Enerji etkin ve sıra bağımlı hazırlık süreli tek makine çizelgeleme problemi için tavlama benzetimi algoritması tabanlı hibrit sezgisel çözüm önerisi

Yıl 2021, Cilt: 36 Sayı: 1, 407 - 420, 01.12.2020

Gülçin Bektur

https://doi.org/10.17341/gazimmfd.598082

Öz

Artan karbondioksit emisyonu ve enerji
tüketimi, enerji etkin çizelgeleme problemlerine ilgiyi arttırmıştır. Bu
çalışmada çok amaçlı enerji etkin tek makine çizelgeleme probleminde enerji
tasarrufunun sağlanması amacıyla hız ayarlama metodu ele alınmıştır. Literatürde
hız ayarlama metodunda, makina yüksek hızda çalıştırıldığında enerji tüketim
oranı artmakta fakat işler daha kısa sürede tamamlanmaktadır. Makine düşük
hızda çalıştırıldığında ise enerji tüketim oranı azalmakta fakat işlerin
tamamlanma zamanı da uzamaktadır. Çalışmada, amaç fonksiyonları toplam tüketilen
enerji miktarının ve geciken iş sayısının enküçüklenmesidir. Problem plastik
parça üreten bir üretim işletmesindeki çizelgeleme problemi üzerinden
tanımlanmıştır. İşler sıra bağımlı hazırlık süresine sahip olup, bir işin
hazırlık süresi kendisinden önce tamamlanan işe bağlıdır. Probleme özgü bir
matematiksel model önerilmiştir. Problemin çok amaçlı çözümünde ε-kısıt yöntemi
kullanılmıştır. İlgili yöntemin kullanımıyla küçük boyutlu problemler için tüm
Pareto etkin çözümler elde edilmektedir. Fakat problemin NP- zor yapısı sonucu
büyük boyutlu problemlerin çözümü için çok amaçlı sezgisel bir algoritma
önerilmiştir. Önerilen algoritmanın başarısı NSGA II algoritmasıyla
karşılaştırılarak gösterilmiştir. 

Anahtar Kelimeler

Enerji etkin tek makine çizelgeleme, ε-kısıt yöntemi, çok amaçlı sezgisel algoritma, sıra bağımlı hazırlık süreleri, çok amaçlı matematiksel model

