BOZULMA VE ÖĞRENME ETKİLERİ ALTINDAKİ BULANIK İŞLEM SÜRELERİ İLE ÇİZELGE TAMAMLANMA SÜRESİNİN EN AZA İNDİRİLMESİ

Yıl 2020, Cilt: 31 Sayı: 1, 1 - 17, 30.04.2020

Oğuzhan Ahmet Arık , Mehmet Duran Toksarı

Öz

Bu çalışma tek makine çizelgeleme
problemlerinde öğrenme ve bozulma etkileri altındaki belirsiz işlem sürelerini
incelemektedir. Öğrenme etkisi, bozulma etkisi ve işlem süresi gibi
parametrelerdeki belirsizliği ifade edebilmek için bulanık sayılar
kullanılmıştır. Çalışmaya konu olan ve belirsiz parametrelere sahip problemin
amaç fonksiyonu çizelge tamamlanma süresinin en aza indirilmesidir. Literatürde
birçok tek makine çizelgeleme problemi deterministik parametreler ile
incelenmiştir. Bu çalışmada ise karar vericilerin öğrenme ve bozulma etkileri
altındaki gerçek hayat tek makine çizelgeleme problemlerinin belirsizliği ile
başa çıkabilmelerine olanak tanıyacak bir metot tanıtılmaktadır. Problemin
karmaşıklığı nedeni ile birçok kısıt doğrusal değildir. Bulanık doğrusal
olmayan karma tam sayılı bir matematiksel model problemin çözümü için
önerilmiştir ve ayrıca bir sayısal örnek çalışma içerisinde verilmiştir.    

Anahtar Kelimeler

Çizelgeleme, Bulanık, Bozulma, Öğrenme Etkisi

MINIMIZING MAKESPAN WITH FUZZY PROCESSING TIMES UNDER JOB DETERIORATION AND LEARNING EFFECT

Öz

This paper
proposes a single machine/processor scheduling problem considering uncertain
processing times under job deterioration and learning effect. In order to
express uncertainty of parameters such as processing times, effects of
deterioration and learning, fuzzy numbers are used. The objective function in
this study is to minimize the makespan (maximum completion time) where the
parameters of the problem are fully uncertain. 
In the literature, many single machine scheduling problems have been
interested in deterministic model parameters such as processing times, due
dates and release dates.  This study
introduces a way for decision makers to cope with real life ambiguity and
imprecision in single machine scheduling problems with uncertain processing
time under uncertain effects of job deterioration and learning. Due to
complexity of the problem, most of constraints are non-linear. A numerical
example is illustrated and a fuzzy mixed integer nonlinear programming model is
proposed in this study.

Anahtar Kelimeler

Scheduling, Fuzzy, Job Deterioration, Learning Effect, Mixed Integer Nonlinear Programming

Kaynakça

• Ahmadizar, F., Hosseini, L., (2011). Single-machine scheduling with a position-based learning effect and fuzzy processing times. Int. J. Adv Man. Tech., 65, 693-698.Ahmadizar, F., Hosseini, L., (2013). Minimizing makespan in a single-machine scheduling problem with a learning effect and fuzzy processing times. Int. J. Adv. Man. Technol., 65, 581-587.Alidaee, B., Womer, N. K., (1999). Scheduling with time dependent processing times: Review and extensions. J. Operat. Res. Soc., 50(7), 711-720.Arık, O . (2019). Dissatisfaction levels of earliness and tardiness durations by relaxing common due date on single machine scheduling problems. Journal of Multidisciplinary Modeling and Optimization, 2 (1), 1-15.Arık, O. A. (2019). Credibility based chance constrained programming for project scheduling with fuzzy activity durations. An International Journal of Optimization and Control: Theories & Applications, 9(2), 208–215.Arık, O.A., Toksarı, M.D., (2018a). Multi-objective fuzzy parallel machine scheduling problems under fuzzy job deterioration and learning effects. International Journal of Production Research, 56(7), 2488-2505. Arık, O. A., & Toksarı, M. D. (2018b). Fuzzy chance constrained programming technique for single machine earliness/tardiness scheduling problem under effects of fuzzy learning and deterioration. Sakarya University Journal of Science, 22(2), 652–662.Arık, O. A., & Toksarı, M. D. (2019). Fuzzy Parallel Machine Scheduling Problem Under Fuzzy Job Deterioration and Learning Effects With Fuzzy Processing Times. In M. Ram (Ed.), Advanced Fuzzy Logic Approaches in Engineering Science (pp. 49–67). IGI Global. https://doi.org/DOI: 10.4018/978-1-5225-5709-8.ch003Arindam, R., Kumar, M.M., Samarjit, K., Manoranjan, M., (2007). Two storage inventory model with fuzzy deterioration over a random planning horizon. Math. and Comp. Modelling 46(11), 1419-1433.Bachman, A., Janiak, A., (2000). Minimizing maximum lateness under linear deterioration. Eur. J. Operat. Res., 126(3), 557-566.Bachman, A., Janiak, A., (2004). Scheduling jobs with position-dependent processing times. J. Operat. Res. Soc., 55, 257-264.Bellman, R. E., Zadeh, L. A., (1970). Decision-making in a fuzzy environment. Management Science, 17, 141-164.Biskup, D., (1999). Single-machine scheduling with learning considerations. Eur. J. Operat. Res., 115(1), 173-178.Browne, S., Yechiali, U., (1990). Scheduling deteriorating jobs on a single processor. Operat. Res., 38, 495-498. Chanas, S., Kasperski, A., (2001). Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates. Eng. App. of Artif. Intel., 14, 377-386.Chanas, S., Kasperski, A., (2003). On two single machine scheduling problems with fuzzy processing times and fuzzy due dates. Eur. J. Operat. Res., 147, 281-296.Chanas, S., Kasperski, A., (2004). Possible and necessary optimality of solutions in the single machine scheduling problem with fuzzy parameters. Fuzzy Sets and Systems, 142(3), 359-371.Cheng, B., Li, K., Chen, B., (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, 29-34. Cheng, T.C.E., Wu, C.C., Lee, W.C., (2008). Some scheduling problems with deteriorating jobs and learning effects. Comp. Ind. Eng., 54(4), 972-982. Duenas, A., Petrovic, D., (2008). Multi-objective genetic algorithm for single machine scheduling problem under fuzziness. Fuzzy Optim. Decis. Making, 7, 87-104. Gupta, J. N. D., Gupta, S. K., (1988). Single facility scheduling with nonlinear processing times. Comput. Ind. Eng., 14, 387-393.Han, S., Ishii, H., Fujii, S., (1994). One machine scheduling problem with fuzzy due dates. Eur. J. Operat. Res., 79, 1-12.Harikrishnan, K.K., Ishii, H., (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, 141-147.Hsu, Y. S., Lin, B.M.T., (2003). Minimization of maximum lateness under linear deterioration. Omega, 31, 459-469.Ishii, H., Tada, M., (1995). Single machine scheduling problem with fuzzy precendence relation. Eur. J. Operat. Res., 87(2), 284-288.Itoh, T., Ishii, H., (1999). Fuzzy due-date scheduling problem with fuzzy processing time. Intl. Trans. in Op. Res., 6, 639-647.Itoh, T., Ishii, H., (2005). One machine scheduling problem with fuzzy random due-dates. Fuzzy Optim. Dec. Making, 4, 71-78.Kanaya, Z. A., (2010). An interactive method for fuzzy multi objective nonlinear programming problems. JKAU Sci., 22(1), 103-112.Kasperski, A., (2007). Some general properties of a fuzzy single machine scheduling problem. Intern. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(1), 43-46. Kassem, M.A.E., Ammar, E.I., (1995). Stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints. Fuzzy Sets and Systems, 74(3), 343-351.Kuo, W.H. Yang, D.L., (2006b). Single machine group scheduling with a time dependent learning effect. Eur. J. Operat. Res., 33, 2099-2112.Kuo, W.H., Yang, D.L., (2006a). Minimizing the total completion time in a single machine scheduling problem with a time dependent learning effect. Eur. J. Operat. Res., 174(2), 1184-1190.Lam, S.S., Cai, X., (2002). Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates. Nonlinear Analysis: Real World Applications, 3, 307-316.Li, J., Sun, K., Xu, D., Li, H., (2010). Single machine due date assignment scheduling problem with customer service level in fuzzy environment. Applied Soft Computing, 10, 849-858.Li, J., Yuan, X., Lee, E.S., Xu, D., (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, 4126-4139.Li, X., Ishii, H., Chen, M., (2015). Single machine parallel-batching scheduling problem with fuzzy due-date and fuzzy precedence relation. International Journal of Production Research, 53(9), 2707-2717. Li, X., Ishii, H., Masuda, T., (2012). Single machine batch scheduling problem with fuzzy batch size. Computers and Industrial Engineering, 62(3), 688-692. Liao, L.M., Liao, C.J., (1998). Single machine scheduling problem with fuzzy due date and processing time. J. Chinese Inst. Eng., 21(2), 189-196.Mazdeh, M.M., Zaerpour, F., Jahantigh, F.F., (2010). A fuzzy modeling for single machine scheduling problem with deteriorating jobs. Int. J. Ind. Eng. Computations, 1(2), 147-157.Moghaddam, R.T., Javadi, B., Jolai, F., Ghodratnama, A., (2010). The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem, Applied Soft Computing, 10, 919-925.Mosheiov, G. (1994). Scheduling jobs under simple linear deterioration. Computational Operat., 21(6), 653-659.Mosheiov, G., (1991) .V-shaped policies for scheduling deteriorating jobs. Operat. Res., 39, 979-991.Mosheiov, G., (1995). Scheduling jobs with step-deterioration; Minimizing makespan on a single machine. Comput. Ind. Eng., 28, 869-879.Mosheiov, G., (1996). K-shaped policies to schedule deteriorating jobs. J. Operat. Res. Soc., 47, 1184-1191.Mosheiov, G., (2001). Scheduling problems with a learning effect. Eur. J. Operat. Res., 132, 687-693.Mosheiov, G., Sidney, J. B., (2003). Scheduling with general job-dependent learning curves. Eur. J. Operat. Res., 147, 665-670.Muthusamy, K., Sung, S.C., Vlach, M., Ishii, H., (2003). Scheduling with fuzzy delays and fuzzy precedences. Fuzzy Sets and Systems, 134, 387-395.Nasseri, S.H., (2008). Fuzzy nonlinear optimization. The Journal of Nonlinear Analysis and its Applications, 1(4), 230-235.Osman, M., El-Banna, A., (1993). Stability of Multiobjective Nonlinear Programming. Problems with Fuzzy Parameters Mathematics and Computers in Simulation, 35, 321-326.Sakawa, M., Yana, H., (1989). An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, 30(3), 221-238. Sung, S.C., Vlach, M., (2003). Single machine scheduling to minimize the number of late jobs under uncertainty. Fuzzy Sets and Systems, 139, 421-430. Tanaka, H., Asai, K., (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems. 13, 1-10.Toksarı, M. D., Guner, E., (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),801-808. Toksarı, M. D., Guner, E., (2009). Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration. Comput. Operat. Res., 36(8), 2394-2417.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.Toksarı, M.D., Arık, O.A., (2018). Genetic algorithm applied to the flow shop scheduling problem under effects of fuzzy learning and deterioration with a common fuzzy due date. New Trends and Issues Proceedings on Humanities and Social Sciences, 4(10), 306-316.Wang, C., Wang, D., Ip, W.H., Yuen, D.W., (2002). The single machine ready time scheduling problem with fuzzy processing times. Fuzzy Sets and Systems, 127, 117-129.Wang, J.B., (2007). Single-machine scheduling problems with the effects of learning and deterioration. Omega, 35(4), 397-402.Wang, X., Cheng, T.C.E., (2007). Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan. Eur. J. Operat. Res., 178(1), 57-70.Zimmermann, H. J., (1983). Fuzzy mathematical programming. Comput. Ops. Res., 10(4), 291-298.