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The Study of Group Scheduling Problems with General Dual-Position-Based Job Processing Times

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Abstract

Scheduling with group technology has been a vivid research area in the past decades. However, group technology with general dual-effect variable processing times needs to be further explored although this kind of group technology plays an important role in some actual manufacturing scenarios. Accordingly, this paper considers group scheduling problems with a kind of general group variable processing times model, where the actual processing time of each job in group is variable due to the dual effect of both the job position and the group position. The objectives of two types of considered problems are to minimize the makespan and the total completion time, respectively. Based on the decomposition analysis, the mathematical logic analysis and the computational complexity proof, it is obtained that the makespan minimization problem and the total completion time minimization problem are both polynomially solvable under the condition that the group number is constant. For three special cases of considered problems, polynomial solving algorithms with lower computational complexity are proposed.

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References

  1. Ham, I., Hitomi, K., Yoshida, T.: Group Technology: Applications to Production Management. Kluwer-Nijhoff, Boston (1985)

    Book  Google Scholar 

  2. Allahverdi, A., Gupta, J.N.D., Aldowaisan, T.: A review of scheduling research involving setup considerations. Omega 27(2), 219–239 (1999)

    Article  Google Scholar 

  3. Burbidge, J.L.: Group Technology in the Engineer Industry. Mechanical Engineering Publication, London (1979)

    Google Scholar 

  4. Cheng, T.C.E., Kovalyov, M.Y., Tuzikov, A.V.: Single machine group scheduling with ordered criteria. J. Oper. Res. Soc. 47, 315–320 (1996)

    Article  MATH  Google Scholar 

  5. Potts, C.N., Van Wassenhove, L.N.: Integrating scheduling with batching and lot-sizing: a review of algorithms and complexity. J. Oper. Res. Soc. 43, 395–406 (1992)

    Article  MATH  Google Scholar 

  6. Webster, S., Baker, K.R.: Scheduling groups of jobs on a single machine. Oper. Res. 43(4), 692–703 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Remy, J.: Resource constrained scheduling on multiple machines. Inf. Process. Lett. 91(4), 177–182 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Xu, D., Cheng, Z., Yin, Y., Li, H.: Makespan minimization for two parallel machines scheduling with a periodic availability constraint. Comput. Oper. Res. 36(6), 1809–1812 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Xu, D., Sun, K., Li, H.: Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan. Comput. Oper. Res. 35(4), 1344–1349 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Xu, D., Yin, Y., Li, H.: A note on scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan. Eur. J. Oper. Res. 197(2), 825–827 (2009)

    Article  MATH  Google Scholar 

  11. Domnguez, E., Jerez, J., Llopis, L., Morante, A.: RealNet: a neural network architecture for real-time systems scheduling. Neural Comput. Appl. 13(4), 281–287 (2004)

    Article  Google Scholar 

  12. Yin, Y.Q., Xu, J., Cheng, T.C.E., Wu, C.-C., Wang, D.-J.,: Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work. Nav. Res. Logist. 63, 172–183 (2016)

  13. Yin, Y.Q., Cheng, S.R., Cheng, T.C.E., Wang, D.J., Wu, C.C.: Just-in-time scheduling with two competing agents on unrelated parallel machines. Omega 63, 41–47 (2016a)

    Article  Google Scholar 

  14. Zhao, C.L., Tang, H.Y.: Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan. Appl. Math. Model. 34(3), 837–841 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing times. Eur. J. Oper. Res. 152, 1–13 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Biskup, D.: A state-of-the-art review on scheduling with learning effects. Eur. J. Oper. Res. 188, 315–329 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Janiak, A., Rudek, R.: Experience based approach to scheduling problems with the learning effect. IEEE Trans. Syst. Man Cybern. Part A 39, 344–357 (2009)

    Article  Google Scholar 

  18. Yin, Y., Xu, D., Sun, K., Li, H.: Some scheduling problems with general position-dependent and time-dependent learning effects. Inf. Sci. 179(14), 2416–2425 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ng, C.T., Wang, J.B., Cheng, T.C.E.: Two-machine flow shop scheduling with deteriorating jobs to minimize total completion time. Comput. Oper. Res. 37, 83–90 (2010)

    Article  MathSciNet  Google Scholar 

  20. Cheng, T.C.E., Lee, W.C.: Scheduling problems with deteriorating jobs and learning effects including proportional setup times. Comput. Ind. Eng. 58(2), 326–331 (2010)

    Article  Google Scholar 

  21. Kuo, W., Yang, D.L.: Minimizing the makespan in a single machine scheduling problem with the cyclic process of an aging effect. J. Oper. Res. Soc. 59, 416–420 (2008)

