter. J. Prod. Econ., 33, 42.
Kocis, G.R. and I.E. Grossmann (1988). Global Optimization of Nonconvex MINLP Problems in Process Synthesis. Ind. Eng. Chem. Res., 27, 1407.
Liu, M.L. and N.V. Sahinidis (1995). Process Planning in a Fuzzy Environment. Submitted for publication in Eger. J. Oper. Res.
Modiano, E.M. (1987). Derived Demand and Capacity Planning Under Uncertainty. Oper. Res.. 35, 185–197.
Pinto J. and I.E. Grossmann (1994). Optimal Cyclic Scheduling of Multistage Continuous Multiproduct Plants. Submitted for publication.
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.
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.
Pistikopoulos, E.N. and M.G. Ierapetritou (1995). A Novel Approach for Optimal Process Design Under Uncertainty. Comput. chem. Engng., 19, 1089.
Reinhart, H.J. and D.W.T. Rippin, (1986). Design of flexible batch chemical plants. AIChE Spring National Mtg, New Orleans, Paper No 50e.
Reinhart, H.J. and D.W.T. Rippin, (1987). Design of flexible batch chemical plants. AIChE Annual Mtg, New York, Paper No 92f.
Rotstein, G.E., R. Lavie and D.R. Lewin (1994). Synthesis of Flexible and Reliable Short-Term batch production Plans. Submitted for publication.
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.
Sahinidis, N.V. and I.E. Grossmann (1991). MINLP model for Cyclic Multiproduct Scheduling on Continuous parallel lines. Comput. Chem. Engng., 15, 85.
Schilling, G., Y.-E. Pineau, C.C. Pantelides and N. Shah. Optimal Scheduling of Multipurpose Continuous Plants AIChE 1994 Annual Meeting San Francisco.
Shah, N. and C.C.Pantelides (1992). Design of Multipurpose batch Plants with Uncertain Production Requirements. Ind. Eng. Chem. Res. 31, 1325.
Shimizu, Y. (1989). Application of flexibility analysis for compromise solution in large-scale linear systems. Jl of Chem. Engng of Japan, 22, 189–193.
Straub, D.A. and I.E. Grossmann (1992). Evaluation and optimization of stochastic flexibility in multiproduct batch plants. Comput. chem. Engng., 16. 69.
Straub, D.A. and I.E. Grossmann (1993). Design Optimization of Stochastic Flexibility (1993). Comput. Chem. Engng., 17, 339.
Subrahmanyam, S., J.F. Pekny and G.V. Reklaitis (1994). Design of Batch Chemical Plants under Market Uncertainty. Ind. Eng. Chem. Res., 33, 2688.
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.
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.
Wallace, S. W. (1987). A piecewise linear upper bound on the network recourse function. Math. Prog., 38, 133.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ierapetritou, M.G., Pistikopoulos, E.N. (1996). Global Optimization for Stochastic Planning, Scheduling and Design Problems. In: Grossmann, I.E. (eds) Global Optimization in Engineering Design. Nonconvex Optimization and Its Applications, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5331-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-5331-8_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4754-3
Online ISBN: 978-1-4757-5331-8
eBook Packages: Springer Book Archive