Abstract
This paper studies a single machine scheduling problem to minimize the weighted number of early and tardy jobs with a common due window. There are n non-preemptive and simultaneously available jobs. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The window size is a given parameter but the window location is a decision variable. The objective of the problem is to find a schedule that minimizes the weighted number of early and tardy jobs and the location penalty. We show that the problem is NP-complete in the ordinary sense and develop a dynamic programming based pseudo-polynomial algorithm. We conduct computational experiments, the results of which show that the performance of the dynamic algorithm is very good in terms of memory requirement and CPU time. We also provide polynomial time algorithms for two special cases.
Similar content being viewed by others
References
F.D. Anger, C.Y. Lee and L.A. Martin-Vega, Single machine scheduling with tight windows, Research Report No. 86-16, Industrial and Systems Engineering Department, University of Florida, Florida (1986).
K.S. Baker and G.D. Scudder, Sequencing with earliness and tardiness penalties: a review, Operations Research 38 (1990) 22–36.
T.C.E. Cheng, Optimal common due-date with limited completion time deviation, Computers and Operations Research 15 (1988) 91–96.
T.C.E. Cheng and M.C. Gupta, Survey of scheduling research involving due date determination decisions, European Journal of Operational Research 38 (1989) 156–166.
F.J. Krämer and C.Y. Lee, Common due-window scheduling, Production and Operations Management Society 2 (1993) 262–275.
A. Lann and G. Mosheiov, Single machine scheduling to minimize the number of early and tardy jobs, Computers and Operations Research 23 (1996) 769–781.
C.Y. Lee, Earliness-tardiness scheduling problems with constant size of due date window, Research Report No. 91-17, Industrial and Systems Engineering Department, University of Florida, Florida (1991).
S.D. Liman, S.S. Panwalkar and S. Thongmee, Determination of common due window location in a single machine scheduling problem, European Journal of Operational Research 93 (1996) 68–74.
S.D. Liman and S. Ramaswamy, Earliness-tardiness scheduling problems with a common delivery window, Operations Research Letters 15 (1994) 195–203.
T. Sen and S.K. Gupta, A state-of-art survey of static scheduling research involving due dates, OMEGA 12 (1984) 63–76.
J.A. Ventura and M.X. Weng, Single machine scheduling with a common delivery window, Journal of the Operational Society 47 (1996) 424–434.
M.X.Weng and J.A. Ventura, A note on common due window scheduling, Production and Operations Management 5 (1996) 194–200.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yeung, W., Oğuz, C. & Cheng, T.E. Minimizing Weighted Number of Early and Tardy Jobs with a Common Due Window Involving Location Penalty. Annals of Operations Research 108, 33–54 (2001). https://doi.org/10.1023/A:1016094508744
Issue Date:
DOI: https://doi.org/10.1023/A:1016094508744