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

•An accelerated solution method is proposed to solve the two-stage stochastic program.•The method improves the main structure of the sample average approximation algorithm.•The computational process is significantly accelerated to solve real-sized problems.•The relative optimality gaps are significa...

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Vydané v:Applied Mathematical Modelling Ročník 41; s. 582 - 595
Hlavní autori: Mohammadi Bidhandi, Hadi, Patrick, Jonathan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Elsevier Inc 01.01.2017
Elsevier BV
Predmet:
Approximation
Benders decomposition
Continuity (mathematics)
Integer programming
Mixed integer
Mixed integer linear programming
Sample average approximation
Stochastic models
Stochastic programming
Studies
Supply chain network design
Supply chains
Two-stage stochastic programming
Benders’ decomposition
Supply chain network design
Mixed integer linear programming
Two-stage stochastic programming
Sample average approximation
ISSN:0307-904X, 1088-8691, 0307-904X
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Shrnutí:•An accelerated solution method is proposed to solve the two-stage stochastic program.•The method improves the main structure of the sample average approximation algorithm.•The computational process is significantly accelerated to solve real-sized problems.•The relative optimality gaps are significantly reduced using the proposed method.•An improved model is presented for stochastic supply chain network design problems. 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.
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ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2016.09.019