Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration

Abstract

This paper addresses a serial-batching scheduling problem where the jobs with arbitrary release times are scheduled on parallel machines with the objective to minimize the makespan. The effects of learning and deterioration are considered simultaneously, and each job’s actual processing time depends on the sum of previous jobs’ processing times and the position of the current job. Each machine can process up to \( c \) jobs in the manner of serial batch, i.e., one after another with a setup time for each batch. Structural properties are identified for the special cases of the studied problem. Based on these derived structural properties, we propose a novel hybrid SC-VNS algorithm to solve the studied problem, which combines Society and Civilization (SC) algorithm with Variable Neighborhood Search (VNS). Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The results demonstrate that the proposed hybrid SC-VNS algorithm performs quite better than the compared algorithms in terms of the solution quality and the required running time.

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References

  1. Arroyo, J. E. C., & Leung, J. Y. T. (2017). Scheduling unrelated parallel batching processing machines with non-identical job sizes and unequal ready times. Computers & Operations Research, 78, 117–128.

    Google Scholar 

  2. Biskup, D. (1999). Single-machine scheduling with learning considerations. European Journal of Operational Research, 115(1), 173–178.

    Google Scholar 

  3. Browne, S., & Yechiali, U. (1990). Scheduling deteriorating jobs on a single processor. Operations Research, 38(3), 495–498.

    Google Scholar 

  4. Chen, Z.-L. (1995). A note on single-processor scheduling with time-dependent execution times. Operations Research Letters, 17(3), 127–129.

    Google Scholar 

  5. Cheng, T. C. E., & Ding, Q. (1998). The complexity of scheduling starting time dependent tasks with release times. Information Processing Letters, 65(2), 75–79.

    Google Scholar 

  6. Cheng, T. C. E., Ding, Q., Kovalyov, M. Y., Bachman, A., & Janiak, A. (2003). Scheduling jobs with piecewise linear decreasing processing times. Naval Research Logistics, 50(6), 531–554.

    Google Scholar 

  7. Cheng, T. C. E., & Wang, G. (2000). Single machine scheduling with learning effect consideration. Annals of Operations Research, 98, 273–290.

    Google Scholar 

  8. Cheng, T. C. E., Wu, C. C., & Lee, W.-C. (2008). Some scheduling problems with deteriorating jobs and learning effects. Computers & Industrial Engineering, 54(40), 972–982.

    Google Scholar 

  9. Croce, F. D., Garaix, T., & Grosso, A. (2012). Iterated local search and very large neighborhoods for the parallel-machines total tardiness problem. Computers & Operations Research, 39(6), 1213–1217.

    Google Scholar 

  10. Fan, W., Pei, J., Liu, X., Pardalos, P. M., & Kong, M. (2018). Serial-batching group scheduling with release times and the combined effects of deterioration and truncated job-dependent learning. Journal of Global Optimization, 71(1), 147–163.

    Google Scholar 

  11. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Descrete Mathematics, 5, 287–326.

    Google Scholar 

  12. Gupta, J. N. D., & Gupta, S. K. (1988). Single facility scheduling with nonlinear processing times. Computers & Industrial Engineering, 14(4), 387–393.

    Google Scholar 

  13. Hansen, P., Mladenovic, N., & Perez, J. A. M. (2010). Variable neighborhood search: methods and applications. Annals of Operations Research, 175(1), 367–407.

    Google Scholar 

  14. Huang, X., & Wang, M.-Z. (2011). Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties. Applied Mathematical Modelling, 35(3), 1349–1353.

    Google Scholar 

  15. Hulett, M., Damodaran, P., & Amouie, M. (2017). Scheduling non-identical parallel batch processing machines to minimize total weighted tardiness using particle swarm optimization. Computers & Industrial Engineering, 113, 425–436.

    Google Scholar 

  16. Jiang, L., Pei, J., Liu, X., Pardalos, P. M., & Qian, X. (2016). Uniform parallel batch machines scheduling considering transportation using a hybrid DPSO-GA algorithm. International Journal of Advanced Manufacturing Technology, 89, 1887–1900.

    Google Scholar 

  17. Kumar, A., & Tan, Y. (2015). The demand effects of joint product advertising in online videos. Management Science, 61, 1921–1937.

    Google Scholar 

  18. Lee, C. Y. (1999). Minimizing makespan on a single batch processing machine with dynamic job arrivals. International Journal of Production Research, 37(1), 219–236.

