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We propose a column generation algorithm for solving sequence dependent flowshop scheduling problems (SDST flowshop) to minimize the total weighted tardiness. The continuous relaxation of the set partitioning formulation of the Dantzig-Wolfe decomposition for SDST flowshop is solved by the column generation. The pricing subproblem for the column generation is decomposed into each job-level subproblem...
We propose a new formulation for the column generation for solving flowshop scheduling problems to minimize the total weighted tardiness to derive tighter bounds. In the proposed method, each column represents a two-jobs schedule where the operations of two jobs do not overlap with each other. We show that the lower bound for the original problem can be strengthened by the proposed formulation without...
In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In...
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