Accelerated sample average approximation method for two-stage stochastic programming with binary first-stage variables

This paper proposes an accelerated solution method to solve two-stage stochastic programming problems with binary variables in the first stage and continuous variables in the second stage. To develop the solution method, an accelerated sample average approximation approach is combined with an accelerated Benders' decomposition algorithm. The accelerated sample average approximation approach improves the main structure of the original technique through the reduction in the number of mixed integer programming problems that need to be solved. Furthermore, the recently accelerated Benders' decomposition approach is utilized to expedite the solution time of the mixed integer programming problems. In order to examine the performance of the proposed solution method, the computational experiments are performed on developed stochastic supply chain network design problems. The computational results show that the accelerated solution method solves these problems efficiently. The synergy of the two accelerated approaches improves the computational procedure by an average factor of over 42%, and over 12% in comparison with the original and the recently modified methods, respectively. Moreover, the betterment of the computational process increases substantially with the size of the problem.