Abstract
The n-job two-machine flow shop scheduling problem is studied in this paper, with the criterion of minimizing the sum of job completion times. The scheduling problem is first formulated mathematically. Three heuristic methods are then invented to find near optimal schedules. Three lower bound generation schemata are designed to compute three different lower bounds from which the tightest one is used. To further reduce the search space, some dominance properties are proved. Then a branch-and-bound algorithm is developed to obtain an optimal schedule. Finally, results and analysis of numerical computations are presented.
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