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- W3138911800 abstract "A strongly NP-hard scheduling problem in which non-simultaneously released jobs with delivery times are to be scheduled on a single machine with the objective to minimize the maximum job full completion time is considered. We describe an exact implicit enumeration algorithm (IEA) and a polynomial-time approximation scheme (PTAS) for the single-machine environment. Although the worst-case complexity analysis of IEA yields a factor of $nu!$, $nu>n$, large sets of the permutations of the critical jobs can be discarded by incorporating a heuristic search strategy, in which the permutations of the so-called critical jobs are considered in a special priority order. Not less importantly, in practice, the number $nu$ turns out to be several times smaller than the total number of jobs $n$, and it becomes smaller when $n$ increases. The above characteristics also apply to the proposed PTAS, which worst-case time complexity can be expressed as $O(kappa!kappa k n log n)$, where $kappa$ is the number of the long critical jobs ($kappa<<nu$) and the corresponding approximation factor is $1+1/k$, where $kappa<k$. We show that the probability that a considerable number of permutations (far less than $kappa!$) are enumerated is close to 0. Hence, with a high probability, the running time of PTAS is fully polynomial." @default.
- W3138911800 created "2021-03-29" @default.
- W3138911800 creator A5065182793 @default.
- W3138911800 date "2021-03-17" @default.
- W3138911800 modified "2023-09-27" @default.
- W3138911800 title "Compact enumeration for scheduling one machine." @default.
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