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Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines

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Abstract

Parallel-batching processing and job deterioration are universal in the real industry. Scholars have deeply investigated the problem of parallel-batching scheduling and the problem of scheduling with deteriorating jobs separately. However, the situations where both parallel-batching processing and job deterioration exist simultaneously were seldom considered. This paper studies the parallel-batching scheduling problem with nonlinear processing times on a single machine, and proposes several structural properties and an optimal algorithm to solve it. Based on the above properties and optimal algorithm for the single machine setting, we further study the problem of parallel-batching scheduling with nonlinear processing times under the unrelated parallel machine setting. Since the unrelated parallel machines scheduling problem is NP-hard, a hybrid SFLA-VNS algorithm combining Shuffle Frog Leap Algorithm (SFLA) with Variable Neighborhood Search Algorithm (VNS) is proposed. Computational experiments and comparison are finally conducted to demonstrate the effectiveness of the proposed algorithm.

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References

  1. Lee, C.Y., Uzsoy, R., Martin-Vega, L.A.: Efficient algorithms for scheduling semiconductor burn-in operations. Oper. Res. Int. Journal 40, 764–775 (1992)

    MathSciNet  MATH  Google Scholar 

  2. Malapert, A., Guéret, C., Rousseau, L.M.: A constraint programming approach for a batch processing problem with non-identical job sizes. Eur. J. Oper. Res. 3, 533–545 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Zhang, G., Cai, X., Lee, C.Y., Wong, C.K.: Minimizing makespan on a single batch processing machine with nonidentical job sizes. Nav. Res. Logist. 3, 226–240 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Dupont, L., Dhaenens-Flipo, C.: Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure. Comput. Oper. Res. 7, 807–819 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Li, C., Lee, C.Y.: Scheduling with agreeable release times and due dates on a batch processing machine. Eur. J. Oper. Res. 96, 564–569 (1997)

    MATH  Google Scholar 

  6. Melouk, S., Damodaran, P., Chang, P.-Y.: Minimizing makespan for single machine batch processing with nonidentical job sizes using simulated annealing. Int. J. Prod. Econ. 87, 141–147 (2004)

    Google Scholar 

  7. Kumar, A., Tan, Y.: Demand effects of joint product advertising in online videos. Manage. Sci. 61, 1921–1937 (2015)

    Google Scholar 

  8. Paul, A., Tan, Y., Vakharia, A.: Inventory planning for a modular product family. Prod. Oper. Manag. 24, 1033–1053 (2015)

    Google Scholar 

  9. Tan, Y., Carrillo, J., Cheng, H.K.: The agency model for digital goods. Decis. Sci. 4, 628–660 (2016)

    Google Scholar 

  10. Tan, Y., Carrillo, J.: Strategic analysis of the agency model for digital goods. Prod. Oper. Manag. (2017). https://doi.org/10.1111/poms.12595

    Article  Google Scholar 

  11. Gupta, J.N.D., Gupta, S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, 387–393 (1988)

    Google Scholar 

  12. Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Oper. Res. 3, 495–498 (1990)

    MATH  Google Scholar 

  13. Mosheiov, G.: Scheduling deteriorating jobs under simple linear deterioration. Comput. Oper. Res. 21, 653–659 (1994)

    MATH  Google Scholar 

  14. Cheng, T.C.E., Lee, W.C., Wu, C.C.: Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times. Appl. Math. Model. 35, 1861–1867 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Lai, P., Lee, W.C.: Single-machine scheduling with a nonlinear deterioration function. Inf. Process. Lett. 110, 455–459 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Wang, J., Wang, M.: Single-machine scheduling with nonlinear deterioration. Optimization Letters 6, 87–98 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Pei, J., Liu, X., Pardalos, P.M., Fan, W., Yang, S.: Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times. Ann. Oper. Res. 249, 175–195 (2017)

    MathSciNet  MATH  Google Scholar 

  18. Pei, J., Liu, X., Fan, W., Pardalos, P.M., Shaojun, L.: A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega (2017). https://doi.org/10.1016/j.omega.2017.12.003

    Article  Google Scholar 

  19. Fan, W., Pei, J., Liu, X., Pardalos, P.M., Kong, M.: Serial-batching group scheduling with release times and the combined effects of deterioration and truncated job-dependent learning. J. Global Optim. (2017). https://doi.org/10.1007/s10898-017-0536-7

    Article  MATH  Google Scholar 

  20. Pei, J., Pardalos, P.M., Liu, X., Fan, W., Yang, S.: Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan. Eur. J. Oper. Res. 244(1), 13–25 (2015)

    MathSciNet  MATH  Google Scholar 

  21. Alidaee, B., Womer, N.K.: Scheduling with time dependent processing times: review and extensions. J. Oper. Res. Soc. 50, 711–720 (1999)

    MATH  Google Scholar 

  22. Cheng, T.C.E., Kang, L., Ng, C.T.: Due-date assignment and single machine scheduling with deteriorating jobs. J. Oper. Res. Soc. 55, 198–203 (2004)

    MATH  Google Scholar 

  23. Wu, C.C., Lee, W.C.: Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine. Inf. Process. Lett. 87, 89–93 (2003)

    MathSciNet  MATH  Google Scholar 

  24. Ji, M., He, Y., Cheng, T.C.E.: Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theoret. Comput. Sci. 362, 115–126 (2006)

    MathSciNet  MATH  Google Scholar 

  25. Wang, J.B.: Single-machine scheduling problems with the effects of learning and deterioration. Omega 35, 397–402 (2007)

    Google Scholar 

  26. 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)

    MathSciNet  MATH  Google Scholar 

  27. Toksarı, M.D., Güner, E.: Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach. Int. J. Adv. Manuf. Technol. 38, 801–808 (2008)

