Scheduling to a Common Due Date on Unrelated Parallel-Machine with Deteriorating Jobs

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This paper explores scheduling to a common due date on unrelated machines with resource allocation and deteriorating jobs. The main purpose is to determine the optimal resource allocation and the optimal job sequence so that the cost function that includes the sum of earliness, tardiness, and resource cost will be minimized. Result showed that the problem is polynomial time solvable when the number of machine is fixed.

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Advanced Materials Research (Volumes 605-607)

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521-527

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December 2012

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] M. Pinedo, Scheduling: Theory, Algorithms, and Systems, Springer, (2008).

Google Scholar

[2] S. Browne and U. Yechiali. Dynamic priority rules for cyclic type queues. Advances in Applied Probability Vol. 10 (1989), pp.432-450.

DOI: 10.2307/1427168

Google Scholar

[3] A.S. Kunnathur and S.K. Gupta. Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. European Journal of Operational Research Vol. 47 (1990), pp.56-64.

DOI: 10.1016/0377-2217(90)90089-t

Google Scholar

[4] W. Kubiak and S.L. van de Velde. Scheduling deteriorating jobs to minimize makespan. Naval Research Logistics Vol. 45 (1998), pp.511-523.

DOI: 10.1002/(sici)1520-6750(199808)45:5<511::aid-nav5>3.0.co;2-6

Google Scholar

[5] G. Mosheiov. Multi-machine scheduling with linear deterioration. INFOR Vol. 36 (1998), pp.205-214.

DOI: 10.1080/03155986.1998.11732359

Google Scholar

[6] C.Y. Low, C. -J. Hsu and C. -T. Su. Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration. Computers and Mathematics with Applications Vol. 56 (2008), pp.257-265.

DOI: 10.1016/j.camwa.2007.12.006

Google Scholar

[7] S. Brown and U. Yechiali. Scheduling deteriorating jobs on a single process. Operations Research Vol. 38 (1990), pp.495-498.

DOI: 10.1287/opre.38.3.495

Google Scholar

[8] C. Zhao, Q. Zhang and H. Tang. Scheduling problems under linear deterioration. Acta Automatica Sinica Vol. 29 (2003), pp.531-535.

Google Scholar

[9] J. -B. Wang and Z. -Q. Xia. Scheduling jobs under decreasing linear deterioration. Information Processing Letters Vol. 94 (2005), pp.63-69.

DOI: 10.1016/j.ipl.2004.12.018

Google Scholar

[10] C. -C. Wu, W. -C. Lee and Y. -R. Shiau. Minimizing the total weighted completion time on a single-machine under linear deterioration. International Journal of Advanced Manufacturing Technology Vol. 33 (2007), pp.1237-1243.

DOI: 10.1007/s00170-006-0565-8

Google Scholar

[11] W. -C. Lee, C. -C. Wu and H. -C. Liu. A note on single-machine makespan problem with general deteriorating function. International Journal of Advanced Manufacturing Technology Vol. 40 (2009), pp.1053-1056.

DOI: 10.1007/s00170-008-1421-9

Google Scholar

[12] B. Alidaee and N.K. Womer. Scheduling with time dependent processing times: review and extensions. Journal of the Operational Research Society Vol. 50 (1999), pp.711-720.

DOI: 10.1057/palgrave.jors.2600740

Google Scholar

[13] T.C.E. Cheng, Q. Ding and B.M.T. Lin. A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research Vol. 152 (2004), pp.1-13.

DOI: 10.1016/s0377-2217(02)00909-8

Google Scholar

[14] C. -L. Zhao and H. -Y. Tang. Single machine scheduling problems with deteriorating jobs. Applied Mathematics and Computation Vol. 161 (2005), pp.865-874.

DOI: 10.1016/j.amc.2003.12.073

Google Scholar

[15] Y. Yang, D. -Z. Wang, D. -W. Wang, W.H. Ip and H. -F. Wang. Single machine group scheduling problems with the effects of deterioration and learning. Acta Automatica Sinica Vol. 35 (2009), pp.1290-1295.

