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POZİSYON TABANLI ÖĞRENME VE DOĞRUSAL OLMAYAN BOZULMA ETKİSİ ALTINDA İŞ REDDETMELİ TEK MAKİNE ÇİZELGELEME PROBLEMİ

Year 2019, Volume: 7 Issue: 4, 797 - 805, 04.12.2019
https://doi.org/10.36306/konjes.654950

Abstract

Klasik çizelgeleme problemlerinde işlerin işlem sürelerinin sabit olduğu varsayılır ancak gerçek hayat problemlerinde işler öğrenme ve bozulma etkileri altında iken işlem süreleri değişebilmektedir. Ayrıca işlerin işlem sürelerinin fazla olması, üretim ve sabit giderlerin yüksek olması, ekipman ve işgücü yetersizliği gibi sebeplerden dolayı işletmeler ürünlerin işletme içerisinde üretilmemesini isteyebilir. Ürünler dışarıda üretildiğinde bu durum, işletmelere fason maliyeti olarak yansımaktadır. Çalışmamızda, pozisyon tabanlı öğrenme ve doğrusal olmayan bozulma etkisi altında iş reddetmeli tek makineli çizelgeleme problemleri ele alınmıştır. Maksimum tamamlanma zamanı ve reddetme maliyeti minimizasyonu; toplam tamamlanma zamanı ve reddetme maliyeti minimizasyonu olmak üzere iki farklı amaç fonksiyonu ele alınmış, matematiksel programlama ile problemin atama problemi olarak çözülebileceği gösterilmiş, modeller LINGO programı ile çözülmüştür.Bunun yanında maksimum tamamlanma zamanı minimizasyonu probleminin kabul edilen işlerin işlem süresine göre azalan sırada sıralandığında optimum çizelgenin elde edileceği ispatlanmıştır. Bununla birlikte toplam tamamlanma zamanı minimizasyonu probleminin kabul edilen işlerin işlem süresine göre artan sırada sırada sıralandığında optimum çizelgenin elde edileceği ispatlanmıştır. İki farklı öğrenme oranı, iki farklı bozulma oranı ve iki farklı doğrusal olmayan bozulma oranı için ele alınan çizelgeleme problemleri çözülmüştür.

References

  • Azzouz, A., Ennigrou, M., Ben Said, L., 2017, “Scheduling Problems Under Learning Effects: Classification And Cartography”, International Journal of Production Research, 1-20.
  • Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L., 2000, “Multiprocessor Scheduling with Rejection”, SIAM Journal on Discrete Mathematics, 13(1), 64-78.
  • Biskup, D., 1999, “Single-Machine Scheduling with Learning Considerations”, European Journal of Operational Research, 115(1), 173-178.
  • Cheng, T. C. E., Wu, C. C., Chen, J. C., Wu, W. H., Cheng, S. R., 2013, “Two-Machine Flowshop Scheduling With A Truncated Learning Function To Minimize The Makespan”, International Journal of Production Economics, 141(1), 79-86.
  • Gerstl, E., Mosheiov, G., 2012, “Scheduling On Parallel Identical Machines with Job-Rejection And Position-Dependent Processing Times”, Information Processing Letters, 112(19), 743-747.
  • Koulamas, C., Panwalkar, S. S., 2015, “On the Equivalence of Single Machine Earliness/Tardiness Problems with Job Rejection”, Computers & Industrial Engineering, 87, 1-3.
  • Liu, M., 2013, “Parallel-Machine Scheduling With Past-Sequence-Dependent Delivery Times And Learning Effect”, Applied Mathematical Modelling, 37(23), 9630-9633.
  • Mosheiov, G., 2001,“Scheduling Problems with a Learning Effect”, European Journal of Operational Research, 132 (2001), 687– 693.
  • Shabtay, D., Gaspar, N., Kaspi, M., 2013, “A Survey On Offline Scheduling With Rejection”, Journal of Scheduling, 16(1), 3-28.
  • Toksarı, M. D., 2008, Öğrenme Ve Bozulma Etkileri Altında Hazırlık Zamanlı Paralel Makineli Erken Tamamlanma/Gecikme Çizelgeleme Problemi, Doktora Tezi, Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Ankara.
  • Toksarı, M. D., Güner, E., 2009,“Scheduling Problems With The Nonlinear Effects Of Learning And Deterioration”, The International Journal of Advanced Manufacturing Technology, 45(7-8), 801-807.
  • Toksarı, M. D., Arık, O. A., 2017, “Single Machine Scheduling Problems Under Position-Dependent Fuzzy Learning Effect With Fuzzy Processing Times”, Journal of Manufacturing Systems, 45, 159-179.
  • Zhang, L., Lu, L., Yuan, J., 2010,“Single-Machine Scheduling Under the Job Rejection Constraint”, Theoretical Computer Science, 411(16), 1877-1882.

