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A BICRITERIA SINGLE MACHINE SCHEDULING WITH EXPONENTIAL SUM-OF-LOGARITHM-PROCESSING-TIMES BASED LEARNING EFFECT

Year 2013, Volume: 14 Issue: 2, 99 - 104, 17.03.2015

Abstract

In traditional scheduling problems, most literature assumes that the processing time of a job is fixed. However, there are many situations where the processing time of a job depends on the starting time or the position of the job in a sequence. In such situations, the actual processing time of a job may be more or less than its normal processing time if it is scheduled later. This phenomenon is known as the ‘‘learning effect’’. In this study, we introduce a exponential sum-of-logarithm-processingtimes based learning effect into a single-machine scheduling problem. We consider the following objective function minimize maximum lateness subject to the number of tardy jobs A non-linear programming model are developed for problem. Also the model is tested on an example

References

  • BISKUP, D., A state-of-the-art review on scheduling with learning effects, European Journal of Operational Research, 188(2), 315-329, 2008.
  • BISKUP, D., Single-machine scheduling with learning considerations, European Journal of Operational Research, 115, 173-178, 1999.
  • CHEN, C.L. BULFIN, R.L., Scheduling a single machine to minimize two criteria: maximum tardiness and number of tardy jobs, IIE Transactions, 26, 76-84, 1994.
  • EREN, T., Öğrenme etkili çizelgeleme problemi: Geciken iş sayısı minimizasyonu, Teknoloji Dergisi, 10(4), 235-238, 2007.
  • EREN, T., Solving scheduling problem with time dependent learning effect to number of tardy jobs and range of lateness criteria, Journal of The Faculty of Engineering and Architecture of Gazi University, 23(2), 459-465, 2008.
  • EREN, T., Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu tek makineli çizelgeleme problemi: Geciken iş sayısı minimizasyonu, International Journal of Engineering Research and Development, 6(6), 34-36, 2011.
  • EREN, T., Logaritmik toplam işlem zaman tabanlı öğrenme etkili tek makineli çizelgeleme: geciken iş sayısı minimizasyonu, Nevşehir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 1, 83-88, 2012a
  • EREN, T., Logaritmik Toplam İşlem Zaman Tabanlı Öğrenme Etkili Tek Makineli Çizelgeleme: Toplam Erken Bitirme Ve Toplam Gecikme Minimizasyonu” Niğde Üniversitesi Mühendislik Fakültesi Dergisi, 1 (2), 61-68, 2012b.
  • EREN, T., Minimizing the maximum lateness in a schedulıng problem with a time-dependent learning effect: a non-linear programming model, Journal of The Faculty of Engineering and Architecture of Gazi University, 27 (4), 875-879, 2012c.
  • EREN, T. GÜNER, E., Minimizing total tardiness in a scheduling problem with a learning effect, Applied Mathematical Modelling, 31, 1351-1361, 2007a.
  • EREN, T. GÜNER, E., Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu çizelgeleme problemleri, Trakya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 7-13, 2007b.
  • GAMS 22.5 Development CorporationGAMS – the solver manuals, GAMS user notes, Washington, DC USA, 2007.
  • GUPTA, J.N.D. HARIRI, A.M.A. POTTS, C.N., Single-machine scheduling to minimize maximum tardiness with minimum number of tardy jobs, Annals of Operations Research, 92, 107 -123, 1999.
  • GUPTA, J.N.D. RAMNARAYANAN, R., Single Facility Scheduling with Dual Criteria: Minimizing Maximum Tardiness Subject to Minimum Number of Tardy Jobs, Production Planning and Control, 70, 127-143, 1996.
  • HUO, Y. LEUNG, J.Y.T. ZHAO, H., Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness, European Journal of Operational Research, 177, 116–134, 2007.
  • 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, 1184-1190, 2006a.
  • KUO, W.H. YANG, D.L., Minimizing the makespan in a single machine scheduling problem with a time-based learning effect, Information Processing Letters, 97, 64–67. 2006b.
  • KUO, W.H. YANG, D.L., Single-machine group scheduling with a time dependent learning effect, Computers and Operations Research, 33, 2099-2112, 2006c.
  • LIAO, C.J. HUANG, R.H. TSENG, S.T., Use of Variable Range in Solving Multiple Criteria Scheduling Problems, Computers and Operations Research, 19(5), 453-460, 1992.
  • MOORE, J.M., An n job, one machine sequencing algorithm for minimizing the number of tardy jobs, Management Science, 15, 102–109, 1968.
  • MOSHEIOV, G., Scheduling problems with a learning effect, European Journal of Operational Research, 132, 687-693, 2001.
  • MOSHEIOV, G. SIDNEY, J.B., Note on scheduling with general learning curves to minimize the number of tardy jobs, Journal of the Operational Research Society, 56, 110–112, 2005.
  • NELSON, R.T. SARIN, R.K. DANIELS, R.L. Scheduling with multiple performance measures: the one machine case, Management Science, 32(4), 464–479, 1986.
  • SHANTHIKUMAR, J.G., Scheduling n jobs on one machine to minimize the maximum tardiness with minimum number tardy, Computers Operations Research, 10, 255-266, 1983.
  • WANG, J.B. LINHUI, S. LINYAN, S., Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect, Applied Mathematical Modelling, 34, 2813–2819, 2010.
  • WU, C.C. LEE, W.C. CHEN, T., Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations, Computers & Industrial Engineering, 52, 124-132, 2007.
  • ZHAO,C.L. ZHANG,Q.L. TANG, H.Y., Machine scheduling problems with learning effects, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 11, 741-750, 2004.

