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Heuristics for Online Scheduling on Identical Parallel Machines with Two GoS Levels

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Abstract

This paper considers the online scheduling problem on m (m ≥ 3) parallel machines (the first k machines with grade 1 and the remaining m − k machines with grade 2) with two GoS levels and makespan as the objective function. The jobs arrive over time with grade 1 or 2 and an arrival job can be assigned to a machine only when the grade of the job is no less than the grade of the machine. Three cases are considered: (i) For k = 1, the authors present an online algorithm with competitive ratio of 9/5. (ii) For 1 < k < m − 1, an online algorithm with competitive ratio of 2.280 is proposed. (iii) For k = m − 1, an online algorithm is presented with competitive ratio of 2. All the three algorithms are based on greedy algorithm with a similar structure. At last, numerical instances are given and the average competitive ratios of the instances show good performance of the proposed algorithms.

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References

  1. Mokotoff E, Parallel machine scheduling problems: A survey, Asia-Pacific Journal of Operational Research, 2001, 18(2): 193–242.

    MathSciNet  MATH  Google Scholar 

  2. Franca P M, Gendreau M, Laporte G, et al., A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective, Computers & operations research, 1994, 21(2): 205–210.

    Article  MATH  Google Scholar 

  3. Cheng R and Gen M, Parallel machine scheduling problems using memetic algorithms, Computers & Industrial Engineering, 1997, 33(3-4): 761–764.

    Article  Google Scholar 

  4. Chen Z L and Powell W B, Solving parallel machine scheduling problems by column generation, INFORMS Journal on Computing, 1999, 11(1): 78–94.

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang P C, Chen S H, and Lin K L, Two-phase sub population genetic algorithm for parallel machine-scheduling problem, Expert Systems with Applications, 2005, 29(3): 705–712.

    Article  Google Scholar 

  6. Grisselle C and Armacost R L, Parallel machine scheduling with release time and machine eligibility restrictions, Computers & Industrial Engineering, 1997, 33(1-2): 273–276.

    Article  Google Scholar 

  7. Liao L W and Sheen G J, Parallel machine scheduling with machine availability and eligibility constraints, European Journal of Operational Research, 2008, 184(2): 458–467.

    Article  MathSciNet  MATH  Google Scholar 

  8. Edis E B and Ozkarahan I, A combined integer/constraint programming approach to a resource-constrained parallel machine scheduling problem with machine eligibility restrictions, Engineering Optimization, 2011, 43(2): 135–157.

    Article  MathSciNet  Google Scholar 

  9. Tseng C T, Lee C H, Chiu Y S P, et al., A discrete electromagnetism-like mechanism for parallel machine scheduling under a grade of service provision, International Journal of Production Research, 2017, 55(11): 3149–3163.

    Article  Google Scholar 

  10. Jongho P, Chang S Y, and Lee K, Online and semi-online scheduling of two machines under a grade of service provision, Operations Research Letters, 2006, 34(6): 692–696.

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang Y W, He Y, and Tang C M, Optimal online algorithms for scheduling on two identical machines under a grade of service, Journal of Zhejiang University-Science, 2006, A7(3): 309–314.

    Article  MATH  Google Scholar 

  12. Yong W, Ji M, and Yang Q F, Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision, International Journal of Production Economics, 2012, 135(1): 367–371.

    Article  Google Scholar 

  13. Zhang A, Jiang Y W, and Tan Z Y, Online parallel machines scheduling with two hierarchies, Theoretical Computer Science, 2009, 410(38-40): 3597–3605.

    Article  MathSciNet  MATH  Google Scholar 

  14. Tan Z Y and Zhang A, A note on hierarchical scheduling on two uniform machines, Journal of Combinatorial Optimization, 2010, 20(1): 85–95.

    Article  MathSciNet  MATH  Google Scholar 

  15. Jiang Y W, Online scheduling on parallel machines with two GoS levels, Journal of Combinatorial Optimization, 2008, 16(1): 28–38.

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu M, Xu Y, Chu C, et al., Online scheduling on two uniform machines to minimize the makespan, Theoretical Computer Science, 2009, 410(21-23): 2099–2109.

    Article  MathSciNet  MATH  Google Scholar 

  17. Marvin M and Shabtay Dvir, Scheduling unit length jobs on parallel machines with lookahead information, Journal of Scheduling, 2011, 14(4): 335–350.

    Article  MathSciNet  MATH  Google Scholar 

  18. Hong K S and Leung J Y T, On-line scheduling of real-time tasks, IEEE Transactions on Computers, 1992, 41(10): 1326–1331.

    Article  Google Scholar 

  19. Chen B and Vestjens A, Scheduling on identical machines: How good is LPT in an online setting, Operations Research Letters, 1997, 21(4): 165–169.

    Article  MathSciNet  MATH  Google Scholar 

  20. John N and Seiden S S, An optimal online algorithm for scheduling two machines with release times, Theoretical Computer Science, 2001, 268(1): 133–143.

    Article  MathSciNet  MATH  Google Scholar 

  21. Grissele C and Armacost R L, Minimizing makespan on parallel machines with release time and machine eligibility restrictions, International Journal of Production Research, 2004, 42(6): 1243–1256.

    Article  MATH  Google Scholar 

  22. Lee K, Joseph Y T L, and Pinedo M L, Scheduling jobs with equal processing times subject to machine eligibility constraints, Journal of Scheduling, 2011, 14(1): 27–38.

    Article  MathSciNet  MATH  Google Scholar 

  23. Xu J and Liu Z H, An optimal online algorithm for scheduling on two parallel machines with GoS eligibility constraints, Journal of the Operations Research Society of China, 2016, 4(3): 371–377.

    Article  MathSciNet  MATH  Google Scholar 

  24. Li S S and Zhang Y Z, On-line scheduling on parallel machines to minimize the makespan, Journal of Systems Science and Complexity, 2016, 29(2): 472–477.

    Article  MathSciNet  MATH  Google Scholar 

  25. Cai S, Liu A, and Liu K, Online scheduling of two identical machines under a grade of service provision, Control Conference (CCC), 2017 36th Chinese IEEE, 2017.

  26. Shmoys D B, Joel W, and David P W, Scheduling parallel machines on-line, SIAM Journal on Computing, 1995, 24(6): 1313–1331.

    Article  MathSciNet  MATH  Google Scholar 

  27. Ou J, Joseph Y T L, and Chung L L, Scheduling parallel machines with inclusive processing set restrictions, Naval Research Logistics, 2008, 55(4): 328–338.

    Article  MathSciNet  MATH  Google Scholar 

  28. Huo Y and Joseph Y T L, Fast approximation algorithms for job scheduling with processing set restrictions, Theoretical Computer Science, 2010, 411(44-46): 3947–3955.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Logistics R&D Department, Beijing Jingdong Zhenshi Information Technology Co., Ltd., Beijing, 100176, China

    Shuang Cai

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shuang Cai & Ke Liu

  3. University of Chinese Academy of Sciences, Beijing, 100190, China

    Shuang Cai & Ke Liu

Authors
  1. Shuang Cai
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  2. Ke Liu
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Correspondence to Shuang Cai.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71390334 and 11271356.

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Cai, S., Liu, K. Heuristics for Online Scheduling on Identical Parallel Machines with Two GoS Levels. J Syst Sci Complex 32, 1180–1193 (2019). https://doi.org/10.1007/s11424-019-7427-6

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  • DOI: https://doi.org/10.1007/s11424-019-7427-6

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