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Ordering the structural set of jobs, minimizing the total penalty

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Abstract

The problem of setting up a schedule minimizing the total penalty is solved. A job set

is specified. There are no precedence conditions. Each job

consists of

elementary operations. Job interruptions are allowed. Interruptions of elementary operations are not allowed. The penalty for an operation of a job

to be executed at instantt is

. A schedule is evaluated by a penalty that is the sum of the penalties of all the elementary operations of all jobs in set

. It is assumed that set

is structural. The problem is to find the schedule with a start in a prescribed interval [ T1,T2] with the least penalty. Compatible structural schedules are introduced into consideration. The class of compatible structural schedules contains the solution of the problem. An algorithm solving the problem is proposed having complexity

, in the worst case, whereK is the number of jobs in the set

.

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Literature cited

  1. A. H. G. Rinnooy Kan, Machine Scheduling Problems: Classification, Complexity and Computations, Martinus Nijhoff, The Hague (1976).

    Google Scholar 

  2. K. V. Shakhbazyan and N. B. Lebedinskaya, “On optimal schedules with interruptions for independent jobs in a service system with N servers,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,70, 205–231 (1977).

    Google Scholar 

  3. J. B. Sidney, “Optimal single-machine scheduling with earliness and tardiness penalties,” Oper. Res.,25, No. 1, 62–69 (1977).

    Google Scholar 

  4. N. B. Lebedinskaya, “Minimization of maximum deviation in case of job interruption,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 117–124 (1978).

    Google Scholar 

  5. K. V. Shakhbazyan, “On structural solutions in scheduling theory problems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 239–248 (1978).

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Authors
  1. K. V. Shakhbazyan
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 229–264, 1979.

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Shakhbazyan, K.V. Ordering the structural set of jobs, minimizing the total penalty. J Math Sci 20, 2069–2096 (1982). https://doi.org/10.1007/BF01680572

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  • DOI: https://doi.org/10.1007/BF01680572

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