İKİ ÖLÇÜTLÜ ÜSSEL İŞLEM ZAMAN TABAN TOPLAMLI ÖĞRENME ETKİLİ TEK MAKİNELİ ÇİZELGELEME PROBLEMİ

Year 2013, Volume: 14 Issue: 2, 99 - 104, 17.03.2015

Abstract

Çizelgeleme literatürünün çoğunda işlerin işlem zamanları sabit kabul edilmiştir. Ancak işlerin işlem zamanlarında, başlama zamanı veya pozisyonuna bağlı olarak azalma görülebilmektedir. Bu olgu literatürde öğrenme etkisi olarak bilinmektedir. Bu çalışmada üssel işlem zaman taban toplamlı öğrenme etkili tek makineli çizelgeleme problemi ele alınacaktır. Ele alınan problemlerin amaç fonksiyonu geciken iş sayısı kısıtı altında maksimum gecikmeyi minimize etmektir. Problemi çözmek için doğrusal-olmayan programlama modeli geliştirilmiştir. Geliştirilen model örnek üzerinde uygulanmıştır.

References

  • BISKUP, D., A state-of-the-art review on scheduling with learning effects, European Journal of Operational Research, 188(2), 315-329, 2008.
  • BISKUP, D., Single-machine scheduling with learning considerations, European Journal of Operational Research, 115, 173-178, 1999.
  • CHEN, C.L. BULFIN, R.L., Scheduling a single machine to minimize two criteria: maximum tardiness and number of tardy jobs, IIE Transactions, 26, 76-84, 1994.
  • EREN, T., Öğrenme etkili çizelgeleme problemi: Geciken iş sayısı minimizasyonu, Teknoloji Dergisi, 10(4), 235-238, 2007.
  • EREN, T., Solving scheduling problem with time dependent learning effect to number of tardy jobs and range of lateness criteria, Journal of The Faculty of Engineering and Architecture of Gazi University, 23(2), 459-465, 2008.
  • EREN, T., Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu tek makineli çizelgeleme problemi: Geciken iş sayısı minimizasyonu, International Journal of Engineering Research and Development, 6(6), 34-36, 2011.
  • EREN, T., Logaritmik toplam işlem zaman tabanlı öğrenme etkili tek makineli çizelgeleme: geciken iş sayısı minimizasyonu, Nevşehir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 1, 83-88, 2012a
  • EREN, T., Logaritmik Toplam İşlem Zaman Tabanlı Öğrenme Etkili Tek Makineli Çizelgeleme: Toplam Erken Bitirme Ve Toplam Gecikme Minimizasyonu” Niğde Üniversitesi Mühendislik Fakültesi Dergisi, 1 (2), 61-68, 2012b.
  • EREN, T., Minimizing the maximum lateness in a schedulıng problem with a time-dependent learning effect: a non-linear programming model, Journal of The Faculty of Engineering and Architecture of Gazi University, 27 (4), 875-879, 2012c.
  • EREN, T. GÜNER, E., Minimizing total tardiness in a scheduling problem with a learning effect, Applied Mathematical Modelling, 31, 1351-1361, 2007a.
  • EREN, T. GÜNER, E., Hazırlık ve taşıma zamanlarının öğrenme etkili olduğu çizelgeleme problemleri, Trakya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 7-13, 2007b.
