Column generation for sequence dependent flowshop scheduling to minimize the total weighted tardiness

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. In order to strengthen the lower bound, the additional constraints are imposed to the pricing problems in the proposed algorithm. The cut generation algorithm is developed for the column generation. Computational experiments show that the proposed method can derive the solutions with a smaller duality gap compared with those of the conventional algorithm of ordinary column generation and Lagrangian relaxation with cuts.