Case Study: Stochastic Two Stage Linear Problem
Case study background and problem formulations
Instructions for optimization with PSG RunFile, 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)
——————————————————————–
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 RunFile Environment.
Instructions for importing problems from RunFile to PSG MATLAB.
Download other datasets in RunFile Environment.
Instructions for importing problems from RunFile 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  

Environments  
RunFile  Problem Statement  Data  Solution  
Matlab Toolbox  Data  
Matlab Subroutines  Matlab Code  Data  
R  R Code  Data 
Instructions for importing problems from RunFile to PSG MATLAB.
Sources of Data  


Problem Datasets  # of Variables  # of Scenarios  Objective Value  Solving Time, PC 2.66GHz (sec)  

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  

Environments  
RunFile  Problem Statement  Data  Solution  
Matlab Toolbox  Data  
Matlab Subroutines  Matlab Code  Data  
R  R Code  Data 
Instructions for importing problems from RunFile to PSG MATLAB.
Sources of Data  


Problem Datasets  # of Variables  # of Scenarios  Objective Value  Solving Time, PC 2.66GHz (sec)  

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 multistage 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 twostage problems at POSTS website. For selected problems we converted data to PSG format and solved these problems in PSG RunFile environment. Twostage problems were formulated using PSG Average function applied to Recourse function.
POSTS (a portable stochastic programming test set) gives a set of multistage 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 twostage problems at POSTS website. For selected problems we converted data to PSG format and solved these problems in PSG RunFile environment. Twostage 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