Single facility scheduling with nonlinear processing times
Computers and Industrial Engineering
Scheduling jobs under simple linear deterioration
Computers and Operations Research
Scheduling jobs with step-deterioration; minimizing makespan on a single- and multi-machine
Computers and Industrial Engineering
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs
Computers and Operations Research
A note on single-processor scheduling with time-dependent execution times
Operations Research Letters
Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs
Computers and Operations Research
Advances in Engineering Software
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In this paper, 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.