  • GAMS 22.5 Development CorporationGAMS – the solver manuals, GAMS user notes, Washington, DC USA, 2007.
  • GUPTA, J.N.D. HARIRI, A.M.A. POTTS, C.N., Single-machine scheduling to minimize maximum tardiness with minimum number of tardy jobs, Annals of Operations Research, 92, 107 -123, 1999.
  • GUPTA, J.N.D. RAMNARAYANAN, R., Single Facility Scheduling with Dual Criteria: Minimizing Maximum Tardiness Subject to Minimum Number of Tardy Jobs, Production Planning and Control, 70, 127-143, 1996.
  • HUO, Y. LEUNG, J.Y.T. ZHAO, H., Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness, European Journal of Operational Research, 177, 116–134, 2007.
  • 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, 1184-1190, 2006a.
  • KUO, W.H. YANG, D.L., Minimizing the makespan in a single machine scheduling problem with a time-based learning effect, Information Processing Letters, 97, 64–67. 2006b.
  • KUO, W.H. YANG, D.L., Single-machine group scheduling with a time dependent learning effect, Computers and Operations Research, 33, 2099-2112, 2006c.
  • LIAO, C.J. HUANG, R.H. TSENG, S.T., Use of Variable Range in Solving Multiple Criteria Scheduling Problems, Computers and Operations Research, 19(5), 453-460, 1992.
  • MOORE, J.M., An n job, one machine sequencing algorithm for minimizing the number of tardy jobs, Management Science, 15, 102–109, 1968.
  • MOSHEIOV, G., Scheduling problems with a learning effect, European Journal of Operational Research, 132, 687-693, 2001.
  • MOSHEIOV, G. SIDNEY, J.B., Note on scheduling with general learning curves to minimize the number of tardy jobs, Journal of the Operational Research Society, 56, 110–112, 2005.
  • NELSON, R.T. SARIN, R.K. DANIELS, R.L. Scheduling with multiple performance measures: the one machine case, Management Science, 32(4), 464–479, 1986.
  • SHANTHIKUMAR, J.G., Scheduling n jobs on one machine to minimize the maximum tardiness with minimum number tardy, Computers Operations Research, 10, 255-266, 1983.
  • WANG, J.B. LINHUI, S. LINYAN, S., Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect, Applied Mathematical Modelling, 34, 2813–2819, 2010.
  • WU, C.C. LEE, W.C. CHEN, T., Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations, Computers & Industrial Engineering, 52, 124-132, 2007.
  • ZHAO,C.L. ZHANG,Q.L. TANG, H.Y., Machine scheduling problems with learning effects, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 11, 741-750, 2004.
There are 27 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Articles
Authors

Tamer Eren

Publication Date March 17, 2015
Published in Issue Year 2013 Volume: 14 Issue: 2

Cite

IEEE T. Eren, “İKİ ÖLÇÜTLÜ ÜSSEL İŞLEM ZAMAN TABAN TOPLAMLI ÖĞRENME ETKİLİ TEK MAKİNELİ ÇİZELGELEME PROBLEMİ”, TUJES, vol. 14, no. 2, pp. 99–104, 2015.