Mean Value Cross Decomposition for Two-Stage Stochastic Linear Programming with Recourse

Han-Suk Sohn
2011 Open Operational Research Journal  
We present the mean value cross decomposition algorithm and its simple enhancement for the two-stage stochastic linear programming problem with complete recourse. The mean value cross decomposition algorithm employs the Benders (primal) subproblems as in the so-called "L-shaped" method but eliminates the Benders master problem for generating the next trial first-stage solution, relying instead upon Lagrangian (dual) subproblems. The Lagrangian multipliers used in defining the dual subproblems
more » ... dual subproblems are in turn obtained from the primal subproblems. The primal subproblem separates into subproblems, one for each scenario, each containing only the second-stage variables. The dual subproblem also separates into subproblems, one for each scenario which contains both first-and second-stage variables, and additionally a subproblem containing only the first-stage variables. We then show that the substantial computational savings may be obtained by solving at most iterations only the dual subproblem with the first-stage variables and bypassing the termination test. Computational results are highly encouraging.
doi:10.2174/1874243201105010030 fatcat:kv5ifojtf5b4blyz6qprsnot4u