Construction of two-stage schedules of processing of products on one machine

Authors

  • Yuriy A. Zack

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.4.02

Keywords:

two-stage schedules on one machine, execution times, post-processing tasks and machine readjustments, initial and final times for performing tasks, optimal sequences

Abstract

Various statements, mathematical models and properties of problems of constructing two-stage schedules for performing work on one machine are considered. As criteria of optimality, the execution of schedules in the shortest time and minimization of total losses associated with the completion time of tasks are accepted. Effective approximate methods for solving problems that are illustrated by numerical examples are proposed.

Author Biography

Yuriy A. Zack

Yuriy Zack,

Dokt.-Ing., the scientific expert and consultant, Aachen, Germany.

References

Konvej R.V. Teorija raspisanij / R.V. Konvej, V.L. Maksvell, L.V. Miller. — M.: Fizmatgiz, Nauka, 1975. — 359 s.

Tanaev V.S. Vvedenie v teoriju raspisanij / V.S. Tanaev, V.V. Shkurba. — M.: Fizmatgiz, Nauka, 1975. — 256 s.

Tanaev B.C. Teorija raspisanij. Odnostadijnye sistemy / B.C. Tanaev, B.C. Gordon, Ja.M. Shafranskij. — M.: Fizmatgiz, Nauka, 1984. — 382 s.

Lazarev A.A. Teorija raspisanij. Minimizatsija summarnogo zapazdyvanija dlja odnogo pribora / A.A. Lazarev, E.R. Grafov. — M.: RAN Vychislit. tsentr im. A.A. Dorodnitsyna, 2004. — 150 s.

Hobotov E.N. O nekotoryh modeljah i metodah reshenija zadach planirovanija v diskretnyh proizvodstvah / E.N. Hobotov // Avtomatika i telemehanika, 2007. — № 12. — S. 85–100.

Zak Ju.A. Prikladnye zadachi teorii raspisanij i marshrutizatsii perevozok / Ju.A. Zak. — M.: URSS, 2012. — 394 s.

Zak Ju.A. Svojstva dopustimyh i optimal'nyh posledovatel'nostej vypolnenija rabot na odnoj mashine / Ju.A. Zak // Problemy upravlenija. — 2012. — № 5. — S. 54–61.

Zak Ju.A. Postroenie dopustimyh i optimal'nyh raspisanij vypolnenija rabot na odnoj mashine / Ju.A. Zak // Kibernetika i sistemnyj analiz. — K., 2012. — № 1. — S. 62–82.

Domschke W. Produktionsplanung. Ablauforganisatorische Aspekte / W. Domschke, A. Scholl, S. Voß. — Berlin: Heidelberg: Springer Verlag, 2005. — 456 p.

Carlier J. The one-machine sequencing problem / J. Carlier // European Journal of Operational Research. — 1982. — N 11. — P. 42–47.

Brucker P. Scheduling Algorithms / P. Brucker // Springer-Verlag. — Berlin, Heidelberg und New York, 1998. — 377 p.

Lawler E.L. Sequencing and Scheduling: Algorithms and complexity / E.L. Lawler, J.K. Lenstra, Kann Rinnooy et al. // Logistic of Production and Inventory, S.C. Graves et.al (Hrsg). — 1993. — Amsterdam–London. — P. 445–522.

Blazewicz J. Scheduling under resource constraints: deterministic models / J. Blazewicz, W. Cellary, R. Slowinski // Annals of Operations Research. —1986. — N 7. — Baltzer, Basel. — P. 329–341.

Zgurovskij M.Z. Prinjatie reshenij v setevyh sistemah s ogranichennymi resursami: monogr. / M.Z. Zgurovskij, A.A. Pavlov. — K.: Nauk. dumka, 2010. — 573 s.

Pavlov A.A. Novyj podhod k resheniju zadachi “Minimizatsija summarnogo vzveshennogo opozdanija pri vypolnenii nezavisimyh zadanij s direktivnymi srokami odnim priborom” / A.A. Pavlov, E.B. Misjura // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — K., 2002. — № 2. — S. 7–23.

Published

2018-12-18

Issue

Section

Progressive information technologies, high-efficiency computer systems