Kaynakça

• Ding J. Y., Song S., Wu C., Carbon- efficient scheduling of flow shops by multi- objective optimization, European Journal of Operational Research, 248, 758- 771, 2016.
• Che A., Wu X., Peng J., Yan P., Energy- efficient bi- objective single machine scheduling with power-down mechanism, Computers and Operations Research, 85, 172- 183, 2017.
• Dai, M., Tang, D., Giret, A., Salido, M., Li, W., Energy- efficient scheduling for a flexible flow shop using an improved genetic- simulated annealing algorithm, Robotic and Computer Integrated Manufacturing, 29, 418- 429,2013.
• Mouzon, G., Yildirim, M. B., A framework to minimise total energy consumption and total tardiness on a single machine, International journal of Sustainable Engineering, 105- 116, 2008.
• Mouzon, G., Yildirim, M. B., Twomey, J., Operational methods for minimization of energy consumption of manufacturing equipment, International Journal of Production Research, 45 (18-19), 4247- 4271, 2010.
• Yildirim, M. B., Mouzon, G., Single- machine sustainable production planning to minimize total energy consumption and total completion time using a multiple objective genetic algorithm, IEEE Transactions on Engineering Management, 59 (4), 585- 597, 2012
• Gong, X., Pessemier, T. D., Joseph, W., Martens, L., A generic method for energy- efficient and energy- cost- effective production at the unit process level, Journal of Cleaner Production, 113, 508- 522, 2016
• Che, A., Wu, X., Peng, J., Yan, P., Energy- efficient bi- objective single- machine scheduling with power- down mechanism, Computers and Operations Research, 85, 172- 183, 2017.
• Tarakçı, E., Zaim A.H., Öztaş, O., Design of a genetic algorithmic approach for reducing energy consumption in single machine production systems, Journal of International Trade, Logistics and Law, 4(1), 101, 2018.
• Shrouf, F., Ordieres- Mere, J., Garcia-Sanchez, A., Ortega-Mier, M., Optimizing the production scheduling of a single machine to minimize total energy consumption costs, Journal of Cleaner Production, 67, 197- 207, 2014
• Mikhaylidi, Y., Naseraldin, H., Yedidsion, L., Operations scheduling under electricity time- varying prices, International Journal of Production Research, 53 (23), 7136- 7157, 2015
• Aghelinejad, M., Ouazene, Y., Yalaoui, A., Machine and production scheduling under electricity time varying prices, IEEM, 2016 IEEE International conference on IEEE, 992- 996, 2016.
• Gong, X., Pessemier, T. D., Joseph, W., Martens, L., An energy- cost aware scheduling methodology for sustainable manufacturing, Procedia CIRP, 29, 185- 190, 2015.
• Gong, X., De Pessemier, T., Joseph, W., Martens, L., A power data driven energy-cost-aware production scheduling method for sustainable manufacturing at the unit process level, 2016 IEEE 21 st international conference on IEEE, 1-8, 2016.
• Aghelinejad, M., Ouazene, Y., Yalaoui, A., Preemptive scheduling of a single machine with finite states to minimize energy costs, Springer International Publishing, 591-599, 2017.
• Gong, X., Wee, M., Pessemier, T., Verbrugge, S., Colle, D., Martens, L., Joseph, W., Integrating labor awareness to energy- efficient production scheduling under real time electricity pricing: An empirical study, Journal of Cleaner Production, 168, 239- 253, 2017
• Lee, S., Chung, B. D., Jeon, H. W., Chang, J., A dynamic control approach for energy- efficient production scheduling on a single machine under time- varying electricity pricing, Journal of Cleaner Production, 165, 552- 563, 2017.
• Aghelinejad, M., Ouazene, Y., Yalaoui, A., Production scheduling optimisation with machine state and time- dependent energy costs, International Journal of Production Research, 56 (16), 5558- 5575, 2018.
• Zhang, H., Fang, Y., Pan, R., Ge., C., A new greedy insertion heuristic algorithm with a multi- stage filtering mechanism for energy- efficient single machine scheduling problems, Algorithms, 11 (2): 18, 2018.
• Rubaiee, S., Cinar, S., Yildirim, M. B., An energy- aware multiobjective optimization framework to minimize total tardiness and energy cost on a single machine nonpreemptive scheduling, IEEE Transactions on Engineering Manegement, 99, 1- 16, 2018.
• Artigues, C., Lopez, P., Hait, A., The energy scheduling problem: Industrial case- study and constraint propagation techniques, International Journal of Production Economics, 143, 13- 23, 2013.
• Nattaf, M., Artigues, C., Lopez, P., A hybrid exact method for a scheduling problem with a continuous resorurce and energy constraints, Constraints, 20, 304- 324, 2015.
• Liao, X., Zhang, R., Chiong, R., Multi- objective optimization of single machine scheduling with energy consumption constraints, Computational Intelligence (SSCI), 2017 IEEE Symposium series on IEEE, 1-8, 2017.
• Albers, S., Fujiwara, H., Energy efficient algorithms for flow time minimization, ACM Transactions on Algorithms, 3 (4), 49, 2007.
• Antoniadis, A., Huang, C. C., Non- preemptive speed scaling, Journal of scheduling, 16 (4), 385- 394, 2013.
• Antoniadis, A., Huang, C. C., Ott, S., A fully polynomial- time approximation scheme for speed scaling with speed state, Proceedings of the twenty- sixth annual ACM- SIAM symposium on discrete algorithms, Society for industrial and applied mathematics,1102- 1113, 2015.
• Fang, K., Uhan, N. A., Zhao, F., Sutherland, J. W., Scheduling on a single machine under time- of –use electricity tariffs, Annals of Operations Reserach, 238, 199- 227, 2016.
• Tasgetiren, M. F., Öztop, H., Eliiyi, U., Eliiyi D. T., Pan, Q. K., Energy efficient single machine total weigted tardiness problem with sequence- dependent setup times, International conference on intelligent computing, Springer, 746- 758, 2018.
• Seo, D. K., Klein, C. M., Jang, W., Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models, Computers and Industrial Engineering, 48 (2), 153- 161, 2005.
• Chen, W. J., Minimizing number of tardy jobs on a single machine subject to periodic maintenance, Omega, 37, 591- 599, 2009.
• Cyril, B., Samia, O., Minimizing the number of tardy jobs for the single machine scheduling problem: MIP- based lower and upper bounds, RAIRO, 47 (1), 33-46, 2013.
• Aydilek, A., Aydilek, H., Allahverdi, A., Algorithms for minimizing the number of tardy jobs for reducing production cost with uncertain prpcessing times, Applied mathematical modelling, 45, 982- 996, 2017.
• Bootaki, B., Mahdavi, I., Paydar, M. M., A hybrid GA- AUGMECON method to solve a cubic cell formation problem considering different worker skills, Computers and Industrial Engineering, 75, 31- 40, 2014.
• Hamzadayi, A., Yildiz, G., Modeling and solving static m identical parallel machines scheduling problem with a common server and sequence dependent setup times, Computers and Industrial Engineering, 106, 287- 298, 2017.
• Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA II, IEEE Transactions on evolutionary computation, 6 (2), 182- 197, 2002.
• Durmaz, E., Şahin R., NSGA- II and goal programming approach for the multi- objective single row facility layout problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (3), 941- 955, 2017.
• Wu, X., Che, A., A memetic differential evolution algorithm for energy- efficient parallel machine scheduling. Omega, 82, 155- 165, 2019.
• Lee, Y., Bhaskaran, K., Pinedo, M., A heuristic to minimize the total weighted tardiness with sequence- dependent setups. IIE Transactions, 29 (1), 45-52, 1997.
• Bektur, G., Saraç, T., Two parallel injection machine scheduling under crane constraint, Journal of the Faculty of Engineering and Architecture of Gazi University, 31 (4), 903- 911, 2016.