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Erschienen in: Journal of Scheduling 4/2019

11.12.2017

Parallel machine makespan minimization subject to machine availability and total completion time constraints

verfasst von: Yumei Huo

Erschienen in: Journal of Scheduling | Ausgabe 4/2019

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Abstract

In this paper, we study the parallel machine scheduling subject to machine availability constraint. The jobs can be resumed after being preempted by another job or interrupted by the unavailable intervals. The goal is to minimize the makespan subject to the constraint that the total completion time is minimized. We study two different machine unavailability models. In the first model, each machine has a single unavailable interval which starts from time 0. In the second model, each machine can have multiple unavailable intervals, but at any time, there is at most one machine unavailable. For each model, we show that there is an optimal polynomial time algorithm.

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Literatur
Zurück zum Zitat Aslam, J., Rasala, A., Stein, C. & Young, N. (1999). Improved bicriteria existence theorems for scheduling, In Proceedings of the tenth annual ACM-SIAM symposium on discrete algorithms, pp. 846–847. Aslam, J., Rasala, A., Stein, C. & Young, N. (1999). Improved bicriteria existence theorems for scheduling, In Proceedings of the tenth annual ACM-SIAM symposium on discrete algorithms, pp. 846–847.
Zurück zum Zitat Chen, C. L., & Bulfin, R. L. (1993). Complexity of single machine, multicriteria scheduling problems. European Journal of Operational Research, 70, 115–125.CrossRef Chen, C. L., & Bulfin, R. L. (1993). Complexity of single machine, multicriteria scheduling problems. European Journal of Operational Research, 70, 115–125.CrossRef
Zurück zum Zitat Dileepan, P., & Sen, T. (1988). Bicriteria static scheduling research for a single machine. OMEGA, 16, 53–59.CrossRef Dileepan, P., & Sen, T. (1988). Bicriteria static scheduling research for a single machine. OMEGA, 16, 53–59.CrossRef
Zurück zum Zitat Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling, a survey. Annals of Discrete Mathematics, 5, 287–326.CrossRef Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling, a survey. Annals of Discrete Mathematics, 5, 287–326.CrossRef
Zurück zum Zitat Gupta, J. N. D., Ho, J. C., & Webster, S. (2000). Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines. Journal of Operational Research Society, 51(11), 1330–1339.CrossRef Gupta, J. N. D., Ho, J. C., & Webster, S. (2000). Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines. Journal of Operational Research Society, 51(11), 1330–1339.CrossRef
Zurück zum Zitat Hoogeveen, J. A. (2005). Multicriteria scheduling. European Journal of Operational Research, 167(3), 592–623.CrossRef Hoogeveen, J. A. (2005). Multicriteria scheduling. European Journal of Operational Research, 167(3), 592–623.CrossRef
Zurück zum Zitat Huo, Y. (2014). Makespan minimization on multiple machines subject to machine unavailability and total completion time constraints. In The tenth international conference on algorithmic aspects of information and management (AAIM 2014). Lecture notes in computer science (Vol. 8546, pp. 56–65). Huo, Y. (2014). Makespan minimization on multiple machines subject to machine unavailability and total completion time constraints. In The tenth international conference on algorithmic aspects of information and management (AAIM 2014). Lecture notes in computer science (Vol. 8546, pp. 56–65).
Zurück zum Zitat Huo, Y., & Zhao, H. (2011). Bicriteria scheduling concerned with makespan and total completion time subject to machine availability constraints. Theoretical Computer Science, 412, 1081–1091.CrossRef Huo, Y., & Zhao, H. (2011). Bicriteria scheduling concerned with makespan and total completion time subject to machine availability constraints. Theoretical Computer Science, 412, 1081–1091.CrossRef
Zurück zum Zitat Huo, Y., & Zhao, H. (2015). Total completion time minimization on multiple machines subject to machine availability and makespan constraints. European Journal of Operational Research, 243(2), 547–554.CrossRef Huo, Y., & Zhao, H. (2015). Total completion time minimization on multiple machines subject to machine availability and makespan constraints. European Journal of Operational Research, 243(2), 547–554.CrossRef
Zurück zum Zitat Lee, C.-Y., & Liman, S. D. (1993). Capacitated two-parallel machine scheduling to minimize sum of job completion times. Discrete Applied Mathematics, 41, 211–222.CrossRef Lee, C.-Y., & Liman, S. D. (1993). Capacitated two-parallel machine scheduling to minimize sum of job completion times. Discrete Applied Mathematics, 41, 211–222.CrossRef
