Abstract
For a class of structural sets of penalty functionsΨ={ψi} ni=1 with lower quasiconvex functionsψ i defined for sets of jobsζ={ζi} ni=1 , one gives an algorithm for solving the problem n /1/ preemp ¦ maxψ, having order 0(np), where n is the number of jobs ζi and p is the total length of the completion of all jobs of the setζ.
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Literature cited
K. V. Shakhbazyan, “The ordering of the structural set of jobs, minimizing the total penalty,” Zap, Nauchn. Sem. Leningr. Otd. Mat. Inst.,90, 229–264 (1979).
K. V. Shakhbazyan, “Structural solutions in problems of scheduling theory,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 239–248 (1978).
K. V. Shakhbazyan and N. B. Lebedinskaya, “On optimal schedulings with gaps for independent jobs in a service system with N servers,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,70, 205–231 (1977).
N. B. Lebedinskaya, “The minimization of the maximum penalty in the case of preemption of jobs,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 117–124 (1978).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 102, pp. 61–67, 1980.
In conclusion, the author expresses her gratitude to K. V. Shakhbazyan for his interest in this paper.
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Lebedinskaya, N.B. Minimization of the maximal penalty in the case of preemption of jobs. J Math Sci 22, 1203–1207 (1983). https://doi.org/10.1007/BF01460272
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DOI: https://doi.org/10.1007/BF01460272