Bulanık Bozulma ve Öğrenme Etkileri Altında Tek Makine Erken/Geç Tamamlanma Probleminin Bulanık Şans Kısıtlı Programlama Tekniği ile İncelenmesi

Yıl 2018, , 650 - 660, 01.04.2018

Oğuzhan Ahmet Arık , Mehmet Duran Toksarı

https://doi.org/10.16984/saufenbilder.299354

Cited By: 3

Öz

 Bu çalışmada tek makine
ortamında bulanık bozulma ve öğrenme etkileri altında ağırlıklı erken/geç
tamamlanma maliyetlerinin en aza indirilmesi amaçlanmaktadır. Probleme konu
olan teslim tarihleri, işlem süreleri, öğrenme etkisi katsayıları ve bozulma
etkisi katsayıları belirsizlik altındadır ve belirsizliği modelleyebilmek için
üçgen bulanık sayılardan faydalanılmıştır. Belirsizlik parametrelere ait
değerlerin rassal olarak ifade edilmesi değildir; iyi bilinmeyen, kesin olarak
ifade edilemeyen değerlerin kapalı bir aralık içerisinde tanımlanmasıdır. Öyle
ki, daha önce yapılmamış bir işe ait işlem süresinin ne kadar olacağının
belirlenmesi bulanık sayılardan faydalanılarak, gerçekleşmesi beklenen işlem
süresinin karar verici için uygunluğu modellenebilir. Böylelikle,
parametrelerdeki belirsizlik belirgin bir hale getirilerek modellenebilir.
Öğrenme etkisi bir işin sürekli olarak yapılan tekrarları neticesinde, iş yapan
birimin işi her seferde kazandığı tecrübe ile daha kısa sürede yapmasını ifade
etmektedir. Yapılan iş tekrarı artıkça işlem iş tekrarlarındaki işlem süresi
giderek azalacaktır. Bozulma etkisi ise iş parçasının işlem için kuyrukta
beklerken veya işlenirken, çevre koşulları ya da sistem karakteristikleri
gereği işlem süresinin giderek artmasıdır. Bu çalışmada işlem süreleri, teslim
tarihleri, bozulma etkisi ve öğrenme etkisi bulanık sayılar ile ifade
edilmiştir. Bulanık sayılar ile ifade edilen bir parametreye ait bir değerin
gerçekleşme olayının şans değeri ise güvenilirlik fonksiyonu ile kurgulanmış ve
güvenirlik temelli şans kısıtlı algoritma tekniği ile model oluşturulmuştur.
Son olarak tam sayılı bulanık doğrusal olmayan matematiksel model sunulmuş ve
örnek veri seti ile problem çözülmüştür. 

Anahtar Kelimeler

Tek makine, erken ve geç tamamlanma, bulanık parametreler, şans kısıtlı programlama, karma tam sayılı doğrusal olmayan bulanık programlama

Fuzzy chance constrained programming technique for single machine earliness/tardiness scheduling problem under effects of fuzzy learning and deterioration

Öz

To minimize total weighted earliness/tardiness costs of the
jobs under effects of deterioration and learning on a single machine in a fully
fuzzy environment, a mixed integer fuzzy non-linear mathematical programming
model is presented in this study. Parameters in this study such as processing
times, learning effect and deterioration effect are considered as fuzzy numbers
because of their uncertainties. Learning and deterioration effects have been
considered in scheduling problems for twenty years. Earliness/tardiness
scheduling problems are significant for manufactures that adopt themselves in
Just-in-Time philosophy. In order to model the real life complexity of Just-in-Time
manufactures, earliness/tardiness scheduling problems can be used with mixed
integer mathematical programming models. In this study, fuzzy chance
constrained mathematical programming technique is used to find crisp equivalent
of the proposed mixed integer fuzzy non-linear mathematical programming model
and solve it.  

Anahtar Kelimeler

Single machine, earliness and tardiness, fuzzy parameters, chance constrained programming, fuzzy mixed integer nonlinear programming

