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In this study, we consider the scheduling problem for two-machine flowshops with jobs of the different release times. In many real situations, jobs can be arrived at different times due to progress of jobs in the preceding stage or the status of supply of raw materials. We set the objective function of this problem to minimize the total tardiness of jobs. This job arrival constraint tends to reduce the scheduling efficiency of the production system especially in the sense of total tardiness. We developed dominance properties, lower bound and heuristics for upper bound, and adopted them to a branch-and-bound algorithm to obtain the optimal schedule for the objective of minimizing total tardiness. To test the performance of the proposed algorithm and evaluate the efficiency of the dominance properties and the lower bound, we randomly generate the problem instances and test the problem instances with the proposed algorithms. The experiment results show that CPU times are reduced by our lower bound and dominance properties.

A branch-and-bound algorithm to minimize total tardiness in a two-machine flowshop problem with different release time