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Multi-machine scheduling with deterioration effects and maintenance activities for minimizing the total earliness and tardiness costs

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Abstract

The due date assignment has become a challenging issue related to the interaction between various participants of the supply chain. In this paper, we consider the total earliness and tardiness penalty scheduling simultaneously with the deterioration effects and maintenance activities on an unrelated parallel machine setting. We aim to determine jointly the optimal maintenance activity positions, the optimal common due date for all the jobs, and the optimal schedule to minimize the sum of the earliness and tardiness costs. If the number of machines is fixed, we introduce a polynomial time algorithm for solving the problem. We also propose an efficient polynomial time algorithm with a lower order time complexity for finding the optimal solution of a special case of the problem.

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References

  1. Adiri I, Bruno J, Frostig E, Rinnooy Kan AHG (1989) Single machine flow-time scheduling with a single breakdown. Acta Inform 26:679–696

    Article  MathSciNet  MATH  Google Scholar 

  2. Adiri I, Frostig E, Rinnooy Kan AHG (1991) Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs. Nav Res Logist 38:261–271

    Article  MathSciNet  MATH  Google Scholar 

  3. Birge J, Frenk JBG, Mittenthal J, Rinnooy Kan AHG (1990) Single-machine scheduling subject to stochastic breakdowns. Nav Res Logist 37:664–677

    Article  MathSciNet  Google Scholar 

  4. Brucker P (2001) Scheduling algorithms. Springer, Berlin

    Book  MATH  Google Scholar 

  5. Chen WJ (2007) An efficient algorithm for scheduling jobs on a machine with periodic maintenance. Int J Adv Manuf Technol 34:1173–1182

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Frostig E (1991) A note on stochastic scheduling on a single machine subject to breakdown—the preemptive repeat model. Probab Eng Inform Sci 5:349–354

    Article  MathSciNet  MATH  Google Scholar 

  8. Gawiejnowicz S (2008) Time-dependent scheduling. Springer, Berlin

    MATH  Google Scholar 

  9. Gawiejnowicz S, Kononov A (2010) Complexity and approximability of scheduling resumable proportionally deteriorating jobs. Eur J Oper Res 200:305–308

    Article  MATH  Google Scholar 

  10. Gordon V, Proth JM, Chu C (2002) A survey of the state-of-art of common due date assignment and scheduling research. Eur J Oper Res 139:1–25

    Article  MathSciNet  MATH  Google Scholar 

  11. Gordon VS, Proth JM, Strusevich VA (2004) Scheduling with due date assignment. In: Leung JY (ed) Handbook of scheduling: algorithms, models and performance analysis. CRC Press, Boca Raton

    Google Scholar 

  12. Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discret Math 5:287–326

    Article  MathSciNet  MATH  Google Scholar 

  13. Hsu CJ, Cheng TCE, Yang DL (2011) Unrelated parallel-machine scheduling with rate-modifying activities to minimize the total completion time. Inf Sci 181:4799–4803

    Article  MathSciNet  MATH  Google Scholar 

  14. Hsu CJ, Yang SJ, Yang DL (2011) Two due date assignment problems with position-dependent processing time on a single-machine. Comput Ind Eng 60:796–800

    Article  Google Scholar 

  15. Hsu CJ, Yang SJ, Yang DL (2011) Due-date assignment and maintenance activity scheduling problem with linear deteriorating jobs. J Mar Sci Tech 19:97–100

    Google Scholar 

  16. Huang X, Wang JB, Wang XR (2010) A generalization for single-machine scheduling with deteriorating jobs to minimize earliness penalties. Int J Adv Manuf Technol 47:1225–1230

    Article  Google Scholar 

  17. Janiak A, Rudek R (2006) Scheduling problems with position dependent job processing times. In: Janiak A (ed) Scheduling in computer and manufacturing systems. WKL, Poland, pp 26–38

    Google Scholar 

  18. Ji M, He Y, Cheng TCE (2006) Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theor Comput Sci 362:115–126

    Article  MathSciNet  MATH  Google Scholar 

  19. Jozefowska J (2007) Just-in-time scheduling: models and algorithms for computer and manufacturing systems. Springer, Berlin

    MATH  Google Scholar 

  20. Kuo WH, Yang DL (2008) A note on due-date assignment and single-machine scheduling with deteriorating jobs. J Oper Res Soc 59:857–859

    Article  MATH  Google Scholar 

  21. Lee WC, Wu CC (2008) Multi-machine scheduling with deteriorating jobs and scheduled maintenance. Appl Math Model 32:362–373