    Google Scholar 

  28. Ji, M., Cheng, T.C.E.: Parallel-machine scheduling of simple linear deteriorating jobs. Theoret. Comput. Sci. 410, 3761–3768 (2009)

    MathSciNet  MATH  Google Scholar 

  29. Mazdeh, M.M., Zaerpour, F., Zareei, A., Hajinezhad, A.: Parallel machines scheduling to minimize job tardiness and machine deteriorating cost with deteriorating jobs. Appl. Math. Model. 34, 1498–1510 (2010)

    MathSciNet  MATH  Google Scholar 

  30. Li, S., Yuan, J.: Parallel-machine scheduling with deteriorating jobs and rejection. Theoret. Comput. Sci. 411, 3642–3650 (2010)

    MathSciNet  MATH  Google Scholar 

  31. Wang, J., Wang, L., Wang, D., Wang, X.: Single-machine scheduling with a time-dependent deterioration. Int. J. Adv. Manuf. Technol. 43, 805–809 (2009)

    Google Scholar 

  32. Qi, X., Zhou, S., Yuan, J.: Single machine parallel-batch scheduling with deteriorating jobs. Theoret. Comput. Sci. 410, 830–836 (2009)

    MathSciNet  MATH  Google Scholar 

  33. Miao, C., Zhang, Y., Cao, Z.: Bounded parallel-batch scheduling on single and multi-machines for deteriorating jobs. Inf. Process. Lett. 111, 798–803 (2011)

    MathSciNet  MATH  Google Scholar 

  34. Li, S., Ng, C.T., Cheng, T.C.E., Yuan, J.: Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan. Eur. J. Oper. Res. 210, 482–488 (2011)

    MathSciNet  MATH  Google Scholar 

  35. Wu, Y., Wang, M., Wang, J.: Some single-machine scheduling with both learning and deterioration effects. Appl. Math. Model. 35, 3731–3736 (2011)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  37. Lenstra, J.K., Rinnooy, A.H.G., Brucker, P.: Complexity of machine scheduling problems. J. Sched. 1, 343–362 (1977)

    MathSciNet  MATH  Google Scholar 

  38. Eusuff, M.M., Lansey, K.E.: Optimization of water distribution network design using the shuffled frog leaping algorithm. J. Water Resour. Plan. Manag. 129, 210–225 (2003)

    Google Scholar 

  39. Hansen, P., Mladenović, N.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1977)

    MathSciNet  MATH  Google Scholar 

  40. Hansen, P., Mladenović, N., Pérez, J.A.M.: Variable neighbourhood search: methods and applications. 4OR 175, 367–407 (2008)

    MathSciNet  MATH  Google Scholar 

  41. Zhou, S., Liu, M., Chen, H., Li, X.: An effective discrete differential evolution algorithm for scheduling uniform parallel batch processing machines with non-identical capacities and arbitrary job sizes. Int. J. Prod. Econ. 179, 1–11 (2016)

    Google Scholar 

  42. Jiang, L., Pei, J., Liu, X., Pardalos, P.M., Yang, Y., Qian, X.: Uniform parallel batch machines scheduling considering transportation using a hybrid DPSO-GA algorithm. Int. J. Adv. Manuf. Technol. (2016). https://doi.org/10.1007/s00170-016-9156-5

    Article  Google Scholar 

  43. Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 2, 154–160 (1994)

    MATH  Google Scholar 

  44. Borges, P., Eid, T., Bergseng, E.: Applying simulated annealing using different methods for the neighborhood search in forest planning problems. Eur. J. Oper. Res. 233, 700–710 (2014)

    MathSciNet  MATH  Google Scholar 

  45. Liang, X., Li, W., Zhang, Y., Zhou, M.C.: An adaptive particle swarm optimization method based on clustering. Soft. Comput. 19, 431–448 (2015)

    Google Scholar 

  46. Lei, D., Guo, X.: A shuffled frog-leaping algorithm for job shop scheduling with outsourcing options. Int. J. Prod. Res. 54, 1–12 (2016)

    Google Scholar 

  47. Huang, X., Wang, J., Wang, L., Gao, W., Wang, X.: Single machine scheduling with time-dependent deterioration and exponential learning effect. Comput. Ind. Eng. 58, 58–63 (2010)

    Google Scholar 

  48. Lai, P.J., Wu, C.C., Lee, W.C.: Single-machine scheduling with logarithm deterioration. Optimization Letters 6, 1719–1730 (2012)

    MathSciNet  MATH  Google Scholar 

  49. Rudek, R.: Some single-machine scheduling problems with the extended sum-of-processing-time-based aging effect. Int. J. Adv. Manuf. Technol. 59, 299–309 (2012)

    Google Scholar 

  50. Cheng, T.C.E., Tseng, S.C., Lai, P.J., Lee, W.C.: Single-machine scheduling with accelerating deterioration effects. Optimization Letters 8, 543–554 (2014)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71871080, 71601065, 71690235, 71501058, 71601060, 71801071), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province (No. SK2017A0055), the Philosophy and Social Science Cultivation Project of Hefei University of Technology (No. JS2017AJRW0031), the Fundamental Research Funds for the Central Universities (JZ2018HGBZ0129), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology), Ministry of Education. Panos M. Pardalos is partially supported by the project of Distinguished International Professor by the Chinese Ministry of Education (MS2014HFGY026).

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Correspondence to Min Kong or Jun Pei.

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Kong, M., Liu, X., Pei, J. et al. Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines. J Glob Optim 78, 693–715 (2020). https://doi.org/10.1007/s10898-018-0705-3

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