Abstract
In this paper we consider the NP-hard 1|r j |ΣT j scheduling problem, suggesting a polynomial algorithm to find its approximate solution with the guaranteed absolute error. The algorithm employs a metric introduced in the parameter space. In addition, we study the possible application of such an approach to other scheduling problems.
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Lazarev, A.A. and Kvaratskheliya, A.G., Metrics in Scheduling Problems, Dokl. Math., 2010, vol. 81, no. 3, pp. 497–499.
Lazarev, A.A. and Gafarov, E.R., Teoriya raspisanii. Minimizatsiya summarnogo zapazdyvaniya dlya odnogo pribora (Scheduling Theory. Total Tardiness Minimization for a Single Machine), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2006.
Lazarev, A.A., Sadykov, R.R., and Sevastyanov, S.V., A Scheme of Approximation Solution of Problem 1|r j|Lmax, J. Appl. Industr. Math., 2007, vol. 1, no. 4, pp. 468–480.
Baptiste, P., Scheduling Equal-Length Jobs on Identical Parallel Machines, Discret. Appl. Math., 2000, no. 103, pp. 21–32.
Du, J. and Leung, J.Y.-T., Minimizing Total Tardiness on One Machine Is NP-Hard, Math. Oper. Res., 1990, no. 15(3), pp. 483–495.
Graham, R.L., Lawler, E.L., Lenstra, J.K., et al., Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey, Ann. Discret. Math., 1979, no. 5, pp. 287–326.
Lawler, E.L., A Pseudopolynomial Algorithm for Sequencing Jobs to Minimize Total Tardiness, Ann. Discret. Math., 1977, no. 1, pp. 331–342.
Lawler, E.L., A Fully Polynomial Approximation Scheme for the Total Tardiness Problem, Oper. Res. Lett., 1982, no. 1, pp. 207–208.
Lazarev, A.A. and Werner, F., Algorithms for Special Cases of the Single Machine Total Tardiness Problem and an Application to the Even-Odd Partition Problem, Math. Comp. Model., 2009, no. 49, pp. 2078–2089.
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Original Russian Text © A.A. Lazarev, P.S. Korenev, A.A. Sologub, 2015, published in Upravlenie Bol’shimi Sistemami, 2015, No. 57, pp. 123–137.
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Lazarev, A.A., Korenev, P.S. & Sologub, A.A. A metric for total tardiness minimization. Autom Remote Control 78, 732–740 (2017). https://doi.org/10.1134/S0005117917040142
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DOI: https://doi.org/10.1134/S0005117917040142