    Article  MathSciNet  MATH  Google Scholar 

  22. Low C, Hsu CJ, Su CT (2008) Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration. Comput Math Appl 56:257–265

    Article  MathSciNet  MATH  Google Scholar 

  23. Lodree EJ Jr, Geiger CD (2010) A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration. Eur J Oper Res 201:644–648

    Article  MathSciNet  MATH  Google Scholar 

  24. Ma Y, Chu C, Zuo C (2010) A survey of scheduling with deterministic machine availability constraints. Comput Ind Eng 58:199–211

    Article  Google Scholar 

  25. Mosheiov G (2001) Parallel machine scheduling with a learning effect. J Oper Res Soc 52:1165–1169

    Article  MATH  Google Scholar 

  26. Mosheiov G, Oron D (2006) Due-date assignment and maintenance activity scheduling problem. Math Comput Model 44:1053–1057

    Article  MathSciNet  MATH  Google Scholar 

  27. Mott JL, Kandel A, Baker TP (1986) Discrete mathematics for computer scientists and mathematicians. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  28. Ozturkoglu Y, Bulfin RL (2011) A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine. Int J Adv Manuf Technol 57:753–762

    Article  Google Scholar 

  29. Panwalkar SS, Smith ML, Seidmann A (1982) Common due date assignment to minimize total penalty for the one machine scheduling problem. Oper Res 30:391–399

    Article  MATH  Google Scholar 

  30. Pinedo M, Rammouz E (1988) A note on stochastic scheduling on a single machine subject to breakdown and repair. Probab Eng Inform Sci 2:41–49

    Article  MATH  Google Scholar 

  31. Rudek R (2011) Some single-machine scheduling problems with the extended sum-of-processing-time-based aging effect. Int J Adv Manuf Technol. doi:10.1007/s00170-011-3481-5

  32. Wang JB (2010) Flow shop scheduling with deteriorating jobs under dominating machines to minimize makespan. Int J Adv Manuf Technol 48:719–723

    Article  Google Scholar 

  33. Wang D, Wang JB (2010) Single-machine scheduling with simple linear deterioration to minimize earliness penalties. Int J Adv Manuf Technol 46:285–290

    Article  Google Scholar 

  34. Wang JB, Wang LY, Wang D, Wang XY (2009) Single-machine scheduling with a time-dependent deterioration. Int J Adv Manuf Technol 43:805–809

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  36. Wu CC, Shiau YR, Lee LH, Lee WC (2009) Scheduling deteriorating jobs to minimize the makespan on a single machine. Int J Adv Manuf Technol 40:1230–1236

    Article  Google Scholar 

  37. Yang SJ, Hsu CJ, Yang DL (2010) Single-machine scheduling with due-date assignment and aging effect under a deteriorating maintenance activity consideration. Int J Inf Manag Sci 21:177–195

    MathSciNet  MATH  Google Scholar 

  38. Yang SJ, Hsu CJ, Yang DL (2011) Single-machine scheduling and slack due-date assignment with aging effect and deteriorating maintenance. Optim Lett. doi:10.1007/s11590-011-0382-3

  39. Yang DL, Lee HT, Yang SJ (2012) Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties. J Chin Inst Ind Eng 29:282–289

    Google Scholar 

  40. Yang SJ, Yang DL (2010) Single-machine scheduling problems with aging/deteriorating effect under an optional maintenance activity consideration. Infor 48:171–179

    Google Scholar 

  41. Zhao CL, Tang HY, Cheng CD (2009) Two-parallel machines scheduling with rate-modifying activities to minimize total completion time. Eur J Oper Res 198:354–357

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Nan Kai University of Technology, Nan-Tou, 542, Taiwan

    Hsin-Tao Lee & Suh-Jenq Yang

  2. Department of Information Management, National Formosa University, Yun-Lin, 632, Taiwan

    Dar-Li Yang

Authors
  1. Hsin-Tao Lee
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  2. Dar-Li Yang
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  3. Suh-Jenq Yang
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Correspondence to Suh-Jenq Yang.

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Lee, HT., Yang, DL. & Yang, SJ. Multi-machine scheduling with deterioration effects and maintenance activities for minimizing the total earliness and tardiness costs. Int J Adv Manuf Technol 66, 547–554 (2013). https://doi.org/10.1007/s00170-012-4348-0

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  • DOI: https://doi.org/10.1007/s00170-012-4348-0

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