Case Study: Stochastic Two Stage Linear Problem

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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
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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# 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
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.

Sources of Data
  • Mulvey, M. and A. Ruszczynski (1992): A New Scenario Decomposition Method for Large Scale Stochastic Optimization,
    Technical Report SOR-91-19, Dept. of Civil Engineering and Operations Research, Princeton Univ. Princeton, N.J. 08544.
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
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.

Sources of Data
  • Ho, K. and E. Loute (1981): A Set of Linear Programming Test Problems, Mathematical Programming, 20, P. 245-250.
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 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