Research Article
Year 2015,
Volume: 7 Issue: 1, 19 - 24, 15.01.2015
Abstract
Bu çalışmada tek makineli çizelgelemede öğrenme etkisi analiz edilmiş, performans ölçütü olarak da toplam tamamlanma zamanı ve maksimum gecikme alınmıştır. Çalışmada problemin klasik (öğrenme etkisiz) durumda en iyi çözümü garanti eden Smith Algoritması [1] (maksimum gecikmeyi minimize etme kısıtı altında toplam tamamlanma zamanını minimize etme) ve Van Vassenhove ve Gelder algoritmasının [2] (toplam tamamlanma zamanı ve maksimum gecikmeyi aynı anda minimize etme) öğrenme etkili durumda optimal çözümü garanti etmediği gösterilmiştir. Problemleri çözmek için matematiksel programlama modelleri geliştirilmiştir.
Keywords
Çizelgeleme öğrenme etkisi toplam tamamlanma zamanı maksimum gecikme matematiksel programlama
References
- [1] Smith, W.E. “Various optimizers for single-stage production”, Naval Research Logistics Quarterly 3, 59- 66, 1956. [2] Van Wassenhove, L.N., Gelders, L.F., “Solving a bicriterion scheduling problem”, European Journal of Operational Research, 4(1), 42-48, 1980. [3] Wright, T.P., “Factors Affecting The Cost of Airplanes”, Journal of The Aeronautical Sciences, 3, 122-128, 1936. [4] Biskup, D., “Single-machine scheduling with learning considerations”, European Journal of Operational Research, 115, 173–178, 1999. [5] Mosheiov, G., Scheduling problems with a learning effect European Journal of Operational Research, 132 (3) 2001, 687-693 [6] Mosheiov, G., Sidney, J.B., “Scheduling with general job-dependent learning curves”, European Journal of Operational Research, 147, Issue 3, 16 June 2003, Pages 665-670 [7] Koulamas, C., Kyparisis, G.J., “Single-machine and two-machine flowshop scheduling with general learning functions”, European Journal of Operational Research, 178 (2), 402-407, 2007. [8] Yang, D.L., Kuo, W.H., “Single-machine scheduling with an actual time-dependent learning effect”, Journal of the Operational Research Society, 58, 1348–1353, 2007. [9] Eren, T., Güner, E., “Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu çizelgeleme problemleri”, Trakya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8 (1), 7-13, 2007. [10] Cheng, T.C.E., Wu, C.C., Lee W.C., “Some scheduling problems with sum-of-processing-times-based and jobposition- based learning effects” Information Sciences, 178 (11), 2476-2487, 2008. [11] Cheng, T.C.E. Lai, P.J., Wu, C.C., Lee W.C., “Singlemachine scheduling with sum-of-logarithm processingtimes- based learning considerations”, Information Sciences, 179 (18), 3127-3135, 2009. [12] Wu, C.C., Lee, W.C., “Single-machine scheduling problems with a learning effect”, Applied Mathematical Modelling, 32 (7), 1191-1197, 2008. [13] Wu, C.C., Lee, W.C., “Single-machine and flowshop scheduling with a general learning effect model”, Computers & Industrial Engineering, 56 (4), 1553- 1558, 2009. [14] Wang, J.B., “Single-machine scheduling with general learning functions”, Computers & Mathematics with Applications, 56 (8), 1941-1947, 2008. [15] Wang, J.B., “Single-machine scheduling with a sum-ofactual- processing-time-based learning effect”, Journal of the Operational Research Society 61, 172–177, 2010. [16] Yin, Y., Xu, D., Sun, K., Li, H., “Some scheduling problems with general position-dependent and timedependent learning effects”, Information Sciences, 179 (14), 2416-2425, 2009. [17] Sun, K.B., Li, H.X., “Some single-machine scheduling problems with actual time and position dependent learning effects”, Fuzzy Information and Engineering, 1 (2), 161-177, 2009. [18] Lee, W.C., Wu, C.C., “Some single-machine and mmachine flowshop scheduling problems with learning considerations”, Information Sciences, 179 (22), 3885- 3892, 2009. [19] Zhang, X., Yan, G., “Machine scheduling problems with a general learning effect”, Mathematical and Computer Modelling, 51 (1–2), 84-90, 2010. [20] Lee, W.C., Wu, C.C., Hsu, P.H., “A single-machine learning effect scheduling problem with release times”, Omega, 38 (1–2), 3-11, 2010. [21] Wang, J.B., Wang, D., Zhang, G.D., “Single-machine scheduling with learning functions”, Applied Mathematics and Computation, 216 (4), 1280-1286, 2010, [22] Wang, J.B., Sun, L., Sun, L., “Single machine scheduling with exponential sum-of-logarithm processing-times based learning effect”, Applied Mathematical Modelling, 34 (10), 2813-2819, 2010. [23] Wang, J.B., Sun, L.H., Sun, L.Y., “Scheduling