Abstract
We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for this problem that compute approximate solutions of any positive e accuracy and run in O(n) time for any fixed values of m, μ and ∈. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines [12], multiprocessor tasks [5,11,13], and classical open, flow and job shops [14,15].
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References
A.K. Amoura, E. Bampis, C. Kenyon and Y. Manoussakis, Scheduling independent multiprocessor tasks, Proceedings of the 5th European Symposium on Algorithms (1997), LNCS 1284, 1–12.
L. Bianco, J. Blazewicz, P. Dell Olmo and M. Drozdowski, Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors, Annals of Operations Research 58 (1995), 493–517.
J. Blazewicz, P. Dell Olmo, M. Drozdowski and M. Speranza, Scheduling multiprocessor tasks on the three dedicated processors, Information Processing Letters 41 (1992), 275–280.
J. Chen and C.-Y. Lee, General multiprocessor tasks scheduling, Naval Research Logistics, in press.
J. Chen and A. Miranda, A polynomial time approximation scheme for general multiprocessor job scheduling, Proceedings of the 31st ACM Symposium on the Theory of Computing (1999), 418–427.
M. Drozdowski, Scheduling multiprocessor tasks-an overview, European Journal on Operations Research, 94 (1996), 215–230.
J. Du and J. Leung, Complexity of scheduling parallel task systems, SI AM Journal on Discrete Mathematics, 2 (1989), 473–487.
M.D. Grigoriadis and L.G. Khachiyan, Coordination complexity of parallel pricedirective decomposition, Mathematics of Operations Research 21 (1996), 321–340.
J.A. Hoogeveen, S.L. van de Velde and B. Veltman, Complexity of scheduling multiprocessor tasks with prespecified processor allocations, Discrete Applied Mathematics 55 (1994), 259–272.
K. Jansen, M. Mastrolilli and R. Solis-Oba, Approximation algorithms for flexible job shop problems, Proceedings of the 4th Latin American Theoretical Informatics (2000), LNCS 1776, Springer Verlag, 68–77.
K. Jansen and L. Porkolab, Linear-time approximation schemes for scheduling malleable parallel tasks, Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms (1999), 490–498.
K. Jansen and L. Porkolab, Improved approximation schemes for scheduling unrelated parallel machines, Proceedings of the 31st ACM Symposium on the Theory of Computing (1999), 408–417.
K. Jansen and L. Porkolab, General multiprocessor task scheduling: approximate solution in linear time, Proceedings of the 6th International Workshop on Algorithms and Data Structures (1999), LNCS 1663, Springer Verlag, 110–121.
K. Jansen, R. Solis-Oba and M.I. Sviridenko, Makespan minimization in job shops: a polynomial time approximation scheme, Proceedings of the 31st ACM Symposium on the Theory of Computing (1999), 394–399.
K. Jansen, R. Solis-Oba and M.I. Sviridenko, A linear time approximation scheme for the job shop scheduling problem, Proceedings of the 2nd Workshop on Approximation Algorithms (1999), LNCS 1671, Springer Verlag, 177–188.
E.L. Lawler, J.K. Lenstra, A.H.G. Rinnoy Kan and D.B. Shmoys, Sequencing and scheduling: algorithms and complexity, in: Handbook of Operations Research and Management Science, Vol. 4, North-Holland, 1993, 445–522.
S.A. Plotkin, D.B. Shmoys and E. Tardos, Fast approximation algorithms for fractional packing and covering problems, Mathematics of Operations Research 20 (1995), 257–301.
D.B. Shmoys, C. Stein and J. Wein, Improved approximation algorithms for shop scheduling problems, SI AM Journal on Computing, 23 (1994), 617–632.
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Jansen, K., Porkolab, L. (2000). Polynomial Time Approximation Schemes for General Multiprocessor Job Shop Scheduling. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_74
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DOI: https://doi.org/10.1007/3-540-45022-X_74
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