Under Position Dependent Learning and Nonlinear Deterioration Effect on a Single Machine Scheduling Problem with Job Rejection

Year 2019, Volume: 7 Issue: 4, 797 - 805, 04.12.2019
https://doi.org/10.36306/konjes.654950

Abstract

Jobs processing times are constant in classical scheduling problems but in real life problems, jobs processing times can vary because of learning and deterioration effects. Managers may also want to ensure that do not produce products within the companies due to reasons such as excessive processing times, high production costs and fixed costs, equipment and labor shortages. If they want to do jobs outside the companies, they face with outsource cost. In this study, we consider single machine scheduling problem with job rejection under position-dependent learning and nonlinear deterioration effect. There are two scheduling problems with different objective functions. They base on minimization of makespan and minimization of total completion time. It is pointed out that the problem can be solve as assignment problem. For this purpose, a mathematical model is constructed and solved by LINGO. It is proved that for this minimization of makespan objective function, optimum schedule can be obtained when the accepted jobs are scheduled decreasing order according to the accepted jobs’ processing times. Furthermore it is proved that for this minimization of total completion time objective function, optimum schedule can be obtained when the accepted jobs are scheduled increasing order according to the accepted jobs’ processing times. The scheduling problems under study are solved for two different learning rates, two different deterioration rates and two different nonlinear deterioration rates.

References

  • Azzouz, A., Ennigrou, M., Ben Said, L., 2017, “Scheduling Problems Under Learning Effects: Classification And Cartography”, International Journal of Production Research, 1-20.
  • Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L., 2000, “Multiprocessor Scheduling with Rejection”, SIAM Journal on Discrete Mathematics, 13(1), 64-78.
  • Biskup, D., 1999, “Single-Machine Scheduling with Learning Considerations”, European Journal of Operational Research, 115(1), 173-178.
  • Cheng, T. C. E., Wu, C. C., Chen, J. C., Wu, W. H., Cheng, S. R., 2013, “Two-Machine Flowshop Scheduling With A Truncated Learning Function To Minimize The Makespan”, International Journal of Production Economics, 141(1), 79-86.
  • Gerstl, E., Mosheiov, G., 2012, “Scheduling On Parallel Identical Machines with Job-Rejection And Position-Dependent Processing Times”, Information Processing Letters, 112(19), 743-747.
  • Koulamas, C., Panwalkar, S. S., 2015, “On the Equivalence of Single Machine Earliness/Tardiness Problems with Job Rejection”, Computers & Industrial Engineering, 87, 1-3.
  • Liu, M., 2013, “Parallel-Machine Scheduling With Past-Sequence-Dependent Delivery Times And Learning Effect”, Applied Mathematical Modelling, 37(23), 9630-9633.
  • Mosheiov, G., 2001,“Scheduling Problems with a Learning Effect”, European Journal of Operational Research, 132 (2001), 687– 693.
  • Shabtay, D., Gaspar, N., Kaspi, M., 2013, “A Survey On Offline Scheduling With Rejection”, Journal of Scheduling, 16(1), 3-28.
  • Toksarı, M. D., 2008, Öğrenme Ve Bozulma Etkileri Altında Hazırlık Zamanlı Paralel Makineli Erken Tamamlanma/Gecikme Çizelgeleme Problemi, Doktora Tezi, Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Ankara.
  • Toksarı, M. D., Güner, E., 2009,“Scheduling Problems With The Nonlinear Effects Of Learning And Deterioration”, The International Journal of Advanced Manufacturing Technology, 45(7-8), 801-807.
  • Toksarı, M. D., Arık, O. A., 2017, “Single Machine Scheduling Problems Under Position-Dependent Fuzzy Learning Effect With Fuzzy Processing Times”, Journal of Manufacturing Systems, 45, 159-179.
  • Zhang, L., Lu, L., Yuan, J., 2010,“Single-Machine Scheduling Under the Job Rejection Constraint”, Theoretical Computer Science, 411(16), 1877-1882.
There are 13 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Article
Authors

M. Duran Toksarı

Berrin Atalay

Publication Date December 4, 2019
Submission Date April 2, 2018
Acceptance Date May 23, 2019
Published in Issue Year 2019 Volume: 7 Issue: 4

Cite

IEEE M. D. Toksarı and B. Atalay, “POZİSYON TABANLI ÖĞRENME VE DOĞRUSAL OLMAYAN BOZULMA ETKİSİ ALTINDA İŞ REDDETMELİ TEK MAKİNE ÇİZELGELEME PROBLEMİ”, KONJES, vol. 7, no. 4, pp. 797–805, 2019, doi: 10.36306/konjes.654950.