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SİPARİŞ KABULÜ VE ÇİZELGELENMESİ BÜTÜNLEŞİK PROBLEMİ İÇİN BİR MATEMATİKSEL MODEL

Year 2025, Volume: 36 Issue: 1, 47 - 64, 30.04.2025

Büşra Tutumlu , Tuğba Saraç

https://doi.org/10.46465/endustrimuhendisligi.1601313

Abstract

Literatürde yer alan çizelgeleme konulu çalışmalarda genellikle işlerin tamamının kabul edileceği varsayımı ile tüm işler çizelgelenmektedir. Ancak pek çok işletme kapasite kısıtları nedeniyle gelen siparişlerin hepsini kabul etme şansına sahip değildir. Böyle bir durumda hangi işlerin kabul edileceği önemli bir karar problemidir. Bu nedenle, bu çalışmada sipariş kabulü ve çizelgeleme problemleri bütünleşik olarak ele alınmıştır hem hangi işlerin seçileceğine hem de nasıl çizelgeleneceklerine eş zamanlı karar verilmiştir. Literatürde bu iki önemli problemi birlikte ele alan çalışmalardan farklı olarak sıra ve makine bağımlı hazırlık süreleri, hazır olma zamanları, son teslim zamanları ve iş bölünmesi problem özellikleri göz önünde bulundurulmuştur. Ele alınan problem için amacı toplam karın enbüyüklenmesi olan bir matematiksel model önerilmiştir. Önerilen modelin performansını gösterebilmek için rassal türetilen test problemleri kullanılmıştır. Elde edilen test sonuçları iş bölünmesine izin vermenin toplam karı %33,74’e kadar arttırabileceğini ortaya koymuştur.

Keywords

Sipariş kabulü ve paralel makine çizelgeleme problemi sıra ve makine bağımlı hazırlık süreleri hazır olma zamanları son teslim zamanları iş bölünmesi

