Research Article
Year 2014,
Volume: 6 Issue: 1, 15 - 20, 15.01.2014
Abstract
Klasik çizelgeleme problemlerinde işlem zamanları sabit kabul edilmektedir. Halbuki işlem zamanı çeşitli durumlarda bozulma ve öğrenme olgusuyla artar veya azalabilir. Bu makalede bozulma ve öğrenme etkili tek makineli çizelgeleme problemi ele alınmıştır. Ele alınan problemlerin amaç fonksiyonları: maksimum tamamlanma zamanı, toplam tamamlanma zamanı, tamamlanma zamanlarının k’ıncı kuvvetlerinin toplamı, toplam ağırlıklı tamamlanma zamanı, maksimum gecikme ve geciken iş sayısı şeklindedir. Problemleri çözmek için doğrusal-olmayan programlama modelleri geliştirilmiştir.
References
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[7] Wang, J.B., (2009) “Single-machine scheduling with learning effect and deteriorating jobs”, Computers & Industrial Engineering, 57: 1452–1456. [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: 972–982. [9] Sun, L., (2009) “Single-machine scheduling problems with deteriorating jobs and learning effects”, Computers & Industrial Engineering, 57: 843–846. [10] Wang J.B., Huang X., Wang, X.Y. Yin, N., Wang, L.Y., (2009) “Learning effect and deteriorating jobs in the single machine scheduling problems”, Applied Mathematical Modelling, 33: 3848–3853. [11] Wang, J.B., Hsu, C.J., Yang, D.L., (2012) “Single-machine scheduling with effects of exponential learning and general deterioration”, Applied Mathematical Modelling, basımda. [12] Huang, X., Wang, J.B., Wang, L.Y. 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[16] Toksarı, M.D., Oron, D., Güner, E., (2009) “Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning”, Mathematical and Computer Modelling, 50: 401-406 [17] Cheng, T.C.E., Lee, W.C., Wu, C.C., (2010) “Scheduling problems with deteriorating jobs and learning effects including proportional setup times”, Computers & Industrial Engineering 58: 326–331. [18] Yang, D.L., Kuo, W.H., (2010) “Some scheduling problems with deteriorating jobs and learning effects”, Computers & Industrial Engineering, 58: 25–28. [19] Wang, J.B., Guo, Q., (2010) “A due-date assignment problem with learning effect and deteriorating jobs”, Applied Mathematical Modelling, 34: 309–313. [20] Wang, J.B., Wang, C., (2011) “Single-machine due-window assignment problem with learning effect and deteriorating jobs”, Applied Mathematical Modelling, 35: 4017–4022 [21] Yang, S.J., Yang, D.L., (2010) “Single-machine group scheduling problems under the effects of deterioration and learning”, Computers & Industrial Engineering, 58: 754–758. [22] Huang, X., Wang, M.Z., Wang, J.B., (2011) “Single-machine group scheduling with both learning effects and deteriorating jobs”, Computers & Industrial Engineering, 60: 750–754. [23] Yang, S.J., (2011) “Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine”, Applied Mathematical Modelling, 35: 4008–4016. [24] Bai, J., Li, Z.R., Huang, X., (2012). Single-machine group scheduling with general deterioration and learning effects, Applied Mathematical Modelling, 36: 1267–1274. [25] Wang, J.B., Wang, D., Zhang, G.D., (2010). “Single-machine scheduling problems with both deteriorating jobs and learning effects”, Applied Mathematical Modelling, 34: 2831–2839. [26] Yang, S.J., (2010) “Single-machine scheduling problems with both start-time dependent learning and position dependent aging effects under deteriorating maintenance consideration”, Applied Mathematics and Computation, 217: 3321–3329. [27] Yang, S.J., (2012) “Single-machine scheduling problems simultaneously with deterioration and learning effects under deteriorating multi-maintenance activities consideration”, Computers & Industrial Engineering, 62: 271–275. [28] Toksarı, 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: 1361–1365. [29] Yang, D.L., Kuo, W.H., (2011). “Scheduling with deteriorating jobs and learning effects”, Applied Mathematics and Computation, 218: 2069–2073. [30] Lee, W.C., (2012) “Single-machine scheduling with past-sequence-dependent setup times and general effects of deterioration and learning”, Optimation Letters, in press. [31] 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 Discrete Mathematics. 5: 287–326. [32] Bachman, A. Janiak, A. (2000) “Minimizing maximum lateness under linear deterioration”, European Journal of Operational Research, 126: 557–566. [33] Cheng, T.C.E. Wang, G. (2000) “Single machine scheduling with learning effect considerations”, Annals of Operations Reseach, 98: 273–290. [34] Moore, J.M., (1968) “An n job, one machine sequencing algorithm for minimizing the number of tardy jobs” Management Science, 15: 102–109. [35] GAMS 22.5, Development Corporation, GAMS – the solver manuals, GAMS user notes, Washington, DC, USA, 2007.
Year 2014,
Volume: 6 Issue: 1, 15 - 20, 15.01.2014
Abstract
Traditional scheduling models assume that the processing times of jobs are constant. However, there are many situations where the processing time of the job may be subject to change due to deteriorating andr learning phenomena. This paper studies the single-machine scheduling problem with deteriorating and learning effects. We consider the following objective functions: the makespan, the total completion time, the sum of the kth power of completion times, sum of weighted completion times, the maximum lateness and number of tardy jobs minimization. Non-linear programming models are developed for solving these problems.