jobs with an exponential sum-of-actual-processingtimebased learning effect”, Computers & Mathematics with Applications, 60 (9), 2673-2678, 2010. [24] Wang, L.Y, Wang, J.J., Wang, J.B., Feng, E.M., “Scheduling jobs with general learning functions”, Journal of Systems Science and Systems Engineering, 20 (1), 119-125, 2011. [25] Wang, J.B., Wang, J.J., “Single-machine scheduling jobs with exponential learning functions”, Computers & Industrial Engineering, 60 (4), 755-759, 2011. [26] Wang, J.B., Wang, J.J., “Scheduling jobs with a general learning effect model”, Applied Mathematical Modelling, 37 (4), 2364-2373, 2013. [27] Lai, P.J., Lee, W.C, “Single-machine scheduling with general sum-of-processing-time-based and position based learning effects”, Omega, 39 (5), 467-471, 2011. [28] Bai, J., Wang, M.Z., Wang, J.B., “Single machine scheduling with a general exponential learning effect”, Applied Mathematical Modelling, 36 (2), 829-835, 2012. [29] Zhang, X., Yan, G., Huang, W., Tang, G., “A note on machine scheduling with sum-of-logarithm processingtime- based and position-based learning effects”, Information Sciences, 187, 298-304, 2012. [30] Lu, Y.Y., Wei, C.M., Wang, J.B., “Several singlemachine scheduling problems with general learning effects”, Applied Mathematical Modelling, basımda, 2012. [31] Kuo, W.H., Yang D.L., “Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect”, European Journal of Operational Research, 174 (2), 1184-1190, 2006. [32] Yin, Y., Xu, D., Wang, J., “Single-machine scheduling with a general sum-of-actual-processing-timesbased and job-position-based learning effect”, Applied Mathematical Modelling, 34 (11), 3623-3630, 2010. [33] Wu, C.C., Hsu, P.H., Lai, K., “Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times”, Journal of Manufacturing Systems, 30 (1) 54-62, 2011. [34] Wu, C.C., Hsu, P.H., Chen, J.C., Wang, N.S., Wu, W.H., “Branch-and-bound and simulated annealing algorithms for a total weighted completion timescheduling with ready times and learning effect, The International Journal of Advanced Manufacturing Technology, 55 (1-4), 341-353, 2011. [35] Wu, C.C., Hsu, P.H., Chen, J.C., Wang, N.S., “Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times”, Computers & Operations Research, 38 (7), 1025-1034, 2011. [36] Wu, CC., Yin, Y., Cheng, S.R., “Some single-machine scheduling problems with a truncation learning effect”, Computers & Industrial Engineering, 60 (4), 790-795, 2011. [37] Low, C., Lin W.Y., “Minimizing the total completion time in a single-machine scheduling problem with a learning effect”, Applied Mathematical Modelling, 35 (4), 1946-1951, 2011. [38] Lee, W.C., “Scheduling with general position-based learning curves”, Information Sciences, 181 (24), 5515- 5522, 2011. [39] Rudek, R., “Scheduling problems with position dependent job processing times: computational complexity results”, Annals of Operations Research, 196 (1), 491-516, 2012. [40] Eren, T., “Tek Makineli Çizelgelemede Genel Öğrenme Fonksiyonları: Optimal Çözümler”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 19 (2),76- 80, 2013. [41] Eren, T., “Zamana-bağımlı öğrenme etkili çizelgeleme probleminde maksimum gecikme minimizasyonu: Doğrusal-olmayan programlama modeli”, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 23 (2), 459-465, 2008. [42] Eren, T., “Zamana-bağımlı öğrenme etkili tek makineli çizelgeleme problemleri”, Sigma Mühendislik ve Fen Bilimleri Dergisi, 31 (2), 214-221, 2013. [43] Eren, T., Güner, E., “Öğrenme etkili çizelgeleme probleminde maksimum gecikmenin enküçüklenmesi için çözüm yaklaşımları”, V. Ulusal Üretim Araştırmaları Sempozyumu, İstanbul Ticaret Üniversitesi, İstanbul, s. 243-248, 25-27 Kasım, 2005. [44] Cheng, T.C.E., Wang, G., “Single machine scheduling with learning effect considerations”, Annals of Operations Research, 98 (1-4), 273-290, 2000. [45] Wu, C.C., Lee, W.C., Chen, T., “Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations”, Computers and Industrial Engineering, 52 (1), 124-132, 2007. [46] Jiang, Z., Chen, F., Wu, C., “Minimizing the maximum lateness in a single-machine scheduling problem with the normal time-dependent and job-dependent learning effect”, Applied Mathematics and Computation, 218 (18), 9438-9441, 2012. [47] GAMS 22.5, Development Corporation, GAMS– the solver manuals, GAMS user notes, Washington, DC, USA, 2007.
Year 2015,
Volume: 7 Issue: 1, 19 - 24, 15.01.2015
Abstract
In this study; learning effect on single machine scheduling is analyzed of total completion time and maximum tardiness is taken as a performance criteria. This study shows that Smith Algorithm [1] (minimizing total completion time subject to minimum maximum tardiness) and Van Vassenhove ve Gelder algorithm [2] (minimizing total completion time and minimize maximum tardiness simultaneously) which guarantees the best solution in classical situation (without learning effect), cannot guarantee the best results in the situation with learning effect. Mathematical programming models are developed for solving these problems.
Keywords
Scheduling learning effect total completion time maximum tardiness mathematical programming
References
- [1] Smith, W.E. “Various optimizers for single-stage production”, Naval Research Logistics Quarterly 3, 59- 66, 1956. [2] Van Wassenhove, L.N., Gelders, L.F., “Solving a bicriterion scheduling problem”, European Journal of Operational Research, 4(1), 42-48, 1980. [3] Wright, T.P., “Factors Affecting The Cost of Airplanes”, Journal of The Aeronautical Sciences, 3, 122-128, 1936. [4] Biskup, D., “Single-machine scheduling with learning considerations”, European Journal of Operational Research, 115, 173–178, 1999. [5] Mosheiov, G., Scheduling problems with a learning effect European Journal of Operational Research, 132 (3) 2001, 687-693 [6] Mosheiov, G., Sidney, J.B., “Scheduling with general job-dependent learning curves”, European Journal of Operational Research, 147, Issue 3, 16 June 2003, Pages 665-670 [7] Koulamas, C., Kyparisis, G.J., “Single-machine and two-machine flowshop scheduling with general learning functions”, European Journal of Operational Research, 178 (2), 402-407, 2007. [8] Yang, D.L., Kuo, W.H., “Single-machine scheduling with an actual time-dependent learning effect”, Journal of the Operational Research Society, 58, 1348–1353, 2007. [9] Eren, T., Güner, E., “Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu çizelgeleme problemleri”, Trakya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8 (1), 7-13, 2007. [10] Cheng, T.C.E., Wu, C.C., Lee W.C., “Some scheduling problems with sum-of-processing-times-based and jobposition- based learning effects” Information Sciences, 178 (11), 2476-2487, 2008. [11] Cheng, T.C.E. Lai, P.J., Wu, C.C., Lee W.C., “Singlemachine scheduling with sum-of-logarithm processingtimes- based learning considerations”, Information Sciences, 179 (18), 3127-3135, 2009. [12] Wu, C.C., Lee, W.C., “Single-machine scheduling problems with a learning effect”, Applied Mathematical Modelling, 32 (7), 1191-1197, 2008. [13] Wu, C.C., Lee, W.C., “Single-machine and flowshop scheduling with a general learning effect model”, Computers & Industrial Engineering, 56 (4), 1553- 1558, 2009. [14] Wang, J.B., “Single-machine scheduling with general learning functions”, Computers & Mathematics with Applications, 56 (8), 1941-1947, 2008. [15] Wang, J.B., “Single-machine scheduling with a sum-ofactual- processing-time-based learning effect”, Journal of the Operational Research Society 61, 172–177, 2010. [16] Yin, Y., Xu, D., Sun, K., Li, H., “Some scheduling problems with general position-dependent and timedependent learning effects”, Information Sciences, 179 (14), 2416-2425, 2009. [17] Sun, K.B., Li, H.X., “Some single-machine scheduling problems with actual time and position dependent learning effects”, Fuzzy Information and Engineering, 1 (2), 161-177, 2009. [18] Lee, W.C., Wu, C.C., “Some single-machine and mmachine flowshop scheduling problems with learning considerations”, Information Sciences, 179 (22), 3885- 3892, 2009. [19] Zhang, X., Yan, G., “Machine scheduling problems with a general learning effect”, Mathematical and Computer Modelling, 51 (1–2), 84-90, 2010. [20] Lee, W.C., Wu, C.C., Hsu, P.H., “A single-machine learning effect scheduling problem with release times”, Omega, 38 (1–2), 3-11, 2010. [21] Wang, J.B., Wang, D., Zhang, G.D., “Single-machine scheduling with learning functions”, Applied Mathematics and Computation, 216 (4), 1280-1286, 2010, [22] Wang, J.B., Sun, L., Sun, L., “Single machine scheduling with exponential sum-of-logarithm processing-times based learning effect”, Applied Mathematical Modelling, 34 (10), 2813-2819, 2010. [23] Wang, J.B., Sun, L.H., Sun, L.Y., “Scheduling jobs with an exponential