Minimizing tardiness in a two-machine flow-shop

The two-machine flow-shop scheduling problem with the objective of minimizing total tardiness is considered in this paper. Dominance criteria are developed to establish the precedence constraints between jobs in an optimal schedule. A lower bound on the total tardiness of the problem is derived by constructing the sequence of jobs from front to back to simplify the bounding procedure. A branch-and-bound algorithm incorporating these properties is proposed to expedite the search for an optimal sequence. Computational experiments are conducted and the results demonstrate that the proposed algorithm surpasses an existing one in terms of both computation times and sizes of the problems solved.