Zurück zum Zitat Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1, 343–362.CrossRef Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1, 343–362.CrossRef
Zurück zum Zitat Leung, J. Y.-T., & Pinedo, M. L. (2003). Minimizing total completion time on parallel machines with deadline constraints. SIAM Journal on Computing, 32, 1370–1388.CrossRef Leung, J. Y.-T., & Pinedo, M. L. (2003). Minimizing total completion time on parallel machines with deadline constraints. SIAM Journal on Computing, 32, 1370–1388.CrossRef
Zurück zum Zitat Leung, J. Y.-T., & Pinedo, M. L. (2004). A note on the scheduling of parallel machines subject to breakdown and repair. Naval Research Logistics, 51, 60–72.CrossRef Leung, J. Y.-T., & Pinedo, M. L. (2004). A note on the scheduling of parallel machines subject to breakdown and repair. Naval Research Logistics, 51, 60–72.CrossRef
Zurück zum Zitat Leung, J. Y.-T., & Young, G. H. (1989). Minimizing schedule length subject to minimum flow time. SIAM Journal on Computing, 18(2), 314–326.CrossRef Leung, J. Y.-T., & Young, G. H. (1989). Minimizing schedule length subject to minimum flow time. SIAM Journal on Computing, 18(2), 314–326.CrossRef
Zurück zum Zitat Liu, Z., & Sanlaville, E. (1995). Preemptive scheduling with variable profile, precedence constraints and due dates. Discrete Applied Mathematics, 58, 253–280.CrossRef Liu, Z., & Sanlaville, E. (1995). Preemptive scheduling with variable profile, precedence constraints and due dates. Discrete Applied Mathematics, 58, 253–280.CrossRef
Zurück zum Zitat Ma, Y., Chu, C., & Zuo, C. (2010). A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering, 58(2), 199–211.CrossRef Ma, Y., Chu, C., & Zuo, C. (2010). A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering, 58(2), 199–211.CrossRef
Zurück zum Zitat McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12.CrossRef McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12.CrossRef
Zurück zum Zitat Panwalkar, S. S., Dudek, R. K., & Smith, M. L. (1973). Sequencing research and the industrial scheduling problem. In S. E. Elmaghraby (Ed.), Proceedings of the symposium on the theory of scheduling and its application (pp. 29–38). New York: Springer. Panwalkar, S. S., Dudek, R. K., & Smith, M. L. (1973). Sequencing research and the industrial scheduling problem. In S. E. Elmaghraby (Ed.), Proceedings of the symposium on the theory of scheduling and its application (pp. 29–38). New York: Springer.
Zurück zum Zitat Pinedo, M. (2012). Scheduling: Theory, models and algorithms (4th ed.). New York: Springer.CrossRef Pinedo, M. (2012). Scheduling: Theory, models and algorithms (4th ed.). New York: Springer.CrossRef
Zurück zum Zitat Saidy, H., & Taghvi-Fard, M. (2008). Study of scheduling problems with machine availability constraint. Journal of Industrial and Systems Engineering, 1(4), 360–383. Saidy, H., & Taghvi-Fard, M. (2008). Study of scheduling problems with machine availability constraint. Journal of Industrial and Systems Engineering, 1(4), 360–383.
Zurück zum Zitat Sanlaville, E., & Schmidt, G. (1998). Machine scheduling with availability constraints. Acta Informatica, 35, 795–811.CrossRef Sanlaville, E., & Schmidt, G. (1998). Machine scheduling with availability constraints. Acta Informatica, 35, 795–811.CrossRef
Zurück zum Zitat Schmidt, G. (2000). Scheduling with limited machine availability. European Journal of Operational Research, 121(1), 1–15.CrossRef Schmidt, G. (2000). Scheduling with limited machine availability. European Journal of Operational Research, 121(1), 1–15.CrossRef
Zurück zum Zitat Stein, C., & Wein, J. (1997). On the existence of schedules that are near-optimal for both makespan and total weighted completion time. Operations Research Letters, 21(3), 115–122.CrossRef Stein, C., & Wein, J. (1997). On the existence of schedules that are near-optimal for both makespan and total weighted completion time. Operations Research Letters, 21(3), 115–122.CrossRef
Zurück zum Zitat T’kindt, V., & Billaut, J. C. (2002). Multicriteria scheduling: Theory, models and algorithms. Heidelberg: Springer.CrossRef T’kindt, V., & Billaut, J. C. (2002). Multicriteria scheduling: Theory, models and algorithms. Heidelberg: Springer.CrossRef
Metadaten
Titel
Parallel machine makespan minimization subject to machine availability and total completion time constraints
verfasst von
Yumei Huo
Publikationsdatum
11.12.2017
Verlag
Springer US
Erschienen in
Journal of Scheduling / Ausgabe 4/2019
Print ISSN: 1094-6136
Elektronische ISSN: 1099-1425
DOI
https://doi.org/10.1007/s10951-017-0551-z

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