sum-of-actual-processingtimebased learning effect”, Computers & Mathematics with Applications, 60 (9), 2673-2678, 2010. [24] Wang, L.Y, Wang, J.J., Wang, J.B., Feng, E.M., “Scheduling jobs with general learning functions”, Journal of Systems Science and Systems Engineering, 20 (1), 119-125, 2011. [25] Wang, J.B., Wang, J.J., “Single-machine scheduling jobs with exponential learning functions”, Computers & Industrial Engineering, 60 (4), 755-759, 2011. [26] Wang, J.B., Wang, J.J., “Scheduling jobs with a general learning effect model”, Applied Mathematical Modelling, 37 (4), 2364-2373, 2013. [27] Lai, P.J., Lee, W.C, “Single-machine scheduling with general sum-of-processing-time-based and position based learning effects”, Omega, 39 (5), 467-471, 2011. [28] Bai, J., Wang, M.Z., Wang, J.B., “Single machine scheduling with a general exponential learning effect”, Applied Mathematical Modelling, 36 (2), 829-835, 2012. [29] Zhang, X., Yan, G., Huang, W., Tang, G., “A note on machine scheduling with sum-of-logarithm processingtime- based and position-based learning effects”, Information Sciences, 187, 298-304, 2012. [30] Lu, Y.Y., Wei, C.M., Wang, J.B., “Several singlemachine scheduling problems with general learning effects”, Applied Mathematical Modelling, basımda, 2012. [31] Kuo, W.H., Yang D.L., “Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect”, European Journal of Operational Research, 174 (2), 1184-1190, 2006. [32] Yin, Y., Xu, D., Wang, J., “Single-machine scheduling with a general sum-of-actual-processing-timesbased and job-position-based learning effect”, Applied Mathematical Modelling, 34 (11), 3623-3630, 2010. [33] Wu, C.C., Hsu, P.H., Lai, K., “Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times”, Journal of Manufacturing Systems, 30 (1) 54-62, 2011. [34] Wu, C.C., Hsu, P.H., Chen, J.C., Wang, N.S., Wu, W.H., “Branch-and-bound and simulated annealing algorithms for a total weighted completion timescheduling with ready times and learning effect, The International Journal of Advanced Manufacturing Technology, 55 (1-4), 341-353, 2011. [35] Wu, C.C., Hsu, P.H., Chen, J.C., Wang, N.S., “Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times”, Computers & Operations Research, 38 (7), 1025-1034, 2011. [36] Wu, CC., Yin, Y., Cheng, S.R., “Some single-machine scheduling problems with a truncation learning effect”, Computers & Industrial Engineering, 60 (4), 790-795, 2011. [37] Low, C., Lin W.Y., “Minimizing the total completion time in a single-machine scheduling problem with a learning effect”, Applied Mathematical Modelling, 35 (4), 1946-1951, 2011. [38] Lee, W.C., “Scheduling with general position-based learning curves”, Information Sciences, 181 (24), 5515- 5522, 2011. [39] Rudek, R., “Scheduling problems with position dependent job processing times: computational complexity results”, Annals of Operations Research, 196 (1), 491-516, 2012. [40] Eren, T., “Tek Makineli Çizelgelemede Genel Öğrenme Fonksiyonları: Optimal Çözümler”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 19 (2),76- 80, 2013. [41] Eren, T., “Zamana-bağımlı öğrenme etkili çizelgeleme probleminde maksimum gecikme minimizasyonu: Doğrusal-olmayan programlama modeli”, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 23 (2), 459-465, 2008. [42] Eren, T., “Zamana-bağımlı öğrenme etkili tek makineli çizelgeleme problemleri”, Sigma Mühendislik ve Fen Bilimleri Dergisi, 31 (2), 214-221, 2013. [43] Eren, T., Güner, E., “Öğrenme etkili çizelgeleme probleminde maksimum gecikmenin enküçüklenmesi için çözüm yaklaşımları”, V. Ulusal Üretim Araştırmaları Sempozyumu, İstanbul Ticaret Üniversitesi, İstanbul, s. 243-248, 25-27 Kasım, 2005. [44] Cheng, T.C.E., Wang, G., “Single machine scheduling with learning effect considerations”, Annals of Operations Research, 98 (1-4), 273-290, 2000. [45] Wu, C.C., Lee, W.C., Chen, T., “Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations”, Computers and Industrial Engineering, 52 (1), 124-132, 2007. [46] Jiang, Z., Chen, F., Wu, C., “Minimizing the maximum lateness in a single-machine scheduling problem with the normal time-dependent and job-dependent learning effect”, Applied Mathematics and Computation, 218 (18), 9438-9441, 2012. [47] 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, 2015 |
| Submission Date | October 24, 2017 |
| Published in Issue | Year 2015 Volume: 7 Issue: 1 |
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