Kaynakça

• D. Biskup. (1999). Single-machine scheduling with learning considerations. Eur. J. Operat. Res. 115, pp 173-178.
• G. Mosheiov. (2001). Scheduling problems with a learning effect. Eur. J. Operat. Res. 132, pp 687-693.
• G. Mosheiov, J. B. Sidney. (2003). Scheduling with general job-dependent learning curves. Eur. J. Operat. Res. 147, pp 665-670.
• A. Bachman, A. Janiak. (2004). Scheduling jobs with position-dependent processing times. J. Operat. Res. Soc. 55, pp 257-264.
• Kuo, W. H., & Yang, D. L. (2006). Minimizing the total completion time in a single machine scheduling problem with a time dependent learning effect. Eur. J. Operat. Res. 174(2), pp 1184-1190.
• C. Koulamas, G.J. Kyparisis. (2007). Single machine and two machine flowshop scheduling with general learning functions. Eur. J. Operat. Res. 178 (2), pp 402-407.
• T. Eren, E. Güner, (2007). Minimizing total tardiness in a scheduling problem with a learning effect. Applied Mathematical Model. 31(7), pp 1351-1361.
• J. N. D. Gupta, S. K. Gupta. (1988). Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, pp 387-393.
• S. Browne, U. Yechiali. (1990). Scheduling deteriorating jobs on a single processor. Operat. Res. 38, pp 495-498.
• G. Mosheiov. (1991). V-shaped policies for scheduling deteriorating jobs. Operat. Res. 39, pp 979-991.
• G. Mosheiov. (1994). Scheduling jobs under simple linear deterioration. Computational Operat. 21(6), pp 653-659.
• G. Mosheiov. (1995). Scheduling jobs with step-deterioration; Minimizing makespan on a single machine. Comput. Ind. Eng. 28, pp 869-879.
• G. Mosheiov, ⋀-shaped policies to schedule deteriorating jobs. J. Operat. Res. Soc. 47 (1996) 1184-1191.
• X. Wang, T.C.E. Cheng. (2007). Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan. Eur. J. Operat. Res. 178(1), pp 57-70.
• J.B. Wang. (2007). Single-machine scheduling problems with the effects of learning and deterioration. Omega. 35(4), pp 397-402.
• T.C.E. Cheng, C.C. Wu, W.C. Lee. (2008). Some scheduling problems with deteriorating jobs and learning effects. Comp. Ind. Eng. 54(4), pp 972-982.
• M. D. Toksarı, E. Guner. (2008). Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: A mixed nonlinear integer programming approach. Adv. Man. Technol. 38(7–8), pp 801-808.
• M. D. Toksarı, E. Güner. (2009). Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration. Comput. Operat. Res. 36(8), pp 2394-2417.
• J.B. Wang, X. Huang, X.Y. Wang, N. Yin, L.Y. Wang. (2009). Learning effect and deteriorating jobs in the single machine scheduling problems. App. Math. Modeling. 33, pp 3848-3853.
• J.B. Wang, Q. Guo. (2010). A due-date assignment problem with learning effect and deteriorating jobs. App. Math. Modeling. 34, pp 309-313.
• Y.B. Wu, M.Z. Wang, J.B. Wang. (2011). Some single-machine scheduling with both learning and deterioration effects. App. Math. Modeling. 35, pp 3731-3736.
• S.J. Yang. (2011). Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine. App. Mathematical Modeling. 35, pp 4008-4016.
• W.C. Lee, P.J. Lai. (2011). Scheduling problems with general effects of deterioration and learning. Information Sciences. 181, pp 1164-1170.
• J. Bai, Z.R. Li, X. Huang. (2012). Single-machine group scheduling with general deterioration and learning effects. App. Math. Model. 36, pp 1267-1274.
• S.J. Yang. (2012). Single-machine scheduling problems simultaneously with deterioration and learning effects under deteriorating multi-maintenance activities consideration. Comput. Ind. Eng. 62, pp 271-275.
• J.B. Wang, C.J. Hsu, D.L. Yang. (2013). Single-machine scheduling with effects of exponential learning and general deterioration. App. Math. Modeling. 37, pp 2293-2299.
• J.B. Wang, L. Liu, C. Wang. (2013). Single machine SLK/DIF due window assignment problem with learning effect and deteriorating jobs. App. Math. Modeling. 37, pp 8394-8400.
• S. H. Pakzad-Moghaddam, H. Mina, R. Tavakkoli-Moghaddam. (2014). An approach for modeling a new single machine scheduling problem with deteriorating and learning effects. Computers & Industrial Engineering. 78, pp 33-43.
• X. Huang, M. Z. Wang, P. Ji. (2014). Parallel machines scheduling with deteriorating and learning effects. Optimization Letters. 8(2), pp 493-500.
• S. Han, H. Ishii, S. Fujii. (1994). One machine scheduling problem with fuzzy due dates. Eur. J. Operat. Res. 79, pp 1-12.
• H. Ishii, M. Tada. (1995). Single machine scheduling problem with fuzzy precendence relation. Eur. J. Operat. Res. 87(2), pp 284-288.
• L.M. Liao, C.J. Liao. (1998). Single machine scheduling problem with fuzzy due date and processing time. J. Chinese Inst. Eng. 21(2), pp 189-196.
• T. Itoh, H. Ishii. (1999). Fuzzy due-date scheduling problem with fuzzy processing time. Intl. Trans. in Op. Res. 6, pp 639-647.
• S, Chanas, A. Kasperski. (2001). Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates. Eng. App. of Artif. Intel. 14, pp 377-386.
• S.S. Lam, X. Cai. (2002). Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates. Nonlinear Analysis: Real World Applications. 3, pp 307-316.
• C. Wang, D. Wang, W.H. Ip, D.W. Yuen. (2002). The single machine ready time scheduling problem with fuzzy processing times. Fuzzy Sets and Systems. 127, pp 117-129.
• S, Chanas, A. Kasperski. (2003). On two single machine scheduling problems with fuzzy processing times and fuzzy due dates. Eur. J. Operat. Res. 147, pp 281-296.
• S.C. Sung, M. Vlach. (2003). Single machine scheduling to minimize the number of late jobs under uncertainty. Fuzzy Sets and Systems. 139, pp 421-430.
• K. Muthusamy, S.C. Sung, M. Vlach, H. Ishii. (2003). Scheduling with fuzzy delays and fuzzy precedences. Fuzzy Sets and Systems. 134, pp 387-395.
• S, Chanas, A. Kasperski. (2004). Possible and necessary optimality of solutions in the single machine scheduling problem with fuzzy parameters. Fuzzy Sets and Systems. 142(3), pp 359-371.
• T. Itoh, H. Ishii. (2005). One machine scheduling problem with fuzzy random due-dates. Fuzzy Optim. Dec. Making. 4, pp 71-78.
• K.K. Harikrishnan, H. Ishii. (2005). Single machine batch scheduling problem with resource dependent setup and processing time in the presence of fuzzy due date. Fuzzy Optim. and Dec. Making. 4, pp 141-147.
• A. Kasperski. (2007). Some general properties of a fuzzy single machine scheduling problem. Intern. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 15(1), pp 43-46.
• A. Duenas, D. Petrovic. (2008). Multi-objective genetic algorithm for single machine scheduling problem under fuzziness. Fuzzy Optim. Decis. Making. 7, pp 87-104.
• B. Cheng, K. Li, B. Chen. (2010). Scheduling a single batch-processing machine with non-identical job sizes in fuzzy environment using an improved ant colony optimization. Journal of Manufacturing Systems. 29, pp 29-34.
• J. Li, K. Sun, D. Xu, H. Li. (2010). Single machine due date assignment scheduling problem with customer service level in fuzzy environment. Applied Soft Computing. 10, pp 849-858.
• R.T. Moghaddam, B. Javadi, F. Jolai, A. Ghodratnama. (2010). The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem. Applied Soft Computing. 10, pp 919-925.
• J. Li, X. Yuan, E.S. Lee, D. Xu. (2011). Setting due dates to minimize the total weighted possibilistic mean value of the weighted earliness–tardiness costs on a single machine. Computers and Mathematics with Applications. 62, pp 4126-4139.
• X. Li, H. Ishii, T. Masuda. (2012). Single machine batch scheduling problem with fuzzy batch size. Computers and Industrial Engineering. 62(3), pp 688-692.
• X. Li, H. Ishii, M. Chen. (2015). Single machine parallel-batching scheduling problem with fuzzy due-date and fuzzy precedence relation. International Journal of Production Research. 53(9), pp 2707-2717.
• T. Bentrcia, L.H. Mouss, N.K. Mouss, F. Yalaoui, L. Benyoucef. (2015). Evaluation of optimality in the fuzzy single machine scheduling problem including discounted costs. Int. J. Adv. Manuf. Technol. 80, pp 1369-1385.
• M.M. Mazdeh, F. Zaerpour, F.F. Jahantigh. (2010). A fuzzy modeling for single machine scheduling problem with deteriorating jobs. Int. J. Ind. Eng. Computations. 1(2), pp 147-157.
• F. Ahmadizar, L. Hosseini. (2011). Single-machine scheduling with a position-based learning effect and fuzzy processing times. Int. J. Adv Man. Tech. 65, pp 693-698.
• F. Ahmadizar, L. Hosseini. (2013). Minimizing makespan in a single-machine scheduling problem with a learning effect and fuzzy processing times. Int. J. Adv. Man. Technol. 65, pp 581-587.
• L. Zadeh. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Sys. 1, pp 3-28.
• B. Liu, Y-K. Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems. 10(4), pp 445-450.
• A. Charnes, W.W. Cooper. (1959). Chance- constrained programming. Management Sci. 6, pp 73-79.
• B.Liu, K. Iwamura. (1998). Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems. 94, pp 227-282.
• B. Alidaee, N.K. Womer. (1999). Scheduling with time dependent processing times: review and extensions. Journ. of Operation Research Society. 50(7), pp 711-720.