Scheduling n jobs on one machine to minimize the maximum tardiness with minimum number

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Abstract

The “one machine” scheduling problem is considered with the dual objective of minimizing the maximum tardiness with minimum number of tardy jobs. A simple procedure is introduced to obtain an optimal schedule with minimum “maximum tardiness” when the set of nontardy jobs is specified. A branch and bound algorithm is presented to obtain the optimal schedule that minimizes the maximum tardiness with minimum number of tardy jobs. A condition is also given to identify an initial set of early jobs. Several theorems are formulated and proved in order to justify the elimination of much branching.

References (15)

  • E.C.P. Kao

    A multiple objective decision theoretic approach to one-machine scheduling problems

    Comput. Ops Res.

    (1980)
  • K.R. Baker et al.

    Sequencing with due-dates and early start times to minimize maximum tardiness

    Naval Res. Logistics Quart.

    (1974)
  • P. Bratley et al.

    Scheduling with earliest start and due date constraints

    Naval Res. Logistics Quart.

    (1971)
  • R.N. Burns

    Scheduling to minimize the weighted sum of completion times with secondary criteria

    Naval Res. Logistics Quart.

    (1976)
  • R.W. Conway et al.

    Theory of Scheduling

    (1967)
  • H. Emmons

    One machine sequencing to minimize mean flow time with minimum number tardy

    Naval Res. Logistics Quart.

    (1975)
  • H. Emmons

    A note on a scheduling problem with dual criteria

    Naval Res. Logistics Quart.

    (1975)
There are more references available in the full text version of this article.

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Dr. J. G. Shanthikumar is an Assistant Professor of Industrial Engineering and Operations Research at Syracuse University. He holds a B.Sc degree in Mechanical Engineering from the University of Sri Lanka, and an M.A. Sc. and Ph.D. in Industrial Engineering from the University of Toronto. He has published in the areas of production systems modelling and analysis, queueing theory, reliability, scheduling and simulation in AIIE Transactions, Australian Journal of Statistics. Engineer (Sri Lanka), European Journal of Operational Research, IEEE Transaction of Computers, INFOR, International Journal of Production Research, Journal of Applied Probability, Journal of Operations Research Society of Japan. Microelectronics and Reliability. Naval Research Logistic Quarterly, Operations Research, and Performance Evaluation.

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