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Single-machine scheduling with past-sequence-dependent setup times and general effects of deterioration and learning. (English) Zbl 1288.90031

Summary: Scheduling with learning effect and deteriorating jobs has become more popular. However, most of the research assume that the setup time is negligible or a part of the job processing time. In this paper, we propose a model where the deteriorating jobs, the learning effect, and the setup times are present simultaneously. Under the proposed model, the setup time is past-sequence-dependent and the actual job processing time is a general function of the processing times of the jobs already processed and its scheduled position. We provide the optimal schedules for some single-machine problems.

MSC:

90B35 Deterministic scheduling theory in operations research
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[1] Alidaee B., Womer N.K.: Scheduling with time dependent processing times: Review and extensions. J. Oper. Res. Soc. 50, 711–720 (1999) · Zbl 1054.90542 · doi:10.1057/palgrave.jors.2600740
[2] Biskup D.: A state-of-the-art review on scheduling with learning effect. Eur. J. Oper. Res. 188, 315–329 (2008) · Zbl 1129.90022 · doi:10.1016/j.ejor.2007.05.040
[3] Biskup D., Herrmann J.: Single-machine scheduling against due dates with past-sequence-dependent setup times. Eur. J. Oper. Res. 191, 587–592 (2008) · Zbl 1147.90010 · doi:10.1016/j.ejor.2007.08.028
[4] 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) · Zbl 1030.90023 · doi:10.1016/S0377-2217(02)00909-8
[5] Cheng T.C.E., Lee W.C., Wu C.C.: Scheduling problems with deteriorating jobs and learning effects including proportional setup times. Comput. Ind. Eng. 58, 326–331 (2010) · doi:10.1016/j.cie.2009.11.008
[6] 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) · doi:10.1016/j.cie.2007.11.006
[7] Gawiejnowicz S.: Time-Dependent Scheduling, Monographs in Theoretical Computer Science, An EATCS Series. Springer, Berlin (2008)
[8] Huang X., Wang M.Z., Wang J.B.: Single-machine group scheduling with both learning effects and deteriorating jobs. Comput. Ind. Eng. 60, 750–754 (2011) · doi:10.1016/j.cie.2011.01.009
[9] Janiak A., Rudek R.: A note on a makespan minimization problem with a multi-abilities learning effect. OMEGA Int. J. Manag. Sci. 38, 213–217 (2010) · doi:10.1016/j.omega.2009.09.004
[10] Ji M., Cheng T.C.E.: Parallel-machine scheduling with simple linear deterioration to minimize total completion time. Eur. J. Oper. Res. 188, 342–347 (2008) · Zbl 1149.90343 · doi:10.1016/j.ejor.2007.04.050
[11] Ji M., Cheng T.C.E.: Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan. Eur. J. Oper. Res. 202, 90–98 (2010) · Zbl 1173.90407 · doi:10.1016/j.ejor.2009.05.021
[12] Koulamas C., Kyparisis G.J.: Single-machine scheduling problems with past-sequence-dependent setup times. Eur. J. Oper. Res. 187, 1045–1049 (2008) · Zbl 1137.90498 · doi:10.1016/j.ejor.2006.03.066
[13] Kuo W.H., Yang D.L.: Single machine scheduling with past-sequence-dependent setup times and learning effects. Inf. Process. Lett. 102, 22–26 (2007) · Zbl 1184.68132 · doi:10.1016/j.ipl.2006.11.002
[14] Lai P.J., Lee W.C.: Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects. Omega Int. J. Manag. Sci. 39, 467–471 (2011) · doi:10.1016/j.omega.2010.10.002
[15] Lai, P.J., Wu, C.C., Lee, W.C.: Single-machine scheduling with logarithm deterioration. Optim. Lett. doi: 10.1007/s11590-011-0362-7 (2011) · Zbl 1258.90041
[16] Lee W.C.: A note on deteriorating jobs and learning in single-machine scheduling problems. Int. J. Bus. Econ. 3, 83–89 (2004)
[17] Lee W.C.: Scheduling with general position-based learning curves. Inf. Sci. 181, 5515–5522 (2011) · Zbl 1239.90051 · doi:10.1016/j.ins.2011.07.051
[18] Pinedo M.: Scheduling: Theory, Algorithms, and Systems. Prentice Hall, Upper Saddle River, NJ (2002) · Zbl 1145.90394
[19] Rudek R.: Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect. Comput. Ind. Eng. 61, 20–31 (2011) · doi:10.1016/j.cie.2011.02.005
[20] Sun L.: Single-machine scheduling problems with deteriorating jobs and learning effects. Comput. Ind. Eng. 57, 843–846 (2009) · doi:10.1016/j.cie.2009.02.014
[21] Voutsinas T.G., Pappis C.P.: A branch-and-bound algorithm for single-machine scheduling with deteriorating value of jobs. Math. Comput. Model. 52, 55–61 (2010) · Zbl 1201.90087 · doi:10.1016/j.mcm.2009.12.024
[22] Wang J.B.: A note on scheduling problems with learning effect and deteriorating jobs. Int. J. Syst. Sci. 37, 827–833 (2006) · Zbl 1126.90347 · doi:10.1080/00207720600879260
[23] Wang J.B.: Single-machine scheduling problems with the effects of learning and deterioration. OMEGA Int. J. Manag. Sci. 35, 397–402 (2007) · doi:10.1016/j.omega.2005.07.008
[24] Wang J.B., Guo Q.: A due-date assignment problem with learning effect and deteriorating jobs. Appl. Math. Model. 34, 309–313 (2010) · Zbl 1185.90099 · doi:10.1016/j.apm.2009.04.020
[25] Wang X., Cheng T.C.E.: Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan. Eur. J. Oper. Res. 178, 57–70 (2007) · Zbl 1110.90045 · doi:10.1016/j.ejor.2006.01.017
[26] Wang J.B., Sun L.H., Sun L.Y.: Scheduling jobs with an exponential sum-of-actual-processing-time-based learning effect. Comput. Math. Appl. 60, 2673–2678 (2010) · Zbl 1205.90138 · doi:10.1016/j.camwa.2010.09.005
[27] Wang J.B., Wang D., Zhang G.D.: Single-machine scheduling problems with both deteriorating jobs and learning effects. Appl. Math. Model. 34, 2831–2839 (2010) · Zbl 1201.90089 · doi:10.1016/j.apm.2009.12.017
[28] Wang, J.B., Wang, M.Z.: Single-machine scheduling with nonlinear deterioration. Optim. Lett. doi: 10.1007/s11590-010-0253-3 (2010) · Zbl 1259.90040
[29] Xu Z., Sun L., Gong J.: Worst-case analysis for flow shop scheduling with learning effect. Int. J. Prod. Econ. 113, 748–753 (2008) · doi:10.1016/j.ijpe.2007.11.002
[30] Yin N., Wang J.B., Wang D., Wang L.Y., Wang X.Y.: Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times. Int. J. Adv. Manuf. Technol. 46, 707–714 (2010) · doi:10.1007/s00170-009-2116-6
[31] Yin Y.Q., Xu D.H.: Some single-machine scheduling problems with general effects of learning and deterioration. Comput. Math. Appl. 61, 100–108 (2011) · Zbl 1207.90060 · doi:10.1016/j.camwa.2010.10.036
[32] 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. 5, 183–190 (2010) · Zbl 1213.90127 · doi:10.1007/s11590-010-0202-1
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