Öğrenme Etkili Çizelgelemede Maksimimum Gecikme ve Toplam Tamamlanma Zamanı Minimizasyonu
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.
Minimizing the Total Completion Time and Maximum Tardiness on a Scheduling with a Learning Effect
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.
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- [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.