References

  • Atsmony, M. ve Mosheiov, G. (2023). Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection. Journal of Scheduling, 26(2), 193-207. Doi: https://doi.org/10.1007/s10951-022-00745-7
  • Bruni, M. E., Khodaparasti, S. ve Demeulemeester, E. (2020). The distributionally robust machine scheduling problem with job selection and sequence-dependent setup times. Computers & Operations Research, 123, 105017. Doi: https://doi.org/10.1016/j.cor.2020.105017
  • Chen, C. L. (2023). An Iterated population-based metaheuristic for order acceptance and scheduling in unrelated parallel machines with several practical constraints. Mathematics, 11(6), 1433. Doi: https://doi.org/10.3390/math11061433
  • Chua, G. A., Ravindran, A., Senga, J. R. L. ve Viswanathan, S. (2023). Job scheduling for maximum revenue on uniform, parallel machines with major and minor setups and job splitting. Computers & Industrial Engineering, 178, 109147. Doi: https://doi.org/10.1016/j.cie.2023.109147
  • Emami, S., Moslehi, G. ve Sabbagh, M. (2017). A Benders decomposition approach for order acceptance and scheduling problem: A robust optimization approach. Computational And Applied Mathematics, 36, 1471-1515. Doi: https://doi.org/10.1007/s40314-015-0302-8
  • Erişgin Barak, M. Z. ve Koyuncu, M. (2021). Fuzzy order acceptance and scheduling on identical parallel machines. Symmetry, 13(7), 1236. Doi: https://doi.org/10.3390/sym13071236
  • Gerstl, E. ve Mosheiov, G. (2012). Scheduling on parallel identical machines with job-rejection and position-dependent processing times. Information Processing Letters, 112(19), 743-747. Doi: https://doi.org/10.1016/j.ipl.2012.06.009
  • Jiang, D. ve Tan, J. (2016). Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines. Theoretical Computer Science, 616, 94-99. Doi: https://doi.org/10.1016/j.tcs.2015.12.020
  • Kis, T. ve Kovács, A. (2012). On bilevel machine scheduling problems. OR Spectrum, 34(1), 43-68. Doi: https://doi.org/10.1007/s00291-010-0219-y
  • Kones, I. ve Levin, A. (2019). A unified framework for designing EPTAS for load balancing on parallel machines. Algorithmica, 81(7), 3025-3046. Doi: https://doi.org/10.1007/s00453-019-00566-9
  • Krim, H., Zufferey, N., Potvin, J. Y., Benmansour, R. ve Duvivier, D. (2022). Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times. Journal of Scheduling, 1-17. Doi: https://doi.org/10.1007/s10951-021-00711-9
  • Li, S. S., Chen, R. X., Feng, Q. ve Jiao, C. W. (2019). Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection. Journal of Combinatorial Optimization, 38(3), 957-971. Doi: https://doi.org/10.1007/ s10878-019-00429-7
  • Li, Y., Tang, L., Bai, D. ve Coelho, L. C. (2024). Profit maximization through integrated order acceptance and scheduling: A metaheuristic approach. Applied Soft Computing, 159, 111570. Doi: https://doi.org/10.1016/ j.asoc.2024.111570
  • Mahmoudinazlou, S., Alizadeh, A., Noble, J. ve Eslamdoust, S. (2024). An improved hybrid ICA-SA metaheuristic for order acceptance and scheduling with time windows and sequence-dependent setup times. Neural Computing and Applications, 36(2), 599-617. Doi: https://doi.org/10.1007/s00521-023-09030-w
  • Mor, B. ve Mosheiov, G. (2018). A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection. Annals of Operations Research, 271, 1079-1085. Doi: https://doi.org/10.1007/s10479-018-2779-1
  • Mor, B. ve Mosheiov, G. (2024). Due-Date assignment with acceptable lead-times on parallel machines. Computers & Operations Research, 166, 106617. Doi: https://doi.org/10.1016/j.cor.2024.106617
  • Mor, B. ve Mosheiov, G. (2024). Scheduling on parallel dedicated machines with job rejection. International Journal of Production Research, 1-8. Doi: https://doi.org/10.1080/00207543.2024.2314714
