Scheduling Start Time Dependent Tasks with Deadlines and Identical Initial Processing Times on a Single Machine
In this paper, we study the feasibility problem of scheduling a set of start time dependent tasks on a single machine with deadlines, processing rates and identical initial processing times. First, we show that the cases with arbitrary deadlines are strongly NP-complete. Second, we show that the cas...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2003
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/lkcsb_research/871 https://doi.org/10.1016/s0305-0548(01)00077-6 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | In this paper, we study the feasibility problem of scheduling a set of start time dependent tasks on a single machine with deadlines, processing rates and identical initial processing times. First, we show that the cases with arbitrary deadlines are strongly NP-complete. Second, we show that the cases with two distinct deadlines are NP-complete in the ordinary sense. Finally, we give an optimal polynomial algorithm for the makespan problem with two distinct processing rates. We solve a series of open problems in the literature and give a sharp boundary delineating the complexity of the problems. |
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