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On some properties of optimal schedules in the job shop problem with preemption and an arbitrary regular criterion

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  • S. Sevastyanov
  • D. Chemisova
  • I. Chernykh

Abstract

Optimal schedules in the job shop problem with preemption and with the objective of minimizing an arbitrary regular function of operation completion times are studied. It is shown that for any instance of the problem there always exists an optimal schedule that meets several remarkable properties. Firstly, each changeover date coincides with the completion time of some operation, and so, the number of changeover dates is not greater than the total number of operations, while the total number of interruptions of the operations is no more than the number of operations minus the number of jobs. Secondly, every changeover date is “super-integral”, which means that it is equal to the total processing time of some subset of operations. And thirdly, the optimal schedule with these properties can be found by a simple greedy algorithm under properly defined priorities of operations on machines. It is also shown that for any instance of the job shop problem with preemption allowed there exists a finite set of its feasible schedules which contains at least one optimal schedule for any regular objective function (from the continuum set of regular functions). Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • S. Sevastyanov & D. Chemisova & I. Chernykh, 2014. "On some properties of optimal schedules in the job shop problem with preemption and an arbitrary regular criterion," Annals of Operations Research, Springer, vol. 213(1), pages 253-270, February.
    • Handle: RePEc:spr:annopr:v:213:y:2014:i:1:p:253-270:10.1007/s10479-012-1290-3
    DOI: 10.1007/s10479-012-1290-3
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    References listed on IDEAS

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    1. James R. Jackson, 1956. "An extension of Johnson's results on job IDT scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(3), pages 201-203, September.
    2. Sheldon B. Akers & Joyce Friedman, 1955. "A Non-Numerical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 3(4), pages 429-442, November.
    3. D. P. Williamson & L. A. Hall & J. A. Hoogeveen & C. A. J. Hurkens & J. K. Lenstra & S. V. Sevast'janov & D. B. Shmoys, 1997. "Short Shop Schedules," Operations Research, INFORMS, vol. 45(2), pages 288-294, April.
    4. Sheldon B. Akers, 1956. "Letter to the Editor---A Graphical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 4(2), pages 244-245, April.
    5. N. Hefetz & I. Adiri, 1982. "An Efficient Optimal Algorithm for the Two-Machines Unit-Time Jobshop Schedule-Length Problem," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 354-360, August.
    6. Nikhil Bansal & Tracy Kimbrel & Maxim Sviridenko, 2006. "Job Shop Scheduling with Unit Processing Times," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 381-389, May.
    7. Sergey Sevastianov, 1998. "Nonstrict vector summationin multi-operation scheduling," Annals of Operations Research, Springer, vol. 83(0), pages 179-212, October.
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