Abstract
We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected.
We give several techniques for designing scheduling algorithms under this criterion. Many of these techniques show how to reduce a problem with rejection to a (potentially more complex) scheduling problem without rejection. Some of the reductions are based on general properties of certain kinds of linear-programming relaxations of optimization problems, and therefore are applicable to problems outside of scheduling; we demonstrate this by giving an approximation algorithm for a variant of the facility-location problem.
In the last section of the paper we consider a different notion of rejection in the context of scheduling: scheduling jobs with due dates so as to maximize the number of jobs that complete by their due dates, or equivalently to minimize the number of jobs that do not complete by their due date and that thus can be considered “rejected.” We investigate the approximability of a simple version of this problem, giving approximation algorithms and characterizing integrality gaps of a class of linear-programming relaxations.
Research supported by NSF Contract MIP-9612632.
Research supported in part by ARPA contract N00014-95-1-1246 and NSF contract CCR-9624239, as well as grants from the Alfred P. Sloane and David and Lucille Packard foundations.
Research partially supported by NSF Award CCR-9308701 and NSF Career Award CCR-9624828.
Research partially supported by NSF Grant CCR-9626831.
Research partially supported by NSF Grant CCR-9626831 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Y. Bartal, S. Leonardi, A. Marchetti-Spaccamela, J. Sgall, and L. Stougie. Multiprocessor scheduling with rejection. In Proc. 7th SODA, 95–103, 1996.
C. Chekuri, R. Motwani, B. Natarajan, and C. Stein. Approximation techniques for average completion time scheduling. In Proc. 8th SODA, 609–618, 1997.
F. A. Chudak. Improved approximation algorithms for uncapacitated facility location. In Proc. 6th IPCO 1998. To appear.
M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, 1979.
M. Goemans. Improved approximation algorithms for scheduling with release dates. In Proc. 8th SODA, 591–598, 1997.
R.L. Graham, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5:287–326, 1979.
S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. In Proc. 9th SODA, 1998.
L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein. Scheduling tominimize average completion time: Off-line and on-line approximation algorithms. Mathematics of Operations Research, (3):513–544, August 1997.
E. L. Lawler. Scheduling a single machine to minimize the number of late jobs. Preprint, Computer Science Division, Univ. of California, Berkeley, 1982.
E. L. Lawler and J. M. Moore. A functional equation and its application to resource allocation and sequencing problems. In Manag. Sci., volume 16, 77–84, 1969.
E. L. Lawler and D. B. Shmoys. Weighted number of late jobs (preliminary version). To appear in: J.K. Lenstra and D.B. Shmoys (eds.) Scheduling, Wiley.
Maxwell. Personal communication. 1996.
I. M. Ovacik and R. Uzsoy. DecompositionMethods for Complex Factory Scheduling Problems. Kluwer Academic Publishers, 1997.
C. Phillips, C. Stein, and J. Wein. Scheduling jobs that arrive over time. In Proc. of 4th WADS, LNCS, 955, 86–97, Berlin, 1995. Springer-Verlag. To appear in Mathematical Programming B.
M. H. Rothkopf. Scheduling independent tasks on parallel processors. In Manag. Sci., volume 12, 437–447, 1966.
A. S. Schulz and M. Skutella. Random-based scheduling: New approximations and LP lower bounds. In J. Rolim, editor, Randomization and Approximation Techniques in Computer Science, LNCS, 955, 119–133. Springer, Berlin, 1997.
A. S. Schulz and M. Skutella. Scheduling-LPs bear probabilities: Randomized approximations for min-sum criteria. In R. Burkard and G. Woeginger, editors, Algorithms — ESA’97, LNCS, 1284, 416–429. Springer, Berlin, 1997.
D. B. Shmoys, É. Tardos, and K. Aardal. Approximation algorithms for facility location problems. In Proc. of the 29th ACM STOC, 265–274, 1997.
W.E. Smith. Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3:59–66, 1956.
M. E. Dyer and L. A. Wolsey. Formulating the single machine sequencing problem with release dates as a mixed integer program. In Discrete Applied Mathematics, 26, 255–270, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Engels, D.W., Karger, D.R., Kolliopoulos, S.G., Sengupta, S., Uma, R.N., Wein, J. (1998). Techniques for Scheduling with Rejection. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_41
Download citation
DOI: https://doi.org/10.1007/3-540-68530-8_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64848-2
Online ISBN: 978-3-540-68530-2
eBook Packages: Springer Book Archive