Abstract
In this paper we consider generalized version of the classical preemptive open shop problem with sum of weighted job completion times objective. The main result is a (2 + ε)-approximation algorithm for this problem. In the last section we also discuss the possibility of improving our algorithm.
Research supported by a research grant from NSERC (the Natural Sciences and Research Council of Canada) to the first author.
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References
S. Chakrabarti, C. Phillips, A. Schulz, D. Shmoys, C. Stein and J. Wein, Improved Scheduling Algorithms for Minsum Criteria, In Proceedings of ICALP96, LNCS 1099, pp. 646–657.
C. Chekuri and R. Motwani, Precedence constrained scheduling to minimize sum of weighted completion times on a single machine, Discrete Appl. Math. 98(1999), 29–38.
M. X. Goemans, Improved Approximation Algorithms for Scheduling with Release Dates, In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms (1997), 591–598.
T. Gonzalez and S. Sahni, Open Shop Scheduling to Minimize Finish Time, Journal of the ACM 23 (1976) 665–679.
L. Hall, A. Schulz, D. Shmoys and Wein, Scheduling to minimize average completion time: off-line and on-line approximation algorithms, Math. Oper. Res. 22 (1997), 513–544.
H. Hoogeveen, P. Schuurman and G. Woeginger, Non-approximability results for scheduling problems with minsum criteria, In Proceedings of IPCO98, LNCS v 1412, pp. 353–366.
J. Labetoulle, E. Lawler, J. K. Lenstra and A.H. G. Rinnooy Kan, Preemptive scheduling of uniform machines subject to release dates, Progress in combinatorial optimization, pp. 245–261, Academic Press, Toronto, Ont., 1984.
E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys, “Sequencing and Scheduling: Algorithms and Complexity.” In: S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin, eds., Logistics of Production and Inventory, Handbooks in Operations Research and Management Science 4, North—Holland, Amsterdam, The Netherlands (1993) 445–522.
E. L. Lawler, M. G. Luby and V. V. Vazirani, Scheduling Open Shops with Parallel Machines, Operations Research Letters 1 (1982) 161–164.
M. Queyranne and M. Sviridenko, “Approximation Algorithms for Shop Scheduling Problems with Minsum Objective”, submitted for publication.
M. Queyranne and M. Sviridenko, New and Improved Algorithms for Minsum Shop Scheduling, Proceedings of SODA00, pp.871–878.
A.S. Schulz and M. Skutella, “Random-Based Scheduling: New Approximations and LP Lower Bounds.” In: J. Rolim, ed., Randomization and Approximation Techniques in Computer Science (Random’97 Proceedings, 1997) Lecture Notes in Computer Science 1269, Springer, 119–133.
M. Skutella, Convex quadratic and semidefinite programming relaxations in scheduling, to appear in JACM.
V. Tanaev, V. Gordon, and Y. Shafransky, Scheduling theory. Single-stage systems, Mathematics and its Applications, v. 284, Kluwer Academic Publishers Group, Dordrecht, 1994.
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Queyranne, M., Sviridenko, M. (2001). A (2+ε)-Approximation Algorithm for Generalized Preemptive Open Shop Problem with Minsum Objective. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_28
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DOI: https://doi.org/10.1007/3-540-45535-3_28
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