    Article  MATH  Google Scholar 

  22. Mosheiov, G., Sidney, J.: Scheduling with general job-dependent learning curves. Eur. J. Oper. Res. 147(3), 665–670 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mosheiov, G.: Proportionate flowshops with general position-dependent processing times. Inf. Process. Lett. 111(4), 174–177 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yu, X., Zhang, Y., Kai, H.: Minimizing the makespan for scheduling problems with general deterioration effects. Math. Probl. Eng. ID 218981, 1–8 (2013)

    MATH  Google Scholar 

  25. Yin, Y.Q., Wang, Y., Cheng, T.C.E., Liu, W.Q., Li, J.H.: Parallel-machine scheduling of deteriorating jobs with potential machine disruptions. Omega (2016). doi:10.1016/j.omega.2016.07.006

  26. Kuo, W.H., Yang, D.L.: Single-machine group scheduling with a time-dependent learning effect. Comput. Oper. Res. 33(8), 2099–2112 (2006)

    Article  MATH  Google Scholar 

  27. Wu, C.C., Lee, W.C.: Single-machine group-scheduling problems with deteriorating setup times and job-processing times. Int. J. Prod. Econ. 115(1), 128–133 (2008)

    Article  Google Scholar 

  28. Wu, C.C., Shiau, Y.R., Lee, W.C.: Single-machine group scheduling problems with deterioration consideration. Comput. Oper. Res. 35(5), 1652–1659 (2008)

    Article  MATH  Google Scholar 

  29. Wang, J.B., Lin, L., Shan, F.: Single machine group scheduling problems with deteriorating jobs. Int. J. Adv. Manuf. Technol. 39(7–8), 808–812 (2008)

    Article  Google Scholar 

  30. Huang, X., Wang, M.Z., Wang, J.B.: Single-machine group scheduling with both learning effects and deteriorating jobs. Comput. Ind. Eng. 60(4), 750–754 (2011)

    Article  Google Scholar 

  31. Yu, X.Y., Zhang, Y.L., Zhang, Y.H.: Group Scheduling with general position-dependent effect. J. Southeast Univ. 28(3), 355–359 (2012)

    MathSciNet  MATH  Google Scholar 

  32. Yin, Y.Q., Wu, W.H., Cheng, T.C.E., Wu, C.C.: Single-machine scheduling with time-dependent and position-dependent deteriorating jobs. Int. J. Comput. Integr. Manuf. 28(7), 781–790 (2015)

    Article  Google Scholar 

  33. Lee, W.C., Lu, Z.S.: Group scheduling with deteriorating jobs to minimize the total weighted number of late jobs. Appl. Math. Comput. 218(17), 8750–8757 (2012)

    MathSciNet  MATH  Google Scholar 

  34. Lee, W.C., Wu, C.C.: A note on single-machine group scheduling problems with position-based learning effect. Appl. Math. Model. 33(4), 2159–2163 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Yang, S.J., Yang, D.L.: Note on “A note on single-machine group scheduling problems with position-based learning effect”. Appl. Math. Model. 34(12), 4306–4308 (2010)

  36. Zhang, X.G., Yan, G.L.: Single-machine group scheduling problems with deteriorated and learning effect. Appl. Math. Comput. 216(4), 1259–1266 (2010)

    MathSciNet  MATH  Google Scholar 

  37. Qin, H., Zhang, Z., Bai, D.: Permutation flowshop group scheduling with position-based learning effect. Comput. Ind. Eng. 92, 1–15 (2016)

    Article  Google Scholar 

  38. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  39. Kuhn, Harold W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2(1–2), 83–97 (1955)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to express our warmest thanks to the referees for their interest in our work and their valuable comments for improving the paper.

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Xian-Yu Yu & De-Qun Zhou

  2. School of Economics and Management, Southeast University, Nanjing, 210096, China

    Yu-Lin Zhang

Authors
  1. Xian-Yu Yu
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  2. De-Qun Zhou
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  3. Yu-Lin Zhang
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Corresponding author

Correspondence to Xian-Yu Yu.

Additional information

This paper was supported by the National Natural Science Foundation of China (No. 71573121), China Postdoctoral Science Foundation Funded Project (No. 2016M590453) and the Fundamental Research Funds for the Central Universities (Nos. NS2016080 and NR2016005).

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Yu, XY., Zhou, DQ. & Zhang, YL. The Study of Group Scheduling Problems with General Dual-Position-Based Job Processing Times. J. Oper. Res. Soc. China 5, 509–527 (2017). https://doi.org/10.1007/s40305-017-0159-1

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  • DOI: https://doi.org/10.1007/s40305-017-0159-1

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