Bozulma ve öğrenme etkisi altında iş reddetmeli çizelgeleme problemi

Year 2025, Volume: 14 Issue: 2, 1 - 1

Berrin Atalay , M. Duran Toksarı

Abstract

Çalışmamızda, iş reddetmeli çizelgeleme ortamında bozulma ve öğrenme etkisi birlikte ele alınmıştır. İşlerin işlem süresi öğrenme etkisiyle azalırken, bozulma etkisiyle de artacaktır. Bu durum, çalışmamızda dört farklı amaç doğrultusunda incelenmiştir. Ele alınan problemler, tek makineli çizelgeleme problemleri için toplam tamamlanma süresinin en aza indirilmesi, çevrim süresinin (makespan) en aza indirilmesi ve TADC minimizasyonu ile paralel makineli çizelgeleme problemleri için çevrim süresinin en aza indirilmesidir. Üç farklı öğrenme oranı (0.8, 0.7, 0.6) ve iki farklı bozulma oranı (0.2, 0.1) kullanılarak 10 iş, 20 iş ve 30 iş içeren problemler matematiksel modeller ve algoritmalar ile çözülmüş ve karşılaştırma tablosu sunulmuştur.

Keywords

Öğrenme etkisi, bozulma etkisi, iş reddetme, tek makine, paralel makine

Job rejection scheduling problems with deterioration and learning effects

Abstract

In our study, deterioration and the learning effect in the job rejection scheduling environment was considered together. The processing time of the jobs will decrease with the effect of learning, but will also increase with the effect of deterioration. In our study, this situation was examined for four different objectives. These problems are total completion time minimization, makespan minimization and TADC minimization for single machine scheduling problems and parallel machine scheduling problems with makespan minimization. With three different learning rates (0.8, 0.7, 0.6) and two different deterioration rates (0.2, 0.1), 10 jobs, 20 jobs and 30 jobs problems are solved with mathematical models and algorithms and a comparison table is presented.

Keywords

Learning effect, deterioration effect, job rejection, single machine, parallel machines

References

• G. Mosheiov, Scheduling problems with a learning effect. European Journal of Operational Research, 132, 687– 693, 2001. https://doi.org/10.1016/S0377-2217(0 0 )00175-2.
• G. Mosheiov, Parallel machine scheduling with a learning effect. Journal of the Operational Research Society, 52(10), 1165-1169, 2001. https://doi.org/10. 1057/palgrave.jors.2601215.
• D. Biskup, Single-machine scheduling with learning considerations. European Journal of Operational Research, 115(1), 173-178, 1999. https://doi.org/10.10 16/S0377-2217(98)00246-X.
• W. C. A. Lee, note on deteriorating jobs and learning in single-machine scheduling problems. International Journal of Business and Economics, 3(1), 83, 2004.
• J. B. Wang, Single-machine scheduling problems with the effects of learning and deterioration. Omega, 35(4), 397-402, 2007. https://doi.org/10.1016/j.omega.2005. 07.008.
• G. Mosheiov, V-shaped policies for scheduling deteriorating jobs. Operations Research, 39(6), 979-991, 1991. https://doi.org/10.1287/opre.39.6.979.
• A. Kononov, NP-hard cases in scheduling deteriorating jobs on dedicated machines. Journal of the Operational Research Society, 52(6), 708-717, 2001. https://doi. org/10.1057/palgrave.jors.2601117.
• Y. C. Hsieh, D. L. Bricker, Scheduling linearly deteriorating jobs on multiple machines. Computers & Industrial Engineering, 32(4), 727-734, 1997. https://doi.org/10.1016/S0360-8352(97)00025-9.
• Y. Bartal, S. Leonardi, A. Marchetti-Spaccamela, J. Sgall, L. Stougie, Multiprocessor scheduling with rejection. SIAM Journal on Discrete Mathematics, 13(1), 64-78, 2000. https://doi.org/10.1137/S08954801 96300522.
• L. Zhang, L. Lu, J. Yuan, Single-machine scheduling under the job rejection constraint. Theoretical Computer Science, 411(16), 1877-1882, 2010. https:// doi.org/10.1016/j.tcs.2010.02.006.
• M. D. Toksarı, D. Oron, E. Güner, Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning. Mathematical and Computer Modelling, 50(3-4), 401-406, 2009. https://doi.org/10.1016/j.mcm.2009.05.026.
• E. Gerstl, G. Mosheiov, Scheduling on parallel identical machines with job-rejection and position-dependent processing times. Information Processing Letters, 112(19), 743-747, 2012. https://doi.org/10.10 16/j.ipl.2012.06.009.
• B. Mor, G. Mosheiov, Total absolute deviation of job completion times on uniform and unrelated machines. Computers & Operations Research, 38(3), 660-665, 2011. https://doi.org/10.1016/j.cor.2010.08.005.
• Y. Li, G. Li, L. Sun, Z. Xu, Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times. International Journal of Production Economics, 118(2), 424-429, 2009. https://doi.org/10.1016/j.ijpe.2008.11.011.
• D. Oron, Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times. Computers & Operations Research, 35(6), 2071-2078, 2008. https://doi.org/10.1016/j.cor. 2006.10.010.
• J. J. Kanet, Minimizing variation of flow time in single machine systems. Management Science, 27(12), 1453-1459, 1981. https://doi.org/10.1287/mnsc.27.12.1453.