DOI: 10.1016/s1874-1029(08)60110-x

Google Scholar

[16] V.C.Y. Zhu, L.Y. Sun, L.H. Sun and X.H. Li. Single machine scheduling time-dependent jobs with resource dependent ready times. Computers & Industrial Engineering Vol. 58 (2010), pp.84-87.

DOI: 10.1016/j.cie.2009.08.006

Google Scholar

[17] D. Wang, M. -Z. Wang and J. -B. Wang. Single-machine scheduling with learning effect and resource-dependent processing times. Computers & Industrial Engineering Vol. 59 (2010), pp.458-462.

DOI: 10.1016/j.cie.2010.06.002

Google Scholar

[18] W. -H. Kuo and D. -L. Yang. A note on due-date assignment and single-machine scheduling with deteriorating jobs. Journal of the Operational Research Society Vol. 59 (2008), pp.857-859.

DOI: 10.1057/palgrave.jors.2602396

Google Scholar

[19] M.D. Toksa and E. Guner. Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach. International Journal of Advanced Manufacturing Technology Vol. 38 (2008).

DOI: 10.1007/s00170-007-1128-3

Google Scholar

[20] V. S. Gordon and V. A. Strusevich. Single machine scheduling and due date assignment with positionally dependent processing times. European Journal of Operational Research Vol. 198 (2009), P. 57-62.

DOI: 10.1016/j.ejor.2008.07.044

Google Scholar

[21] A. Rudek and R. Rudek. A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models. Computers & Mathematics with Applications Vol. 62 (2011), P. 1870-1878.

DOI: 10.1016/j.camwa.2011.06.030

Google Scholar

[22] C. -L. Zhao and H. -Y. Tang. A note to due-window assignment and single machine schedulingwith deteriorating jobs and a rate-modifying activity. Computers & Operations Research Vol. 39 (2012), P. 1300-1303.

DOI: 10.1016/j.cor.2010.04.006

Google Scholar

[23] K. R. Baker and G. D. Scudder. Sequencing with earliness and tardiness penalties: A review. Operations Research Vol. 38 (1990), pp.22-36.

DOI: 10.1287/opre.38.1.22

Google Scholar

[24] T.C.E. Cheng and M.C. Gupta. Survey of scheduling research involving due date determination decisions. European Journal of Operational Research Vol. 38 (1989), pp.156-166.

DOI: 10.1016/0377-2217(89)90100-8

Google Scholar

[25] V. Gordon, J.M. Proth and C. Chu. A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research Vol. 139 (2002), pp.1-25.

DOI: 10.1016/s0377-2217(01)00181-3

Google Scholar

[26] V. Lauff and F. Werner. Scheduling with common due date, earliness and tardiness penalties for multimachine problems: A survey. Mathematical and Computer Modelling Vol. 40 (2004), pp.637-655.

DOI: 10.1016/j.mcm.2003.05.019

Google Scholar

[27] A. Bachman and A., Janiak. Scheduling deteriorating jobs dependent on resources for the makespan minimization. Operations Research Proceedings 2000: Selected Papers of the Symposium on Operations Research, Dresden, September, pp.29-34.

DOI: 10.1007/978-3-642-56656-1_5

Google Scholar

[28] K.R. Baker and G.D. Scudder. Sequencing with earliness and tardiness penalties: a revlew. Operations Research Vol. 38 (1990), pp.22-36.

DOI: 10.1287/opre.38.1.22

Google Scholar

[29] R.L. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics Vol. 5 (1979), pp.287-326.

DOI: 10.1016/s0167-5060(08)70356-x

Google Scholar

[30] S.S. Panwalkar, M.L. Smith and A. Seidman. Common due date assignment to minimize total penalty cost for the one machine scheduling problem. Operarions Research, Vol. 30 (1982), pp.391-399.

DOI: 10.1287/opre.30.2.391

Google Scholar

[31] P. Brucker. Scheduling Algorithm. Springer-Verlag, Berlin (2004).

Google Scholar

[32] C. -J. Hsu, T.C.E. Cheng and D. -L. Yang. (2011). Unrelated parallel-machine scheduling with rate-modifying activities to minimize the total completion time. Information Sciences Vol. 181 (2011), pp.4799-4803.

DOI: 10.1016/j.ins.2011.06.010

Google Scholar