  • Mosheiov, G. ve Sarig, A. (2024). A common due-date assignment problem with job rejection on parallel uniform machines. International Journal of Production Research, 62(6), 2083-2092. Doi: https://doi.org/10.1080/00207543.2023.2217277
  • Naderi, B. ve Roshanaei, V. (2020). Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling. European Journal of Operational Research, 286(3), 811-827. Doi: https://doi.org/10.1016/j.ejor.2019.10.014
  • Ou, J. ve Zhong, X. (2017). Bicriteria order acceptance and scheduling with consideration of fill rate. European Journal of Operational Research, 262(3), 904-907. Doi: https://doi.org/10.1016/j.ejor.2017.04.036
  • Ou, J., Lu, L. ve Zhong, X. (2023). Parallel-batch scheduling with rejection: Structural properties and approximation algorithms. European Journal of Operational Research, 310(3), 1017-1032. Doi: https://doi.org/10.1016/ j.ejor.2023.04.019
  • Ou, J., Zhong, X. ve Wang, G. (2015). An improved heuristic for parallel machine scheduling with rejection. European Journal of Operational Research, 241(3), 653-661. Doi: https://doi.org/10.1016/j.ejor.2014.09.028
  • Saraç, T. ve Tutumlu, B. (2022). A bi-objective mathematical model for an unrelated parallel machine scheduling problem with job-splitting. Journal of the Faculty of Engineering and Architecture of Gazi University, 37(4), 2293-2307. Doi: https://doi.org/10.17341/gazimmfd.967343
  • Shabtay, D., Karhi, S. ve Oron, D. (2015). Multipurpose machine scheduling with rejection and identical job processing times. Journal of Scheduling, 18(1), 75-88. Doi: https://doi.org/10.1007/s10951-014-0386-9
  • Song, Y., Xue, M., Hua, C. ve Wang, W. (2021). A Column Generation Algorithm for the Resource‐Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines. Mathematical Problems in Engineering, 2021(1), 5566002. Doi: https://doi.org/10.1155/2021/5566002
  • Tarhan, İ. ve Oğuz, C. (2022). A matheuristic for the generalized order acceptance and scheduling problem. European Journal of Operational Research, 299(1), 87-103. Doi: https://doi.org/10.1016/j.ejor.2021.08.024
  • Wang, B. ve Wang, H. (2018). Multiobjective order acceptance and scheduling on unrelated parallel machines with machine eligibility constraints. Mathematical Problems in Engineering, 2018(1), 6024631. Doi: https://doi.org/10.1155/2018/6024631
  • Wang, D., Yin, Y. ve Cheng, T. C. E. (2018). Parallel-machine rescheduling with job unavailability and rejection. Omega, 81, 246-260. Doi: https://doi.org/10.1016/j.omega.2018.04.008
  • Wang, S. ve Ye, B. (2019). Exact methods for order acceptance and scheduling on unrelated parallel machines. Computers & Operations Research, 104, 159-173. Doi: https://doi.org/10.1016/j.cor.2018.12.016
  • Wang, S., Wu, R., Chu, F. ve Yu, J. (2023). An exact decomposition method for unrelated parallel machine scheduling with order acceptance and setup times. Computers & Industrial Engineering, 175, 108899. Doi: https://doi.org/10.1016/j.cie.2022.108899
  • Wu, G. H., Cheng, C. Y., Yang, H. I. ve Chena, C. T. (2018). An improved water flow-like algorithm for order acceptance and scheduling with identical parallel machines. Applied Soft Computing, 71, 1072-1084. Doi: https://doi.org/10.1016/j.asoc.2017.10.015
  • Zhong, X. ve Ou, J. (2017). Improved approximation algorithms for parallel machine scheduling with release dates and job rejection. 4OR, 15, 387-406. Doi: https://doi.org/10.1007/s10288-016-0339-6
  • Zhong, X. ve Ou, J. (2017). Parallel machine scheduling with restricted job rejection. Theoretical Computer Science, 690, 1-11. Doi: https://doi.org/10.1016/j.tcs.2017.05.033
  • Zhong, X., Pan, Z. ve Jiang, D. (2017). Scheduling with release times and rejection on two parallel machines. Journal of Combinatorial Optimization, 33(3), 934-944. Doi: https://doi.org/10.1007/s10878-016-0016-x

