Abstract
In the traditional scheduling problems, it is always assumed that any job has to be processed and the processing time is pre-given and fixed. In this paper, we address the scheduling problems with rejection or with discretely compressible processing times in which we can choose a subset of jobs to process or discretely compress the original processing times. Of course, choosing not to process any job or to process it with a compressed processing time incurs a corresponding penalty or cost. We consider the following problems for the first time: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost, scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties and scheduling with discretely compressible processing times to minimize the sum of total weighted completion time plus total compression cost. We show that they are all NP-hard and design pseudo-polynomial time algorithms through dynamic programming and FPTASs for the first two problems. For the third problem, we present a greedy heuristic. Theoretical analysis shows that it has a bounded worst case performance ratio for a special case and large numbers of simulations tell us that it works very well for the general problem.
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References
Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multiprocessor scheduling with rejection. SIAM Journal of Discrete Maths 13, 64–78 (2000)
Chen, Z., Lu, Q., Tang, G.: Single machine scheduling with discretely controllable processing times. Operations Research Letters 21, 69–76 (1997)
Chen, B., Potts, C.N., Woeginger, G.J.: A review of machine scheduling: complexity, algorithmthms and approximability. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 3, pp. 21–169. Kluwer Academic Publishers, Dordrecht (1998)
Daniels, R.L., Mazzola, J.B.: Flow shop scheduling with resource flexibility. Operations Research 42, 504–522 (1994)
Engels, D.W., Karger, D.R., Kolliopoulos, S.G., Sengupta, S., Uma, R.N., Wein, J.: Techniques for scheduling with rejection. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 490–501. Springer, Heidelberg (1998)
Epstein, L., Noga, J., Woeginger, G.J.: On-line scheduling of unit time jobs with rejection: minimizing the total completion time. Operations Research Letters 30, 415–420 (2002)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling. Annals of Discrete Mathematics 5, 287–326 (1979)
He, Y., Min, X.: On-line uniform machine scheduling with rejection. Computing 65, 1–12 (2000)
Hoogeveen, H., Skutella, M., Woeginger, G.J.: Preemptive Scheduling with rejection. Mathematical Programming, Serial B 94, 361–374 (2003)
Hoogeveen, H., Woeginger, G.J.: Some comments on sequencing with controllable processing times. Computing 68, 181–192 (2002)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexities of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Seiden, S.S.: Preemptive multiprocessor scheduling with rejection. Theoretical Computer Science 262(1), 437–458 (2001)
Sengupta, S.: Algorithms and approximation schemes for minimum lateness/tardiness scheduling with rejection. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 79–90. Springer, Heidelberg (2003)
Vickson, R.G.: Two single machine sequencing problems involving controllable job processing times. AIIE Transactions 12, 258–262 (1980)
Vickson, R.G.: Choosing the job sequence and processing times to minimize the total processing plus flow cost on a single machine. Operations Research 28, 1155–1167 (1980)
Wan, G., Yen, B.P.-C., Li, C.-L.: Single machine scheduling to minimize total compression plus weighted flow cost is NP-hard. Information Processing Letters 79(6), 273–280 (2001)
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Cao, Z., Wang, Z., Zhang, Y., Liu, S. (2006). On Several Scheduling Problems with Rejection or Discretely Compressible Processing Times. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_8
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DOI: https://doi.org/10.1007/11750321_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
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