scholarly journals Two-stage linear decision rules for multi-stage stochastic programming

2018 ◽  
Author(s):  
Merve Bodur ◽  
James R. Luedtke
Keyword(s):  
Stochastic Programming ◽  
Decision Rules ◽  
Two Stage ◽  
Multi Stage ◽  
Linear Decision Rules

scholarly journals Formulation of Two-Stage Stochastic Programming with Fixed Recourse

2019 ◽  
Vol 1 (1) ◽  
pp. 18-21
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Past Experience ◽  
Optimization Techniques ◽  
Random Parameters ◽  
Two Stage ◽  
Second Stage ◽  
Multi Stage ◽  
Time Period ◽  
Primary Model

Stochastic Programming is an asset for the next world researchers due to its uncertainty calculations, which has been skipped in deterministic world experiments as it includes complicated calculations. Two-stage stochastic programming concerns two time period decisions based on some random parameters obtained from past experience or some sort of survey. The objective function for formulating two-stage stochastic programming with fixed recourse includes two parts: first-stage forecast and second-stage fixed decisions based on the experiment results. The constraints are similar to the normal optimization techniques rather some adjustments of requirements and technology assets. The fixed recourse decisions are sort of decisions from the deterministic world.  Formulation techniques of two-stage stochastic programming with fixed recourse may be used for further complications arises in stochastic programming like complete recourse problems, multi-stage problems, etc. And that’s why Two-stage stochastic programming with fixed recourse is called the primary model for stochastic programming.

scholarly journals Formulation of Two-Stage Stochastic Programming with Fixed Recourse

2019 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Past Experience ◽  
Optimization Techniques ◽  
Random Parameters ◽  
Two Stage ◽  
Second Stage ◽  
Multi Stage ◽  
Time Period ◽  
Primary Model

Stochastic Programming is an asset for the next world researchers due to its uncertainty calculations, which has been skipped in deterministic world experiments as it includes complicated calculations. Two-stage stochastic programming concerns two time period decisions based on some random parameters obtained from past experience or some sort of survey. The objective function for formulating two-stage stochastic programming with fixed recourse includes two parts: first-stage forecast and second-stage fixed decisions based on the experiment results. The constraints are similar to the normal optimization techniques rather some adjustments of requirements and technology assets. The fixed recourse decisions are sort of decisions from the deterministic world. Formulation techniques of two-stage stochastic programming with fixed recourse may be used for further complications arises in stochastic programming like complete recourse problems, multi-stage problems, etc. And that’s why Two-stage stochastic programming with fixed recourse is called the primary model for stochastic programming.

scholarly journals A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen
Keyword(s):  
Stochastic Programming ◽  
Benders Decomposition ◽  
Equivalent Model ◽  
Computational Time ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Equivalent ◽  
Location Routing ◽  
Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

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