On the optimal solution of the general min-max sequencing problem

We present a simple, elegant algorithm for finding an optimal solution to a general min-max sequencing problem. This problem assumes many well-known scheduling problems as special cases, including problems with regular objectives (e.g., maximum lateness, maximum tardiness) as well as ones with non-regular objectives (e.g., maximum earliness-tardiness). Our algorithm is a dichotomy procedure in which highly efficient methods for the single-machine minmax lateness problem are leveraged. Despite the NP-hard nature of the problem in question, our method proves to be effective even for large-scale problem instances with hundreds of jobs. The optimal solutions obtained with the proposed method may serve as benchmarks for studying heuristic methods; moreover, our results have significantly raised the bar for such heuristic methods with regard to both problem size and solution time.

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