    Google Scholar 

  19. Lee, W.-C. (2004). A note on deteriorating jobs and learning in single-machine scheduling problems. International Journal of Business and Economics, 3(1), 83.

    Google Scholar 

  20. Leung, J. Y. T., Ng, C. T., & Cheng, T. C. E. (2008). Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times. European Journal of Operational Research, 187(3), 1090–1099.

    Google Scholar 

  21. Li, M., Sethi, S. P., & Zhang, J. (2016). Competing with bandit supply chains. Annals of Operations Research, 240(2), 617–640.

    Google Scholar 

  22. Li, M., & Zhang, J. (2012). Does inventory pooling improve customer service level? Operations Research Letters, 40(2), 96–98.

    Google Scholar 

  23. Li, S., Li, G., & Zhang, S. (2005). Minimizing makespan with release times on identical parallel batching machines. Discrete Applied Mathematics, 148(1), 127–134.

    Google Scholar 

  24. Liang, Z., Feng, Y., Zhang, X., Tao, W., & Chaovalitwongse, W. A. (2015). Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem. Transportation Research Part B: Methodological, 78, 238–259.

    Google Scholar 

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

    Google Scholar 

  26. Liu, X., Shaojun, L., Pei, J., & Pardalos, P. M. (2018). A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs. International Journal of Production Research, 56(17), 5758–5775.

    Google Scholar 

  27. Luo, H., Huang, G. Q., Zhang, Y. F., & Dai, Q. Y. (2011). Hybrid flowshop scheduling with batch-discrete processors and machine maintenance in time windows. International Journal of Production Research, 49(6), 1575–1603.

    Google Scholar 

  28. Mosheiov, G. (2001). Parallel machine scheduling with learning effect. Journal of the Operational Research Society, 52(10), 1165–1169.

    Google Scholar 

  29. Pan, Q. K., Tasgetiren, M. F., & Liang, Y. C. (2011). A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Computers & Operations Research, 35(9), 2807–2839.

    Google Scholar 

  30. Pan, Y., & Liang, Z. (2017). Dual relaxations of the time-indexed ILP formulation for min-sum scheduling problems. Annals of Operations Research, 249(1–2), 197–213.

    Google Scholar 

  31. Pei, J., Cheng, B., Liu, X., Pardalos, P. M., & Kong, M. (2019a). Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Annals of Operations Research, 272(1–2), 217–241.

    Google Scholar 

  32. Pei, J., Liu, X., Fan, W., Pardalos, P. M., Migdalas, A., Goldengorin, B., et al. (2016a). Minimizing the makespan for a serial-batching scheduling problem with arbitrary machine breakdown and dynamic job arrival. International Journal of Advanced Manufacturing Technology, 86(9), 3315–3331.

    Google Scholar 

  33. Pei, J., Liu, X., Fan, W., Pardalos, P. M., Migdalas, A., & Yang, S. (2016b). Scheduling jobs on a single serial-batching machine with dynamic job arrivals and multiple job types. Annals of Mathematics and Artificial Intelligence, 76, 215–228.

    Google Scholar 

  34. Pei, J., Liu, X., Fan, W., Pardalos, P. M., & Shaojun, L. (2019b). A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega, 82, 55–69.

    Google Scholar 

  35. Pei, J., Liu, X., Liao, B., Pardalos, P. M., & Kong, M. (2018). Single-machine scheduling with learning effect and resource-dependent processing times in the serial-batching production. Applied Mathematical Modelling, 58, 245–253.

    Google Scholar 

  36. Pei, J., Liu, X., Pardalos, P. M., Fan, W., Wang, L., & Yang, S. (2016c). Solving a supply chain scheduling problem with non-identical job sizes and release times by applying a novel effective heuristic algorithm. International Journal of System Science, 47(4), 765–766.

    Google Scholar 

  37. Pei, J., Liu, X., Pardalos, P. M., Fan, W., & Yang, S. (2015a). Single machine serial-batching scheduling with independent setup time and deteriorating job processing times. Optimization Letters, 9(1), 91–104.

    Google Scholar 

  38. Pei, J., Liu, X., Pardalos, P. M., Fan, W., & Yang, S. (2017a). Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times. Annals of Operations Research, 249(1–2), 175–195.