Year 2025, Volume: 36 Issue: 1, 47 - 64, 30.04.2025

Büşra Tutumlu , Tuğba Saraç

https://doi.org/10.46465/endustrimuhendisligi.1601313

Abstract

References

  • Atsmony, M. ve Mosheiov, G. (2023). Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection. Journal of Scheduling, 26(2), 193-207. Doi: https://doi.org/10.1007/s10951-022-00745-7
  • Bruni, M. E., Khodaparasti, S. ve Demeulemeester, E. (2020). The distributionally robust machine scheduling problem with job selection and sequence-dependent setup times. Computers & Operations Research, 123, 105017. Doi: https://doi.org/10.1016/j.cor.2020.105017
  • Chen, C. L. (2023). An Iterated population-based metaheuristic for order acceptance and scheduling in unrelated parallel machines with several practical constraints. Mathematics, 11(6), 1433. Doi: https://doi.org/10.3390/math11061433
  • Chua, G. A., Ravindran, A., Senga, J. R. L. ve Viswanathan, S. (2023). Job scheduling for maximum revenue on uniform, parallel machines with major and minor setups and job splitting. Computers & Industrial Engineering, 178, 109147. Doi: https://doi.org/10.1016/j.cie.2023.109147
  • Emami, S., Moslehi, G. ve Sabbagh, M. (2017). A Benders decomposition approach for order acceptance and scheduling problem: A robust optimization approach. Computational And Applied Mathematics, 36, 1471-1515. Doi: https://doi.org/10.1007/s40314-015-0302-8
  • Erişgin Barak, M. Z. ve Koyuncu, M. (2021). Fuzzy order acceptance and scheduling on identical parallel machines. Symmetry, 13(7), 1236. Doi: https://doi.org/10.3390/sym13071236
  • Gerstl, E. ve Mosheiov, G. (2012). Scheduling on parallel identical machines with job-rejection and position-dependent processing times. Information Processing Letters, 112(19), 743-747. Doi: https://doi.org/10.1016/j.ipl.2012.06.009
  • Jiang, D. ve Tan, J. (2016). Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines. Theoretical Computer Science, 616, 94-99. Doi: https://doi.org/10.1016/j.tcs.2015.12.020
  • Kis, T. ve Kovács, A. (2012). On bilevel machine scheduling problems. OR Spectrum, 34(1), 43-68. Doi: https://doi.org/10.1007/s00291-010-0219-y
  • Kones, I. ve Levin, A. (2019). A unified framework for designing EPTAS for load balancing on parallel machines. Algorithmica, 81(7), 3025-3046. Doi: https://doi.org/10.1007/s00453-019-00566-9
  • Krim, H., Zufferey, N., Potvin, J. Y., Benmansour, R. ve Duvivier, D. (2022). Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times. Journal of Scheduling, 1-17. Doi: https://doi.org/10.1007/s10951-021-00711-9
  • Li, S. S., Chen, R. X., Feng, Q. ve Jiao, C. W. (2019). Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection. Journal of Combinatorial Optimization, 38(3), 957-971. Doi: https://doi.org/10.1007/ s10878-019-00429-7
  • Li, Y., Tang, L., Bai, D. ve Coelho, L. C. (2024). Profit maximization through integrated order acceptance and scheduling: A metaheuristic approach. Applied Soft Computing, 159, 111570. Doi: https://doi.org/10.1016/ j.asoc.2024.111570
  • Mahmoudinazlou, S., Alizadeh, A., Noble, J. ve Eslamdoust, S. (2024). An improved hybrid ICA-SA metaheuristic for order acceptance and scheduling with time windows and sequence-dependent setup times. Neural Computing and Applications, 36(2), 599-617. Doi: https://doi.org/10.1007/s00521-023-09030-w
  • Mor, B. ve Mosheiov, G. (2018). A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection. Annals of Operations Research, 271, 1079-1085. Doi: https://doi.org/10.1007/s10479-018-2779-1
  • Mor, B. ve Mosheiov, G. (2024). Due-Date assignment with acceptable lead-times on parallel machines. Computers & Operations Research, 166, 106617. Doi: https://doi.org/10.1016/j.cor.2024.106617
  • Mor, B. ve Mosheiov, G. (2024). Scheduling on parallel dedicated machines with job rejection. International Journal of Production Research, 1-8. Doi: https://doi.org/10.1080/00207543.2024.2314714
  • Mosheiov, G. ve Sarig, A. (2024). A common due-date assignment problem with job rejection on parallel uniform machines. International Journal of Production Research, 62(6), 2083-2092. Doi: https://doi.org/10.1080/00207543.2023.2217277
