Abstract
We consider a nonpreemptive single-machine scheduling problem to minimize mean squared deviation of job completion times about a common due date with maximum tardiness constraint (MSD/Tmax problem), where the common due date is large enough so that it does not constrain the minimization of MSD. The MSD/Tmax problem is classified into three cases according to the value of maximum allowable tardiness Δ: Δ-unconstrained, Δ-constrained and tightly Δ-constrained cases. It is shown that the Δ-unconstrained MSD/Tmax problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date Δ. We also provide bounds to decide when the MSD/Tmax problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples.
| Original language | English |
|---|---|
| Pages (from-to) | 95-104 |
| Number of pages | 10 |
| Journal | European Journal of Operational Research |
| Volume | 129 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2001 Feb 15 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Information Systems and Management
- Management Science and Operations Research
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Modelling and Simulation
- Transportation
Cite this
Minimizing mean squared deviation of completion times with maximum tardiness constraint. / Seo, Jong Hwa; Kim, Chae Bogk; Lee, Dong Hoon.
In: European Journal of Operational Research, Vol. 129, No. 1, 15.02.2001, p. 95-104.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minimizing mean squared deviation of completion times with maximum tardiness constraint
AU - Seo, Jong Hwa
AU - Kim, Chae Bogk
AU - Lee, Dong Hoon
PY - 2001/2/15
Y1 - 2001/2/15
N2 - We consider a nonpreemptive single-machine scheduling problem to minimize mean squared deviation of job completion times about a common due date with maximum tardiness constraint (MSD/Tmax problem), where the common due date is large enough so that it does not constrain the minimization of MSD. The MSD/Tmax problem is classified into three cases according to the value of maximum allowable tardiness Δ: Δ-unconstrained, Δ-constrained and tightly Δ-constrained cases. It is shown that the Δ-unconstrained MSD/Tmax problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date Δ. We also provide bounds to decide when the MSD/Tmax problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples.
AB - We consider a nonpreemptive single-machine scheduling problem to minimize mean squared deviation of job completion times about a common due date with maximum tardiness constraint (MSD/Tmax problem), where the common due date is large enough so that it does not constrain the minimization of MSD. The MSD/Tmax problem is classified into three cases according to the value of maximum allowable tardiness Δ: Δ-unconstrained, Δ-constrained and tightly Δ-constrained cases. It is shown that the Δ-unconstrained MSD/Tmax problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date Δ. We also provide bounds to decide when the MSD/Tmax problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples.
UR - http://www.scopus.com/inward/record.url?scp=0035254259&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035254259&partnerID=8YFLogxK
U2 - 10.1016/S0377-2217(99)00425-7
DO - 10.1016/S0377-2217(99)00425-7
M3 - Article
AN - SCOPUS:0035254259
VL - 129
SP - 95
EP - 104
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -