A conditional value-at risk-based two-stage stochastic programming model for grassland ecosystem restoration—A case study for the three-river source

Abstract In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.

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Two-stage stochastic programming model for the regional-scale electricity planning under demand uncertainty

Energy ◽

10.1016/j.energy.2016.09.112 ◽

2016 ◽

Vol 116 ◽

pp. 1145-1157 ◽

Cited By ~ 15

Author(s):

Yun-Hsun Huang ◽

Jung-Hua Wu ◽

Yu-Ju Hsu

Keyword(s):

Stochastic Programming ◽

Demand Uncertainty ◽

Programming Model ◽

Regional Scale ◽

Two Stage ◽

Electricity Planning ◽

Stochastic Programming Model

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An interval-fuzzy two-stage stochastic programming method for filter management of hydraulic systems

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214563737 ◽

2014 ◽

Vol 229 (15) ◽

pp. 2788-2809

Author(s):

Hui Ji ◽

Songlin Nie ◽

Yeqing Huang

Keyword(s):

Stochastic Programming ◽

Hydraulic System ◽

Programming Model ◽

Optimal Strategies ◽

Management Policy ◽

Continuous Variables ◽

Hydraulic Systems ◽

Two Stage ◽

Interval Numbers ◽

Stochastic Programming Model

An interval-fuzzy two-stage stochastic programming model for filter management of hydraulic system under uncertainties is proposed in this paper. The interval-fuzzy two-stage stochastic programming model integrates the two-stage stochastic programming, fuzzy programming, and interval parameter nonlinear programming into an optimization model of contamination control in hydraulic system. For a typical hydraulic system, it can be used for expressing the uncertainties existed in the purchase cost of filters, contamination ingression and generation rates, and contamination-holding capacity as probability functions, interval numbers, and fuzzy sets. The developed method is applied to examining the decisions on the adoption of bypass filter and selection of filters within multi-segments, multi-period, and multi-option context. All potential scenarios of filters management policy associated with different economic penalties, objectives, and reliability of system are analyzed. The results of the illustrative example show that the reasonable solutions are generated, including binary and continuous variables which help the decision maker identify optimal strategies for filter allocation and selection, planning the adoption of bypass filter under different working conditions.

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