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NP-Hard Scheduling Problems in Planning Process Automation in Discrete Systems of Certain Classes

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Advances in Computer Science for Engineering and Education (ICCSEEA 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 754))

Abstract

In this paper, we consider an intractable problem of total tardiness of tasks minimization on single machine. The problem has a broad applications solutions during planning process automation in systems in various spheres of human activity. We investigate the solutions obtained by the exact algorithm for this problem earlier developed by M.Z. Zgurovsky and A.A. Pavlov. We propose an efficient approximation algorithm with \( O\left( {n^{2} } \right) \) complexity with estimate of the maximum possible deviation from optimum. We calculate the estimate separately for each problem instance. Based on this estimate, we construct an efficient estimate of the deviation from the optimum for solutions obtained by any heuristic algorithms. Our statistical studies have revealed the conditions under which our approximation algorithm statistically significantly yields a solution within 1–2% deviation from the optimum, presumably for any problem size. This makes possible obtaining efficient approximate solutions for real practical size problems that cannot be solved with known exact methods.

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References

  1. Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-26580-3

  2. Zgurovsky, M.Z., Pavlov, A.A.: Prinyatie resheniy v setevyh sistemah s ogranichennymi resursami: Monograph. Naukova dumka, Kiev (2010). (in Russian)

    Google Scholar 

  3. Alhumrani, S.A., Qureshi, R.J.: Novel approach to solve resource constrained project scheduling problem (RCPSP). Int. J. Mod. Educ. Comput. Sci. (IJMECS) 8(9), 60–68 (2016). https://doi.org/10.5815/ijmecs.2016.09.08

    Article  Google Scholar 

  4. Vollmann, T.E., Berry, W.L., Whybark, D.C.: Manufacturing Planning and Control Systems. McGraw-Hill, Boston (2005)

    Google Scholar 

  5. Popinako, D.: ERP-rynok glazami veterana. SK-Press, Kiev, PC Week-Ukr (2011). (in Russian)

    Google Scholar 

  6. Zagidullin, R.R.: Upravlenie mashinostroitelnym proizvodstvom s pomoschyu sistem MES, APS, ERP. TNT, Staryi Oskol (2011). (in Russian)

    Google Scholar 

  7. Zagidullin, R.R.: Planirovanie mashinostroitelnogo proizvodstva. TNT, Staryi Oskol (2017). (in Russian)

    Google Scholar 

  8. Swayamsiddha, S., Parija, S., Sahu, P.K., Singh, S.S.: Optimal reporting cell planning with binary differential evolution algorithm for location management problem. Int. J. Intell. Syst. Appl. (IJISA) 9(4), 23–31 (2017). https://doi.org/10.5815/ijisa.2017.04.03

    Article  Google Scholar 

  9. Soudi, S.: Distribution system planning with distributed generations considering benefits and costs. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 5(9), 45–52 (2013). https://doi.org/10.5815/ijmecs.2013.09.07

    Article  Google Scholar 

  10. Garg, R., Singh, A.K.: Enhancing the discrete particle swarm optimization based workflow grid scheduling using hierarchical structure. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 5(6), 18–26 (2013). https://doi.org/10.5815/ijcnis.2013.06.03

    Article  Google Scholar 

  11. Soltani, N., Soleimani, B., Barekatain, B.: Heuristic algorithms for task scheduling in cloud computing: a survey. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 9(8), 16–22 (2017). https://doi.org/10.5815/ijcnis.2017.08.03

    Article  Google Scholar 

  12. Szwarc, W., Grosso, A., Della Croce, F.: Algorithmic paradoxes of the single machine total tardiness problem. J. Sched. 4(2), 93–104 (2001). https://doi.org/10.1002/jos.69

    Article  MathSciNet  MATH  Google Scholar 

  13. Tansel, B.C., Kara, B.Y., Sabuncuoglu, I.: An efficient algorithm for the single machine total tardiness problem. IIE Trans. 33(8), 661–674 (2001). https://doi.org/10.1080/07408170108936862

    Article  Google Scholar 

  14. Garraffa, M., Shang, L., Della Croce, F., T’Kindt, V.: An exact exponential branch-and-merge algorithm for the single machine total tardiness problem (2017). Preprint, HAL. https://hal.archives-ouvertes.fr/hal-01477835

  15. Koulamas, C.: The single-machine total tardiness scheduling problem: review and extensions. Eur. J. Oper. Res. 202, 1–7 (2010). https://doi.org/10.1016/j.ejor.2009.04.007

    Article  MathSciNet  MATH  Google Scholar 

  16. Chang, S., Matsuo, H., Tang, G.: Worst-case analysis of local search heuristics for the one-machine total tardiness problem. Nav. Res. Logist. 37(1), 111–121 (1990). https://doi.org/10.1002/1520-6750(199002)37:1<111::AID-NAV3220370107>3.0.CO;2-V

    Article  MathSciNet  Google Scholar 

  17. Fisher, M.L.: A dual algorithm for the one machine scheduling problem. Math. Progr. 11(1), 229–251 (1976). https://doi.org/10.1007/BF01580393

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Prospekt Peremohy, Kyiv, 03056, Ukraine

    Alexander Anatolievich Pavlov, Elena Borisovna Misura, Oleg Valentinovich Melnikov & Iryna Pavlovna Mukha

Authors
  1. Alexander Anatolievich Pavlov
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  2. Elena Borisovna Misura
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  3. Oleg Valentinovich Melnikov
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  4. Iryna Pavlovna Mukha
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Corresponding author

Correspondence to Alexander Anatolievich Pavlov .

Editor information

Editors and Affiliations

  1. School of Educational Information Technology, Central China Normal University, Wuhan, Hubei, China

    Zhengbing Hu

  2. Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, Russia

    Sergey Petoukhov

  3. Faculty of Applied Mathematics, National Technical University of Ukraine “Igor Sikorsky Kiev Polytechnic Institute”, Kiev, Ukraine

    Ivan Dychka

  4. Halmos College of Natural Sciences and Oceanography, Nova Southeastern University, Ft. Lauderdale, Florida, USA

    Matthew He

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Pavlov, A.A., Misura, E.B., Melnikov, O.V., Mukha, I.P. (2019). NP-Hard Scheduling Problems in Planning Process Automation in Discrete Systems of Certain Classes. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education. ICCSEEA 2018. Advances in Intelligent Systems and Computing, vol 754. Springer, Cham. https://doi.org/10.1007/978-3-319-91008-6_43

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