On the power of randomization for job shop scheduling with $k$-units length tasks

Mömke, Tobias

doi:10.1051/ita:2008024

On the power of randomization for job shop scheduling with

k

-units length tasks

Mömke, Tobias

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 189-207.

Voir la notice de l'article dans Numdam

Résumé

In the job shop scheduling problem $k$ -units- $J_{m}$ , there are $m$ machines and each machine has an integer processing time of at most $k$ time units. Each job consists of a permutation of $m$ tasks corresponding to all machines and thus all jobs have an identical dilation $D$ . The contribution of this paper are the following results; (i) for $d = o (\sqrt{D})$ jobs and every fixed $k$ , the makespan of an optimal schedule is at most $D + o (D)$ , which extends the result of [3] for $k = 1$ ; (ii) a randomized on-line approximation algorithm for $k$ -units- $J_{m}$ is presented. This is the on-line algorithm with the best known competitive ratio against an oblivious adversary for $d = o (\sqrt{D})$ and $k > 1$ ; (iii) different processing times yield harder instances than identical processing times. There is no $5 / 3$ competitive deterministic on-line algorithm for $k$ -units- $J_{m}$ , whereas the competitive ratio of the randomized on-line algorithm of (ii) still tends to 1 for $d = o (\sqrt{D})$ .

MR Zbl

DOI : 10.1051/ita:2008024

Classification : 68W20, 68W25
Mots-clés : on-line algorithms, randomization, competitive ratio, scheduling

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     author = {M\"omke, Tobias},
     title = {On the power of randomization for job shop scheduling with $k$-units length tasks},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {189--207},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {2},
     year = {2009},
     doi = {10.1051/ita:2008024},
     zbl = {1166.68041},
     mrnumber = {2512254},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2008024/}
}

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Mömke, Tobias. On the power of randomization for job shop scheduling with $k$-units length tasks. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 189-207. doi : 10.1051/ita:2008024. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2008024/

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