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Stochastic Sequencing on One Machine with Earliness and Tardiness Penalties

Published online by Cambridge University Press:  27 July 2009

Frank G. Forst
Frank G. Forst
Affiliation:
School of Business AdministrationLoyola University of Chicago820 N. Michigan Avenue, Chicago, Illinois 60611
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Abstract

In this paper the objective is to find a job sequence that minimizes, stochastically or in expectation, the sum of the total weighted job earliness and the total weighted job tardiness on one machine, when the job processing times are independent and identically distributed random variables. We first derive results for the case in which the jobs share a common, random due date. We then obtain results when the job due dates are distinct, independent random variables.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 291 - 300
Copyright
Copyright © Cambridge University Press 1993

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References

1.Abdul-Razaq, T. & Potts, C. (1988). Dynamic programming state-space relaxation for single-machine scheduling. Journal of the Operational Research Society 39: 141–152.CrossRefGoogle Scholar
2.Bagchi, U., Chang, Y., & Sullivan, R. (1987). Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date. Naval Research Logistics 34: 739–751.3.0.CO;2-3>CrossRefGoogle Scholar
3.Bagchi, U., Sullivan, R., & Chang, Y. (1986). Minimizing mean absolute deviation of completion times about a common due date. Naval Research Logistics 33: 227–240.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.Chang, C.-S. & Yao, D.D. (1990). Rearrangement, majorization, and stochastic scheduling. IBM RC-16250.Google Scholar
6.Eilon, S. & Chowdhury, E. (1977). Minimizing waiting time variance in the single machine problem. Management Science 23: 567–575.CrossRefGoogle Scholar
7.Emmons, H. (1987). Scheduling to a common due date on parallel common processors. Naval Research Logistics 34: 803–810.3.0.CO;2-2>CrossRefGoogle Scholar
8.Carey, M., Tarjan, R., & Wilfong, G. (1988). One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research 13: 330–348.Google Scholar
9.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
10.Hoogeveen, J.A. & van de Velde, S.L. (1991). Scheduling around a small common due date. European Journal of Operational Research 55: 237–242.CrossRefGoogle Scholar
11.Kanet, J. (1981). Minimizing the average deviation of job completion times about a common due date. Naval Research Logistics 28: 643–651.CrossRefGoogle Scholar
12.Panwalkar, S., Smith, M., & Seidmann, A. (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research 30: 391–399.CrossRefGoogle Scholar
13.Pinedo, M. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31:559–572.CrossRefGoogle Scholar
14.Seidmann, A., Panwalkar, S., & Smith, M. (1981). Optimal assignment of due-dates for a single processor scheduling problem. International Journal of Production Research 19: 393–399.CrossRefGoogle Scholar
15.Sundararaghavan, P. & Ahmed, M. (1984). Minimizing the sum of absolute lateness in single machine and multimachine scheduling. Naval Research Logistics 31: 325–333.CrossRefGoogle Scholar
16.Szwarc, W. (1989). Single machine scheduling to minimize absolute deviation of completion times from a common due date. Naval Research Logistics 36: 663–673.3.0.CO;2-X>CrossRefGoogle Scholar