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Certainty Equivalence
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A disaggregation algorithm for the optimization of stochastic planning models
A disaggregation algorithm for the optimization of stochastic planning models,10.1016/S00981354(96)002864,Computers & Chemical Engineering,R. L. Cla
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A disaggregation algorithm for the optimization of stochastic planning models
(
Citations: 43
)
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R. L. Clay
,
I. E. Grossmann
This paper considers stochastic linear programming models for
production planning
where cost coefficient and RHS term uncertainties are represented by finite discrete
probability distribution
functions. The solution of the twostage fixed recourse problem is considered, for which a sensitivitybased successive disaggregation algorithm is proposed. The bounding properties of the aggregate subproblems are examined in the context of the disaggregation algorithm. The partitioning algorithm converges to the
exact solution
in a finite number of iterations, and has a highly parallel decomposition and computer implementation. Example problems for the twostage case are presented to demonstrate the solution technique. Results are compared with the alternative solution methods, variants of Benders decomposition schemes tailored to the dynamic staircase LP structure. Theoretical properties of the algorithm are examined, and several example problems are solved where the certainty equivalent problem involves millions of variables and constraints.
Journal:
Computers & Chemical Engineering
, vol. 21, no. 7, pp. 751774, 1997
DOI:
10.1016/S00981354(96)002864
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Citation Context
(5)
...Clay and Grossmann (
1997
) proposed a stochastic linear programming model for production planning for oil refinery manufacturing under the uncertainties of future supplies, demands, and prices...
Xinhui Zhang
,
et al.
A stochastic production planning model under uncertain seasonal demand...
...inlet stream i ∈ pin and an outlet stream k ∈ pout are shown in eqs (6) and (
7
), where eqn (6)...
...corresponds to the overall flow balance and eqn (
7
) to the individual component balance...
..., , , + × = ∀ ∀ ∈ ∈ ∈ ∀ ∈ 103 (
7
) Treatment Units: Equations (8) and (9) describe the flow balance and the contaminant...
Ramkumar Karuppiah
,
et al.
Global optimization of multiscenario mixed integer nonlinear programmi...
...In devising the appropriate penalty functions, we resort to the introduction of some compensating slack variables (
Clay and Grossmann, 1997
) in the probabilistic constraints to eliminate the possibility of secondstage infeasibility...
C. S. Khor
,
et al.
Stochastic Refinery Planning with Risk Management
...problems include Clay and Grossmann [
5
], and Inderfurth, et al. [22]...
IHsuan Hong
,
et al.
Planning the eScrap Reverse Production System Under Uncertainty in th...
...
Clay and Grossman (1997)
focus on a twostage fixedrecourse problem with stochastic RightHandSide terms and stochastic cost coefficients and propose a sensitivitybased successive disaggregation algorithm...
Işıl Yıldırım
,
et al.
A multiperiod stochastic production planning and sourcing problem with...
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Citations
(43)
A stochastic production planning model under uncertain seasonal demand and market growth
(
Citations: 1
)
Xinhui Zhang
,
Meenakshi Prajapati
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Eugene Peden
Journal:
International Journal of Production Research  INT J PROD RES
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Pathogenic fungi: An unacknowledged risk at coastal resorts? New insights on microbiological sand quality in Portugal
Raquel Sabino
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Marine Pollution Bulletin  MAR POLLUT BULL
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Caracterización molecular de dos nuevas mutaciones de α° talasemia en 2 familias españolas (mutación  ED y  GP)
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Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes
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Ignacio E. Grossmann
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Models for robust tactical planning in multistage production systems with uncertain demands
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