A. A. Lazarev, R. R. Sadykov, S. V. Sevast'yanov, “A scheme of approximation solution of problem $1|R_j|L_{\max}$”, Diskretn. Anal. Issled. Oper., Ser. 2, 13:1 (2006), 57–76; J. Appl. Industr. Math., 1:4 (2007), 468

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Diskretnyi Analiz i Issledovanie Operatsii, Ser. 2, 2006, Volume 13, Issue 1, Pages 57–76 (Mi da18)

This article is cited in 6 scientific papers (total in 6 papers)

A scheme of approximation solution of problem

$1|R_j|L_{\max}$

A. A. Lazarev^a, R. R. Sadykov^a, S. V. Sevast'yanov^b

^a Kazan State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Full-text PDF (300 kB) Citations (6)

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Abstract: The strongly NP-hard scheduling problem of minimizing the maximum lateness on one machine subject to job release dates is under study. We present a general scheme of approximation solution of the problem which is based on searching for a given problem instance another instance, closest to the original in some metric and belonging to a known polynomially solvable class of instances. For a few concrete variants of the scheme (using different polynomially solvable classes of instances) some analytic formulas are found that make it possible, given a problem instance, to compute easily an upper bound on the absolute error of the solution obtained by a chosen scheme.

English version:
Journal of Applied and Industrial Mathematics, 2007, Volume 1, Issue 4, Pages 468–480
DOI: https://doi.org/10.1134/S1990478907040102

Bibliographic databases:

Language: Russian

Citation: A. A. Lazarev, R. R. Sadykov, S. V. Sevast'yanov, “A scheme of approximation solution of problem

$1|R_j|L_{\max}$ ”, Diskretn. Anal. Issled. Oper., Ser. 2, 13:1 (2006), 57–76; J. Appl. Industr. Math., 1:4 (2007), 468–480

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/da18

https://www.mathnet.ru/eng/da/v13/s2/i1/p57

This publication is cited in the following 6 articles:

N. S. Grigoreva, “Algoritm sostavleniya raspisaniya dlya odnogo protsessora s garantirovannoi otsenkoi tochnosti $3/2$ ”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 17:3 (2021), 240–253
Lazarev A.A., Lemtyuzhnikova D.V., Werner F., “A Metric Approach For Scheduling Problems With Minimizing the Maximum Penalty”, Appl. Math. Model., 89:2 (2021), 1163–1176
A. A. Lazarev, D. V. Lemtyuzhnikova, N. A. Pravdivets, “Metric approach for finding approximate solutions of scheduling problems”, Comput. Math. Math. Phys., 61:7 (2021), 1169–1180
A. A. Lazarev, P. Korenev, A. Sologub, “Metric for minimum total delay problem”, Autom. Remote Control, 78:4 (2017), 732–740
A. A. Lazarev, “Estimates of the absolute error and a scheme for an approximate solution to scheduling problems”, Comput. Math. Math. Phys., 49:2 (2009), 373–386
Lazarev A.A., “Estimation of absolute error in scheduling problems of minimizing the maximum lateness”, Doklady Mathematics, 76:1 (2007), 572–574

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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