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Single-machine scheduling with nonlinear deterioration

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Abstract

In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.

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References

  1. Alidaee B.: A heuristic solution procedure to minimize makespan on a single machine with non-linear cost functions. J. Oper. Res. Soc. 41, 1065–1068 (1990)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. 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  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Cheng T.C.E., Wu C.C., Lee W.C.: Some scheduling problems with deteriorating jobs and learning effects. Comput. Ind. Eng. 54, 972–982 (2008)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  7. Gawiejnowicz S.: Scheduling deteriorating jobs subject to job or machine availability constraints. Eur. J. Oper. Res. 180, 472–478 (2007)

    Article  MATH  Google Scholar 

  8. Gawiejnowicz S., Kurc W., Pankowska L.: Pareto and scalar bicriterion optimization in scheduling deteriorating jobs. Comput. Oper. Res. 33, 746–767 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. 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. Discrete Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gupta J.N.D., Gupta S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, 387–393 (1998)

    Article  Google Scholar 

  11. Hadda H.: A \({\left(\frac{4}{3}\right)}\)-approximation algorithm for a special case of the two machine flow shop problem with several availability constraints. Optim. Lett. 3, 583–592 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lee W.-C., Wu C.-C., Chung Y.-H., Liu H.-C.: Minimizing the total completion time in permutation flow shop with machine-dependent job deterioration rates. Comput. Oper. Res. 36, 2111–2121 (2009)

    Article  MATH  Google Scholar 

  13. Lee W.-C., Wu C.-C., Wen C.-C., Chung Y.-H.: A two-machine flowshop makespan scheduling problem with deteriorating jobs. Comput. Ind. Eng. 54, 737–749 (2008)

    Article  Google Scholar 

  14. Lee C.-Y., Yu G.: Parallel-machine scheduling under potential disruption. Optim. Lett. 2, 27–37 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Leung J.Y.T., Ng C.T., Cheng T.C.E.: Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times. Eur. J. Oper. Res. 187, 1090–1099 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kanet J.J.: Minimizing variation of flow time in single machine systems. Manage. Sci. 27(12), 1453–1459 (1981)

    Article  MATH  Google Scholar 

  17. Kononov A., Gawiejnowicz S.: NP-hard cases in scheduling deteriorating jobs on dedicated machines. J. Oper. Res. Soc. 52, 708–717 (2001)

    Article  MATH  Google Scholar 

  18. Kuo W.-H., Yang D.-L.: Single-machine scheduling problems with start-time dependent processing time. Comput. Math. Appl. 53, 1658–1664 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Oron D.: Single machine scheduling with simple linear deterioration to miminize total absolute deviation of completion times. Comput. Oper. Res. 5, 2071–2078 (2008)

    Article  MathSciNet  Google Scholar 

  20. Pardalos P.M., Resende M.G.C.: Handbook of Applied Optimization. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  21. Setamaa-Karkkainen A., Miettinen K., Vuori J.: Heuristic for a new multiobjective scheduling problem. Optim. Lett. 1, 213–225 (2007)

    Article  MathSciNet  Google Scholar 

  22. Tang L., Liu P.: Two-machine flowshop scheduling problems involving a batching machine with transportation or deterioration consideration. Appl. Math. Model. 33, 1187–1199 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  23. Voutsinas T.G., Pappis C.P.: Scheduling jobs with values exponentially deteriorating over time. Int. J. Prod. Econ. 79, 163–169 (2002)

    Article  Google Scholar 

  24. Wang J.-B., Ng C.T., Cheng T.C.E., Liu L.L.: Minimizing total completion time in a two-machine flow shop with deteriorating jobs. Appl. Math. Comput. 180, 185–193 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Wang J.-B., Xia Z.-Q.: Flow shop scheduling with deteriorating jobs under dominating machines. Omega 34, 327–336 (2006)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  27. Wu C.-C., Lee W.-C., Shiau Y.-R.: Minimizing the total weighted completion time on a single machine under linear deterioration. Int. J. Adv. Manuf. Technol. 33, 1237–1243 (2007)

    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, 1652–1659 (2008)

    Article  MATH  Google Scholar 

  29. Zhao, C.-L., Tang, H.-Y.: A note on two-machine no-wait flow shop scheduling with deteriorating jobs and machine availability constraints. Optim. Lett. (2010). doi:10.1007/s11590-010-0202-1

  30. Zhao C.-L., Zhang Q.-L., Tang H.-Y.: Scheduling problems under linear deterioration. Acta Autom. Sin. 29, 531–535 (2003)

    MathSciNet  Google Scholar 

  31. Zhu V.C.Y., Sun L., Sun L., Li X.: Single machine scheduling time-dependent jobs with resource-dependent ready times. Comput. Ind. Eng. 58, 84–87 (2010)

    Google Scholar 

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, China

    Ji-Bo Wang

  2. School of Management Science and Engineering, Dalian University of Technology, Dalian, 116024, China

    Ming-Zheng Wang

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  1. Ji-Bo Wang
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  2. Ming-Zheng Wang
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Correspondence to Ming-Zheng Wang.

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Wang, JB., Wang, MZ. Single-machine scheduling with nonlinear deterioration. Optim Lett 6, 87–98 (2012). https://doi.org/10.1007/s11590-010-0253-3

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  • DOI: https://doi.org/10.1007/s11590-010-0253-3

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