# 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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Dataset1 11,456=360+1,387*8 8 15,535,235.7 1.11 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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.

 Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec) Sources of Data Mulvey, M. and A. Ruszczynski (1995): A New Scenario Decomposition Method for Large Scale Stochastic Optimization, Operations Research, Vol. 43, Issue 3, 477-490. 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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Dataset1 1,856=188+278*6 6 -9.4793089 0.41 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data