Single Machine Scheduling with Step-Deteriorating Processing Times
We study in this paper a scheduling model in which each task has a normal processing time which deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on problems with identical task deteriorating dates. We show that the flow time problem is NP-complete a...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2001
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/lkcsb_research/872 https://doi.org/10.1016/s0377-2217(00)00284-8 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | We study in this paper a scheduling model in which each task has a normal processing time which deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on problems with identical task deteriorating dates. We show that the flow time problem is NP-complete and suggest a pseudo-polynomial algorithm for the makespan problem. We also introduce a general method of solution, which facilitates the identification of solvable cases for some related problems. Finally, we provide a counter-example that invalidates the conjecture of optimality of a switching algorithm reported in the literature. Thus, we solve several unexplored or open problems and obtain a sharp boundary delineating the complexity of the considered problems. |
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