    Google Scholar 

  39. Pei, J., Liu, X., Pardalos, P. M., Fan, W., Yang, S., & Wang, L. (2014). Application of an effective modified gravitational search algorithm for the coordinated scheduling problem in a two-stage supply chain. International Journal of Advanced Manufacturing Technology, 70(1–4), 335–348.

    Google Scholar 

  40. Pei, J., Liu, X., Pardalos, P. M., Li, K., Fan, W., & Migdalas, A. (2017b). Single-machine serial-batching scheduling with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. Optimization Letters, 11(7), 1257–1271.

    Google Scholar 

  41. Pei, J., Liu, X., Pardalos, P. M., Migdalas, A., & Yang, S. (2017c). Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine. Journal of Global Optimization, 67(1), 251–262.

    Google Scholar 

  42. Pei, J., Pardalos, P. M., Liu, X., Fan, W., & Yang, S. (2015b). Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan. European Journal of Operational Research, 244(1), 13–25.

    Google Scholar 

  43. Ray, T., & Liew, K. M. (2003). Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Transactions on Evolutionary Computation, 7(4), 386–396.

    Google Scholar 

  44. Rostami, M., Pilerood, A. E., & Mazdeh, M. M. (2015). Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment. Computers & Industrial Engineering, 85, 206–215.

    Google Scholar 

  45. Rudek, R. (2013). On single processor scheduling problems with learning dependent on the number of processed jobs. Applied Mathematical Modelling, 37, 1523–1536.

    Google Scholar 

  46. Storn, R., & Price, K. (2011). Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.

    Google Scholar 

  47. Sun, L. (2009). Single-machine scheduling problems with deteriorating jobs and learning effects. Computers & Industrial Engineering, 57(3), 843–846.

    Google Scholar 

  48. Sundararaghavan, P. S., & Kunnathur, A. S. (1994). Single machine scheduling with start time dependent processing time: Some solvable cases. European Journal of Operational Research, 78(3), 394–403.

    Google Scholar 

  49. Teyarachakul, S., Chand, S., & Ward, J. (2011). Effect of learning and forgetting on batch size. Production and Operations Management, 20(1), 116–128.

    Google Scholar 

  50. Toksari, M. D. (2011). A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs. Computers & Operations Research, 38(9), 1361–1365.

    Google Scholar 

  51. Wright, T. P. (1936). Factors affecting the cost of airplanes. Journal of the Aeronautical Sciences, 3(4), 122–128.

    Google Scholar 

  52. Wu, C. C., Hsu, P.-H., Chen, J.-C., & Wang, N.-S. (2011). Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times. Computers & Operations Research, 38(7), 1025–1034.

    Google Scholar 

  53. Wu, C. C., Wu, W. H., Wu, W. H., Hsu, P.-H., Yin, Y., & Jianyou, X. (2014). A single-machine scheduling with a truncated linear deterioration and ready times. Information Sciences, 256, 109–125.

    Google Scholar 

  54. Xu, J., Wu, C. C., Yin, Y., Zhao, C., Chiou, Y.-T., & Lin, W.-C. (2016). An order scheduling problem with position-based learning effect. Computers & Operations Research, 74, 175–186.

    Google Scholar 

  55. Yang, D.-L., & Kuo, W.-H. (2009). A single-machine scheduling problem with learning effect in intermittent batch production. Computers & Industrial Engineering, 57(3), 762–765.

    Google Scholar 

  56. Yang-Kuel, L., & Chi-Wei, L. (2013). Dispatching rules for unrelated parallel machine scheduling with release dates. International Journal of Advanced Manufacturing Technology, 67(1–4), 269–279.

    Google Scholar 

  57. Yusriski, R., Sukoyo, T. M., & Hakim, A. H. (2013). Batch scheduling for a single machine with learning effect to minimize total actual flow time. In The 14th Asia pacific industrial engineering and management system conference, Cebu, Philippines, 3–6 December.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71922009, 71871080, 71601065, 71690235, 71690230), 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), 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 and Ministry of Education Engineering Research Center for Intelligent Decision-making and Information Systems Technologies (Hefei University of Technology), Ministry of Education.

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Correspondence to Jun Pei or Xinbao Liu.

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Pei, J., Song, Q., Liao, B. et al. Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration. Ann Oper Res 298, 407–444 (2021). https://doi.org/10.1007/s10479-020-03555-2

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Keywords

  • Parallel machines
  • Serial-batching
  • Release times
  • Learning effect
  • Deteriorating jobs