Minimizing mean squared deviation of completion times with maximum tardiness constraint |
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| Institution: | 1. Key Laboratory of Zoonosis Research, Ministry of Education, Institute of Zoonosis, College of Veterinary Medicine, Jilin University, Changchun, China;2. Mucosal Immunology Laboratory, Pediatric Gastroenterology Unit, Massachusetts General Hospital, United States of America;3. The First Affiliated Hospital of Xinjiang Medical University, Xinjiang, China;4. Xinjiang Veterinary Research Institute, Xinjiang Academy of Animal Sciences, Xinjiang, China;5. Lanzhou Veterinary Research Institute, Chinese Academy of Agricultural Sciences, Lanzhou 730046, China;6. Shanghai Veterinary Research Institute, Chinese Academy of Agricultural Sciences, Shanghai, China |
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| 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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