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Optimal Stochastic Dynamic Scheduling in Multi-Class Queues with Tardiness and/or Earliness Penalties

Published online by Cambridge University Press:  27 July 2009

Dimitrios G. Pandelis  and
Demosthenis Teneketzis
Dimitrios G. Pandelis
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109–2122
Demosthenis Teneketzis
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109–2122
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Abstract

Tasks belonging to N classes arrive for processing in a multi-server facility. Each arriving task has a due date (deterministic or random) associated with the completion of its service. If the service of a task is completed at a time other than the task's due date, an earliness or tardiness penalty is incurred. We determine properties of dynamic nonidling nonpreemptive and dynamic nonidling preemptive scheduling strategies that minimize an infinite horizon expected discounted cost due to the earliness and tardiness penalties. We provide examples that illustrate the properties of the optimal strategies.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 4 , October 1994 , pp. 491 - 509
Copyright
Copyright © Cambridge University Press 1994

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References

1.Altman, E. & Shwartz, A. (1989). Optimal priority assignment: A time sharing approach. IEEE Transactions on Automatic Control 34: 1098–1102.CrossRefGoogle Scholar
2.Baccelli, F., Boyer, P., & Hebuterne, G. (1984). Single server queues with impatient customers. Advances in Applied Probability 16: 887–905.CrossRefGoogle Scholar
3.Baccelli, F. & Trivedi, K.S. (1985). A single server queue in a hard real time environment. Operations Research Letters 4: 161–168.CrossRefGoogle Scholar
4.Baker, K.R. & Scudder, G.D. (1990). Sequencing with earliness and tardiness penalties: A review. Operations Research 38: 22–36.CrossRefGoogle Scholar
5.Bhattacharya, P.P. & Ephremides, A. (1989). Optimal scheduling with strict deadlines. IEEE Transactions on Automatic Control 34: 721–728.CrossRefGoogle Scholar
6.Bhattacharya, P.P. & Ephremides, A. (1991). Optimal allocation of a server between two queues with due times. IEEE Transactions on Automatic Control 36: 1417–1423.CrossRefGoogle Scholar
7.Bhattacharya, P.P. & Ephremides, A. (1991). Stochastic monotonicity properties of multiserver queues with impatient customers. Journal of Applied Probability 28: 673–682.CrossRefGoogle Scholar
8.Du, J. & Leung, J. (1990). Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research 15: 483–495.CrossRefGoogle Scholar
9.Frostig, E. (1991). A note on stochastic scheduling on a single machine subject to breakdown — The preemptive repeat model. Probability in the Engineering and informational Sciences 5: 349–354.CrossRefGoogle Scholar
10.Hall, N.G., Kubiak, W., & Sethi, S. (1991). Earliness-tardiness scheduling problems, II: Deviation of completion times about a restrictive common due date. Operations Research 39: 847–856.CrossRefGoogle Scholar
11.Hall, N.G. & Posner, M.E. (1991). Earliness-tardiness scheduling problems, I: Weighted deviation of completion times about a common due date. Operations Research 39: 836–846.CrossRefGoogle Scholar
12.Huang, C.-C. & Weiss, G. (1992). Scheduling jobs with stochastic processing times and due dates to minimize total tardiness. Preprint.Google Scholar
13.Kaspi, H. & Perry, D. (1983). Inventory systems of perishable commodities. Advances in Applied Probability 15: 674–685.CrossRefGoogle Scholar
14.Kaspi, H. & Perry, D. (1983). Inventory systems of perishable commodities with renewal input and Poisson output. Advances in Applied Probability 16: 402–421.CrossRefGoogle Scholar
15.Kubiak, W., Lou, S., & Sethi, S. (1990). Equivalence of mean flow time problems and mean absolute deviation problems. Operations Research Letters 9: 371–374.CrossRefGoogle Scholar
16.Nain, P. & Ross, K.W. (1986). Optimal priority assignment with hard constraint. IEEE Transactions on Automatic Control 31: 883–888.CrossRefGoogle Scholar
17.Pandelis, D. (1994). Optimal stochastic scheduling and routing in queueing networks. Doctoral dissertation, University of Michigan, Ann Arbor.Google Scholar
18.Pandelis, D.G. & Teneketzis, D. (1993). Stochastic scheduling in priority queues with strict deadlines. Probability in the Engineering and Informational Sciences 7: 273–289.CrossRefGoogle Scholar
19.Panwar, S.S., Towsley, D., & Wolff, J.K. (1988). Optimal scheduling policies for a class of queues with customer deadlines to the beginning of service. Journal of Association for Computing Machinery 35: 832–844.CrossRefGoogle Scholar
20.Perry, D. & Levikson, B. (1989). Continuous production/inventory model with analogy to certain queueing and dam models. Advances in Applied Probability 21: 123–141.CrossRefGoogle Scholar
21.Pinedo, M. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31: 559–572.CrossRefGoogle Scholar
22.Potts, C.N. & Van Wassenhove, L.N. (1992). Single machine scheduling to minimize total late work. Operations Research 40: 586–595.CrossRefGoogle Scholar
23.Ross, K.W. & Chen, B. (1988). Optimal scheduling of interactive and noninteractive traffic in telecommunication sytems. IEEE Transactions on Automatic Control 33: 261–267.CrossRefGoogle Scholar
24.Szwarc, F.W. (1990). Parametric precedence relations in single machine scheduling. Operations Research Letters 9: 133–140.CrossRefGoogle Scholar
25.Towsley, D. & Baccelli, F. (1991). Comparisons of service disciplines in a tandem queueing network with real time constraints. Operations Research Letters 10: 49–55.CrossRefGoogle Scholar