On the geometry, preemptions and complexity of multiprocessor and shop scheduling

Annals of Operations Research

Volumn 159, Issue 1, 2008, Pages 183-213

  Shchepin, Evgeny V ^a   Vakhania, Nodari ^b,c  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b UNIVERSIDAD AUTÓNOMA DEL ESTADO DE MORELOS   (Mexico)

^c Niko Muskhelishvili Institute of Computational Mathematics   (Georgia)

Author keywords

Algorithm; Multiprocessor scheduling; Preemption; Shop scheduling; Time complexity

Indexed keywords

EID: 38749102030     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-007-0266-1     Document Type: Article

References (16)

1. Gonzalez, T., & Sahni, S. (1976). Open shop scheduling to minimize finish time. Journal of the ACM, 23, 665-679.
2. Gonzalez, T., & Sahni, S. (1978a). Preemptive scheduling of uniform processor systems. Journal of the ACM, 25, 92-101.
3. Gonzalez, T., & Sahni, S. (1978b). Flow-Shop and Job-Shop schedules: complexity and approximations. Operations Research, 26, 36-52.
4. Hall, N. G., Lee, T. E., & Posner, M. E. (2002). The complexity of cyclic shop scheduling problems. Journal of Scheduling, 5, 307-327.
5. Hefetz, N., & Adiri, I. (1982). An efficient optimal algorithm for two-machines unit-time job-shop schedule-length problem. Mathematics of Operations Research, 7, 354-360.
6. Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness (Research Report No. 43). Management Science Research Project, University of California, Los Angeles.
7. Lawler, E. L., & Labetoulle, J. (1978). On preemptive scheduling of unrelated parallel processors by linear programming. Journal of the ACM, 25, 612-619.
8. Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Algorithms for scheduling unrelated parallel machines. Annals of Discrete Mathematics, 1, 343-362.
9. Lenstra, J. K., Shmoys, D. B., & Tardos, E. (1990). Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46, 259-271.
10. McNaughton (1959). Scheduling with deadlines and loss functions. Management Science, 6, 1-12.
11. Potts, C. N. (1985). Analysis of a linear programming heuristic for scheduling unrelated parallel machines. Discrete Applied Mathematics, 10, 155-164.
12. Shachnai, H., Tamir, T., & Woeginger, G. (2002). Minimizing makespan and preemption costs on a system of uniform machines. In Proc. 10th European symposium on algorithms.
13. Shchepin, E., & Vakhania, N. (2002). Little-preemptive scheduling on unrelated processors. Journal of Mathematical Modeling and Algorithms, 1, 43-56.
14. Shchepin, E., & Vakhania, N. (2005a). An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters, 33, 127-133.
15. Shchepin, E., & Vakhania, N. (2005b). New tight NP-hardness of preemptive multiprocessor and open-shop scheduling. In Proceedings of 2nd multidisciplinary international conference on scheduling: Theory and applications MISTA 2005 (pp. 606-629).
16. Shchepin, E., & Vakhania, N. (2006). On machine dependency in shop scheduling. In Proceedings of the 9th WSEAS international conference on applied mathematics (pp. 323-331).