On Line Maintenance of Optimal Schedules for a Single Machine
On Line Maintenance of Optimal Schedules for a Single Machine
Amril Aman
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We denote the maximum subadditive penalty as f^ax- ^^^ section studies the competitiveness of on-line reoptimLzation, with and without preemption, when all jobs have consistent, subadditive penalty functions. When preemptions are permitted, we show that the on-line reoptimization strategy is 2-competitive, i. E. , the objective value of the on-line schedule is at most twice the optimal off-line value. When preemption is prohibited, the worst-case ratio increases to (p+2), where p is a specified... ratio of job processing times. 5. 1. 1 Scheduling with Preemptions We now show that, for any k-job problem, the preemptive schedule obtained using on-line reoptimization (without anticipating future job arrivals) has a worst-case performance ratio of 2 relative to the optimal off- line schedule for the l/r^ prec, pmtn/f^^^ problem constructed by the enhanced Forward algorithm (Appendix 1). Theorem 1: For the 1/prec, r^ pmtn/f^^^ problem, on-line reoptimization is 2- competitive. -17- Proof: Let n be the preemptive schedule obtained using on-line reoptiniization for a k-job problem.
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