References
- [1] Cheng, T.C.E., Ding, Q., Lin, B.M.T., (2004) “A concise survey of scheduling with time-dependent processing times”, European Journal of Operational Research, 152: 1–13. [2] Biskup D (2008) A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188: 315–329. [3] Eren, T., (2009) “Human and machine effects in a just-in-time scheduling problem”, Human Factors and Ergonomics in Manufacturing, 19 (4): 294-299. [4] Eren, T., (2013) “Tek Makineli Çizelgelemede Genel Öğrenme Fonksiyonları: Optimal Çözümler”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 19 (2): 76-80. [5] Wang, X., Cheng, T.C.E., (2007) “Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan”, European Journal of Operational Research, 178: 57–70. [6] Wang, J.B., (2007) “Single-machine scheduling problems with the effects of learning and deterioration”, Omega, 35: 397 – 402. [7] Wang, J.B., (2009) “Single-machine scheduling with learning effect and deteriorating jobs”, Computers & Industrial Engineering, 57: 1452–1456. [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: 972–982. [9] Sun, L., (2009) “Single-machine scheduling problems with deteriorating jobs and learning effects”, Computers & Industrial Engineering, 57: 843–846. [10] Wang J.B., Huang X., Wang, X.Y. Yin, N., Wang, L.Y., (2009) “Learning effect and deteriorating jobs in the single machine scheduling problems”, Applied Mathematical Modelling, 33: 3848–3853. [11] Wang, J.B., Hsu, C.J., Yang, D.L., (2012) “Single-machine scheduling with effects of exponential learning and general deterioration”, Applied Mathematical Modelling, basımda. [12] Huang, X., Wang, J.B., Wang, L.Y. Gao, W.J., Wang, X.R., (2010) “Single machine scheduling with time-dependent deterioration and exponential learning effect”, Computers & Industrial Engineering, 58: 58–63. [13] Lee, W.C., Lai, P.J., (2011). “Scheduling problems with general effects of deterioration and learning”, Information Sciences, 181: 1164–1170. [14] Wu, Y.B., Wang, M.Z., Wang, J.B., (2011) “Some single-machine scheduling with both learning and deterioration effects”, Applied Mathematical Modelling, 35: 3731–3736. [15] Wang, L.Y., Wang J.B., Wang, D., Yin, N., Huang X., Feng, E.M., (2009) “Single-machine scheduling with a sum-of-processing-time based learning effect and deteriorating jobs”, Int J Adv Manuf Technol, 45: 336–340. [16] Toksarı, M.D., Oron, D., Güner, E., (2009) “Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning”, Mathematical and Computer Modelling, 50: 401-406 [17] Cheng, T.C.E., Lee, W.C., Wu, C.C., (2010) “Scheduling problems with deteriorating jobs and learning effects including proportional setup times”, Computers & Industrial Engineering 58: 326–331. [18] Yang, D.L., Kuo, W.H., (2010) “Some scheduling problems with deteriorating jobs and learning effects”, Computers & Industrial Engineering, 58: 25–28. [19] Wang, J.B., Guo, Q., (2010) “A due-date assignment problem with learning effect and deteriorating jobs”, Applied Mathematical Modelling, 34: 309–313. [20] Wang, J.B., Wang, C., (2011) “Single-machine due-window assignment problem with learning effect and deteriorating jobs”, Applied Mathematical Modelling, 35: 4017–4022 [21] Yang, S.J., Yang, D.L., (2010) “Single-machine group scheduling problems under the effects of deterioration and learning”, Computers & Industrial Engineering, 58: 754–758. [22] Huang, X., Wang, M.Z., Wang, J.B., (2011) “Single-machine group scheduling with both learning effects and deteriorating jobs”, Computers & Industrial Engineering, 60: 750–754. [23] Yang, S.J., (2011) “Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine”, Applied Mathematical Modelling, 35: 4008–4016. [24] Bai, J., Li, Z.R., Huang, X., (2012). Single-machine group scheduling with general deterioration and learning effects, Applied Mathematical Modelling, 36: 1267–1274. [25] Wang, J.B., Wang, D., Zhang, G.D., (2010). “Single-machine scheduling problems with both deteriorating jobs and learning effects”, Applied Mathematical Modelling, 34: 2831–2839. [26] Yang, S.J., (2010) “Single-machine scheduling problems with both start-time dependent learning and position dependent aging effects under deteriorating maintenance consideration”, Applied Mathematics and Computation, 217: 3321–3329. [27] Yang, S.J., (2012) “Single-machine scheduling problems simultaneously with deterioration and learning effects under deteriorating multi-maintenance activities consideration”, Computers & Industrial Engineering, 62: 271–275. [28] Toksarı, 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: 1361–1365. [29] Yang, D.L., Kuo, W.H., (2011). “Scheduling with deteriorating jobs and learning effects”, Applied Mathematics and Computation, 218: 2069–2073. [30] Lee, W.C., (2012) “Single-machine scheduling with past-sequence-dependent setup times and general effects of deterioration and learning”, Optimation Letters, in press. [31] 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 Discrete Mathematics. 5: 287–326. [32] Bachman, A. Janiak, A. (2000) “Minimizing maximum lateness under linear deterioration”, European Journal of Operational Research, 126: 557–566. [33] Cheng, T.C.E. Wang, G. (2000) “Single machine scheduling with learning effect considerations”, Annals of Operations Reseach, 98: 273–290. [34] Moore, J.M., (1968) “An n job, one machine sequencing algorithm for minimizing the number of tardy jobs” Management Science, 15: 102–109. [35] GAMS 22.5, Development Corporation, GAMS – the solver manuals, GAMS user notes, Washington, DC, USA, 2007.
There are 1 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | January 15, 2014 |
| Submission Date | October 23, 2017 |
| Published in Issue | Year 2014 Volume: 6 Issue: 1 |
Cited By
Sequence Dependent Scheduling Optimization on Plastic Injection Line with Tabu Search Method
Academic Platform Journal of Engineering and Science
Muhammed MOHAMEDSALİH
https://doi.org/10.21541/apjes.923838
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