  • Naderi, B. ve Roshanaei, V. (2020). Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling. European Journal of Operational Research, 286(3), 811-827. Doi: https://doi.org/10.1016/j.ejor.2019.10.014
  • Ou, J. ve Zhong, X. (2017). Bicriteria order acceptance and scheduling with consideration of fill rate. European Journal of Operational Research, 262(3), 904-907. Doi: https://doi.org/10.1016/j.ejor.2017.04.036
  • Ou, J., Lu, L. ve Zhong, X. (2023). Parallel-batch scheduling with rejection: Structural properties and approximation algorithms. European Journal of Operational Research, 310(3), 1017-1032. Doi: https://doi.org/10.1016/ j.ejor.2023.04.019
  • Ou, J., Zhong, X. ve Wang, G. (2015). An improved heuristic for parallel machine scheduling with rejection. European Journal of Operational Research, 241(3), 653-661. Doi: https://doi.org/10.1016/j.ejor.2014.09.028
  • Saraç, T. ve Tutumlu, B. (2022). A bi-objective mathematical model for an unrelated parallel machine scheduling problem with job-splitting. Journal of the Faculty of Engineering and Architecture of Gazi University, 37(4), 2293-2307. Doi: https://doi.org/10.17341/gazimmfd.967343
  • Shabtay, D., Karhi, S. ve Oron, D. (2015). Multipurpose machine scheduling with rejection and identical job processing times. Journal of Scheduling, 18(1), 75-88. Doi: https://doi.org/10.1007/s10951-014-0386-9
  • Song, Y., Xue, M., Hua, C. ve Wang, W. (2021). A Column Generation Algorithm for the Resource‐Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines. Mathematical Problems in Engineering, 2021(1), 5566002. Doi: https://doi.org/10.1155/2021/5566002
  • Tarhan, İ. ve Oğuz, C. (2022). A matheuristic for the generalized order acceptance and scheduling problem. European Journal of Operational Research, 299(1), 87-103. Doi: https://doi.org/10.1016/j.ejor.2021.08.024
  • Wang, B. ve Wang, H. (2018). Multiobjective order acceptance and scheduling on unrelated parallel machines with machine eligibility constraints. Mathematical Problems in Engineering, 2018(1), 6024631. Doi: https://doi.org/10.1155/2018/6024631
  • Wang, D., Yin, Y. ve Cheng, T. C. E. (2018). Parallel-machine rescheduling with job unavailability and rejection. Omega, 81, 246-260. Doi: https://doi.org/10.1016/j.omega.2018.04.008
  • Wang, S. ve Ye, B. (2019). Exact methods for order acceptance and scheduling on unrelated parallel machines. Computers & Operations Research, 104, 159-173. Doi: https://doi.org/10.1016/j.cor.2018.12.016
  • Wang, S., Wu, R., Chu, F. ve Yu, J. (2023). An exact decomposition method for unrelated parallel machine scheduling with order acceptance and setup times. Computers & Industrial Engineering, 175, 108899. Doi: https://doi.org/10.1016/j.cie.2022.108899
  • Wu, G. H., Cheng, C. Y., Yang, H. I. ve Chena, C. T. (2018). An improved water flow-like algorithm for order acceptance and scheduling with identical parallel machines. Applied Soft Computing, 71, 1072-1084. Doi: https://doi.org/10.1016/j.asoc.2017.10.015
  • Zhong, X. ve Ou, J. (2017). Improved approximation algorithms for parallel machine scheduling with release dates and job rejection. 4OR, 15, 387-406. Doi: https://doi.org/10.1007/s10288-016-0339-6
  • Zhong, X. ve Ou, J. (2017). Parallel machine scheduling with restricted job rejection. Theoretical Computer Science, 690, 1-11. Doi: https://doi.org/10.1016/j.tcs.2017.05.033
  • Zhong, X., Pan, Z. ve Jiang, D. (2017). Scheduling with release times and rejection on two parallel machines. Journal of Combinatorial Optimization, 33(3), 934-944. Doi: https://doi.org/10.1007/s10878-016-0016-x
There are 34 citations in total.

Details

Primary Language Turkish
Subjects Industrial Engineering
Journal Section Research Articles
Authors

Büşra Tutumlu 0000-0002-0662-8128

Tuğba Saraç 0000-0002-8115-3206

Publication Date April 30, 2025
Submission Date December 14, 2024
Acceptance Date January 29, 2025
Published in Issue Year 2025 Volume: 36 Issue: 1

Cite

APA Tutumlu, B., & Saraç, T. (2025). SİPARİŞ KABULÜ VE ÇİZELGELENMESİ BÜTÜNLEŞİK PROBLEMİ İÇİN BİR MATEMATİKSEL MODEL. Endüstri Mühendisliği, 36(1), 47-64. https://doi.org/10.46465/endustrimuhendisligi.1601313
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