Minimizing mean squared deviation of completion times with maximum tardiness constraint

Jong Hwa Seo; Chae Bogk Kim; Dong Hoon Lee

doi:10.1016/S0377-2217(99)00425-7

Minimizing mean squared deviation of completion times with maximum tardiness constraint

Jong Hwa Seo, Chae Bogk Kim, Dong Hoon Lee

School of Cybersecurity

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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/T_max problem), where the common due date is large enough so that it does not constrain the minimization of MSD. The MSD/T_max 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/T_max problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/T_max 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/T_max problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/T_max 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	https://doi.org/10.1016/S0377-2217(99)00425-7
Publication status	Published - 2001 Feb 15

ASJC Scopus subject areas

Computer Science(all)
Modelling and Simulation
Management Science and Operations Research
Information Systems and Management

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10.1016/S0377-2217(99)00425-7

Cite this

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title = "Minimizing mean squared deviation of completion times with maximum tardiness constraint",

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.",

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AU - Kim, Chae Bogk

AU - Lee, Dong Hoon

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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.

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Minimizing mean squared deviation of completion times with maximum tardiness constraint

Abstract

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