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Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs. (English) Zbl 1077.90025
Summary: we study a scheduling problem of minimizing the total completion time on a single machine where the processing time of a job is a step function of its starting time and a due date that is common to all jobs. This problem has been shown to be NP-hard in the literature. To derive optimal solutions from a practical aspect, we develop a lower bound and two elimination rules to design branch-and-bound algorithms. Through computational experiments, we show that the proposed properties are effective in curtailing unnecessary explorations during the solution-finding process, and that the synergy of these properties can solve problems with up to 100 jobs in a few seconds.
90B35Scheduling theory, deterministic
68M20Performance evaluation of computer systems; queueing; scheduling
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut