The single machine coupled task scheduling problem includes a set of jobs, each with two separated tasks, and there is an exact delay between the tasks. We investigate the single machine coupled task scheduling problem with the objective of minimizing the makespan under identical processing time for the first task and identical delay period for all jobs, and the time-dependent processing time setting for the second task. Certain healthcare appointment scheduling problems can be modeled as the coupled task scheduling problem. Also, the incorporation of time-dependent processing time for the second task lets the human resource fatigue and the deteriorating health conditions be modeled. We provide optimal solution under certain conditions. In addition, we propose a dynamic program under the condition that the majority of jobs share the same time-dependent characteristic. We develop a heuristic for the general case and show that the heuristic performs well.
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The authors would like to thank the anonymous referees for their valuable suggestions and comments. Mostafa Khatami is the recipient of the UTS International Research Scholarship (IRS) and the UTS President’s Scholarship (UTSP). Amir Salehipour is the recipient of an Australian Research Council Discovery Early Career Researcher Award (project number DE170100234) funded by the Australian Government.
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Khatami, M., Salehipour, A. Coupled task scheduling with time-dependent processing times. J Sched 24, 223–236 (2021). https://doi.org/10.1007/s10951-020-00675-2
- Coupled task scheduling
- Time-dependent processing time
- Simple linear processing time
- Dynamic program
- Healthcare scheduling