Case study background and problem formulations
Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.
PROBLEM: Stochastic Two Stage Linear
Minimize Avg (Recourse) (minimizing average of recourse function)
subject to
ConstVector1 ≤ Linearmulti ≤ ConstVector2 (linear constraints on the first stage variables)
Box constraints (bounds on the first stage variables)
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Avg = Average for Recourse
Linearmulti = Linear Multiple
Box constraints = constraints on individual decision variables
Minimize Avg (Recourse) (minimizing average of recourse function)
subject to
ConstVector1 ≤ Linearmulti ≤ ConstVector2 (linear constraints on the first stage variables)
Box constraints (bounds on the first stage variables)
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Avg = Average for Recourse
Linearmulti = Linear Multiple
Box constraints = constraints on individual decision variables
Recourse = Minimal value of the following second stage subproblem for given first stage variables depending on scenarios
Minimize Linear (minimizing linear objective of the second stage subproblem)
subject to
ConstVector3 ≤ Linearmulti ≤ ConstVector4 (linear constraints on the second stage variables depending on scenarios)
Box constraints (bounds on the second stage variables)
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Problem “problem_TwoStage_stormG2”
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Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Minimize Linear (minimizing linear objective of the second stage subproblem)
subject to
ConstVector3 ≤ Linearmulti ≤ ConstVector4 (linear constraints on the second stage variables depending on scenarios)
Box constraints (bounds on the second stage variables)
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Problem “problem_TwoStage_stormG2”
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# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 | 11,456=360+1,387*8 | 8 | 15,535,235.7 | 1.11 | |||
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Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
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Dataset2 | Problem Statement | Data | Solution | 37,809=360+1,387*27 | 27 | 15,508,982.3 | 2.96 |
Dataset3 | Problem Statement | Data | Solution | 173,735=360+1,387*125 | 125 | 15,512,091.2 | 11.12 |
Dataset4 | Problem Statement | Data | Solution | 1,387,360=360+1,387*1,000 | 1,000 | 15,802,590.2 | 70.30 |
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Problem “problem_TwoStage_pltexpA2”
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# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 | 1,856=188+278*6 | 6 | -9.4793089 | 0.41 | |||
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Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
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Dataset2 | Problem Statement | Data | Solution | 4,636=188+278*16 | 16 | -9.6623073 | 0.77 |
CASE STUDY SUMMARY
POSTS (a portable stochastic programming test set) gives a set of multi-stage linear stochastic programming problems with discrete scenarios for testing algorithms, Derek et al. (1995). Every problem has several sets of scenarios. Problems posted at the POSTS website are general linear stochastic programming in SMPS format. We have selected several two-stage problems at POSTS website. For selected problems we converted data to PSG format and solved these problems in PSG RunFile environment. Two-stage problems were formulated using PSG Average function applied to Recourse function.
POSTS (a portable stochastic programming test set) gives a set of multi-stage linear stochastic programming problems with discrete scenarios for testing algorithms, Derek et al. (1995). Every problem has several sets of scenarios. Problems posted at the POSTS website are general linear stochastic programming in SMPS format. We have selected several two-stage problems at POSTS website. For selected problems we converted data to PSG format and solved these problems in PSG RunFile environment. Two-stage problems were formulated using PSG Average function applied to Recourse function.
References
• Berg, E.V., and Derek H. and B. John (1995): Cargill Financial Services.
URL http://users.iems.northwestern.edu/~jrbirge/html/dholmes/post.html#post_0
• Berg, E.V., and Derek H. and B. John (1995): Cargill Financial Services.
URL http://users.iems.northwestern.edu/~jrbirge/html/dholmes/post.html#post_0