Computational methods for solving two-stage stochastic linear programming problems

1979 ◽  
Vol 30 (2) ◽  
pp. 261-271 ◽  
Author(s):  
Peter Kall
Keyword(s):  
Linear Programming ◽  
Computational Methods ◽  
Stochastic Linear Programming ◽  
Two Stage ◽  
Linear Programming Problems

scholarly journals Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Saeed Ketabchi ◽  
Malihe Behboodi-Kahoo
Keyword(s):  
Linear Programming ◽  
Augmented Lagrangian ◽  
Linear Problem ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
Stochastic Linear Programming ◽  
Two Stage ◽  
Smoothing Techniques ◽  
Linear Programming Problems ◽  
Recourse Problem

The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.

scholarly journals Planning of Electric Power Systems Considering Virtual Power Plants with Dispatchable Loads Included: An Inexact Two-Stage Stochastic Linear Programming Model

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Changyu Zhou ◽  
Guohe Huang ◽  
Jiapei Chen
Keyword(s):  
Linear Programming ◽  
Power System ◽  
Electric Power ◽  
Power Supply ◽  
Power Plants ◽  
Electricity Demand ◽  
Virtual Power ◽  
Stochastic Linear Programming ◽  
Two Stage ◽  
Virtual Power Plants

In this study, an inexact two-stage stochastic linear programming (ITSLP) method is proposed for supporting sustainable management of electric power system under uncertainties. Methods of interval-parameter programming and two-stage stochastic programming were incorporated to tackle uncertainties expressed as interval values and probability distributions. The dispatchable loads are integrated into the framework of the virtual power plants, and the support vector regression technique is applied to the prediction of electricity demand. For demonstrating the effectiveness of the developed approach, ITSLP is applied to a case study of a typical planning problem of power system considering virtual power plants. The results indicate that reasonable solutions for virtual power plant management practice have been generated, which can provide strategies in mitigating pollutant emissions, reducing system costs, and improving the reliability of power supply. ITSLP is more reliable for the risk-aversive planners in handling high-variability conditions by considering peak-electricity demand and the associated recourse costs attributed to the stochastic event. The solutions will help decision makers generate alternatives in the event of the insufficient power supply and offer insight into the tradeoffs between economic and environmental objectives.

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