scholarly journals Progressive Hedging and Sample Average Approximation for the Two-stage Stochastic Traveling Salesman Problem

2017 ◽  
Author(s):  
Pablo Adasme ◽  
Janny Leung ◽  
Ismael Soto
Keyword(s):  
Traveling Salesman Problem ◽  
Sample Average Approximation ◽  
Traveling Salesman ◽  
Two Stage ◽  
Progressive Hedging ◽  
Sample Average ◽  
Average Approximation

scholarly journals A Smoothing Algorithm for a New Two-Stage Stochastic Model of Supply Chain Based on Sample Average Approximation

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Liu Yang ◽  
Yao Xiong ◽  
Xiao-jiao Tong
Keyword(s):  
Supply Chain ◽  
Stochastic Model ◽  
Sample Average Approximation ◽  
Two Stage ◽  
Perishable Product ◽  
Order Stochastic Dominance ◽  
Sample Average ◽  
Optimal Value ◽  
New Variables ◽  
Average Approximation

We construct a new two-stage stochastic model of supply chain with multiple factories and distributors for perishable product. By introducing a second-order stochastic dominance (SSD) constraint, we can describe the preference consistency of the risk taker while minimizing the expected cost of company. To solve this problem, we convert it into a one-stage stochastic model equivalently; then we use sample average approximation (SAA) method to approximate the expected values of the underlying random functions. A smoothing approach is proposed with which we can get the global solution and avoid introducing new variables and constraints. Meanwhile, we investigate the convergence of an optimal value from solving the transformed model and show that, with probability approaching one at exponential rate, the optimal value converges to its counterpart as the sample size increases. Numerical results show the effectiveness of the proposed algorithm and analysis.

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