Journal of Industrial Engineering Research in Production Systems

Journal of Industrial Engineering Research in Production Systems

A Two-objective Fuzzy Linear Programming Model for a Single Batch Processing Machine Scheduling Problem under Time-of-Use Electricity Consumption Policy

Document Type : Research Paper

Authors
Ladan-ol-Sadat Mousavi 1
Fariborz Jolai 2
1 PhD student in industrial engineering, Department of Industrial Engineering, Kish International Campus, University of Tehran, Tehran, Iran
2 Professor, Department of Industrial Engineering, School of Industrial Engineering, Technical School, University of Tehran, Tehran, Iran
10.22084/ier.2023.27325.2111
Abstract
With the reduction of non-renewable energy sources and the increased energy costs in recent years, the decision-making model with energy and electricity consumption consideration is significant. Time-of-Use (ToU) policy is one of the incentive policies in the whole world that provides new opportunities to save electricity consumption and energy costs. This paper considers a batch processing machine scheduling problem with identical jobs and a two-objective function of minimizing the cost of electricity consumed by the machine and minimizing the makespan under the ToU policy. The processing time of jobs is considered fuzzy due to uncertainty in the real world. The effectiveness and efficiency of the proposed model and solution approach to reduce the electricity cost are demonstrated by carrying out two numerical experiments. 
Keywords
Time-of Use Electricity Policy
Batch Processing Machine
Makespan
Fuzzy Processing Time
Fuzzy Multi-Objective Mathematical Model
Subjects
  • APERC, A. (2013). APEC energy demand and supply outlook. Technical report, Asia-Pacific Economic Cooperation.
  • Cheng, J., Chu, F., Xia, W., Ding, J., & Ling, X. (2014, November). Bi-objective optimization for single-machine batch scheduling considering energy cost. In 2014 International Conference on Control, Decision and Information Technologies (CoDIT) (pp. 236-241). IEEE.
  • عطائی، حشمت الله، احمدی زر، فردین، ارکات، & جمال. (2022). زمان‌بندی ماشین‌های موازی یکسان با درنظر گرفتن عملیات مشترک به‌منظور کمینه‌ نمودن مجموع انرژی‌های مصرفی و مجموع زمان‌های دیرکرد.نشریه پژوهش‌های مهندسی صنایع در سیستم‌های تولید، 9(19)، 107-123.‎
  • افسر، & بهنامیان. (2020). زمان‌بندی چندعاملی ماشین‌های موازی ناهمگن با درنظر گرفتن هزینه انرژی و کارهای به‌هنگام.نشریه پژوهش‌های مهندسی صنایع در سیستم‌های تولید، 7(15)، 287-303.‎
  • Cheng, J., Chu, F., & Zhou, M. (2017). An improved model for parallel machine scheduling under time-of-use electricity price. IEEE Transactions on Automation Science and Engineering, 15(2), 896-899.
  • Park, M. J., & Ham, A. (2022). Energy-aware flexible job shop scheduling under time-of-use pricing. International Journal of Production Economics, 248, 108507.
  • Badri, S. A., Daghbandan, A., AghabeiginiyayFatalaki, Z., &Mirzazadeh, M. (2021). Flow shop scheduling under Time-Of-Use electricity tariffs using fuzzy multi-objective linear programming approach. Journal of mathematical modeling, 9(2), 215-227.
  • Rego, M. F., Pinto, J. C. E., Cota, L. P., & Souza, M. J. (2022). A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling. PeerJ Computer Science, 8, e844.
  • Uzsoy, R. (1994). Scheduling a single batch processing machine with non-identical job sizes. The International Journal of Production Research, 32(7), 1615-1635.
  • Tang, L., & Liu, P. (2009). Minimizing makespan in a two-machine flowshop scheduling with batching and release time. Mathematical and Computer Modelling, 49(5-6), 1071-1077.
  • Hadera, H., &Harjunkoski, I. (2013). Continuous-time batch scheduling approach for optimizing electricity consumption cost. In Computer Aided Chemical Engineering. Vol. 32, 403-408.
  • Hejari, S. R., Emami, S., &Arkan, A. (2009). A Heuristic algorithm for minimizing the expected make span in two machine flow shops with fuzzy processing time. Journal of uncertain systems, 3(2), 114-122.
  • Yuan, F., Xu, X., & Yin, M. (2019). A novel fuzzy model for multi-objective permutation flow shop scheduling problem with fuzzy processing time. Advances in Mechanical Engineering, 11(4), 1687814019843699.
  • Wang, G. G., Gao, D., &Pedrycz, W. (2022). Solving multi-objective fuzzy job-shop scheduling problem by a hybrid adaptive differential evolution algorithm. IEEE Transactions on Industrial Informatics, 18(12), 8519-8528.
  • Fowler, J. W., &Mönch, L. (2022). A survey of scheduling with parallel batch (p-batch) processing. European journal of operational research, 298(1), 1-24.
  • Cheng J, Chu F, Chu C, Xia W (2016) Bi-objective optimization of single-machine batch schedulingunder time-of-use electricity prices. RAIRO Oper Res 50(4–5):715–732
  • Wu, P., Cheng, J., & Chu, F. (2021). Large-scale energy-conscious bi-objective single-machine batch scheduling under time-of-use electricity tariffs via effective iterative heuristics. Annals of Operations Research, 296(1), 471-494.‏
  • Cheng J, Chu F, Liu M, Wu P, Xia W (2017) Bi-criteria single-machine batch scheduling with machineon/off switching under time-of-use tariffs. Comput Ind Eng 112:721–734
  • Cheng J, Chu F, Liu M, Xia W (2016) Single-machine batch scheduling under time-of-use tariffs: newmixed-integer programming approaches. In: Proceedings of the 2016 IEEEinternational conferenceon systems, man, and cybernetics (SMC), pp 3498–3503.
  • Wang S, Liu M, Chu F, Chu C (2016) Bi-objective optimization of a single machine batch schedulingproblem with energy cost consideration. J Clean Prod 137:1205–1215
  • Zhang, S., Che, A., Wu, X., & Chu, C. (2018). Improved mixed-integer linear programming model and heuristics for bi-objective single-machine batch scheduling with energy cost consideration. Engineering Optimization, 50(8), 1380-1394.‏
  • Zhou, S., Jin, M., & Du, N. (2020). Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times. Energy, 209, 118420.
  • Zhou, S., Li, X., Du, N., Pang, Y., & Chen, H. (2018). A multi-objective differential evolution algorithm for parallel batch processing machine scheduling considering electricity consumption cost. Computers &Operations Research, 96, 55-68.
  • Jia, Z. H., Zhang, Y. L., Leung, J. Y. T., & Li, K. (2017). Bi-criteria ant colony optimization algorithm for minimizing makespan and energy consumption on parallel batch machines. Applied Soft Computing, 55, 226-237.‏
  • Jia Z-H, Wang Y, Wu C, Yang Y, Zhang X-Y, Chen H-P (2019). Multi-objective energy-aware batchscheduling using ant colony optimization algorithm. Comput Ind Eng 131:41–56.
  • Qian, S. Y., Jia, Z. H., & Li, K. (2020). A multi-objective evolutionary algorithm based on adaptive clustering for energy-aware batch scheduling problem. Future Generation Computer Systems, 113, 441-453.‏
  • Rocholl, J., Mönch, L., & Fowler, J. W. (2018, December). Electricity power cost-aware scheduling of jobs on parallel batch processing machines. In 2018 Winter Simulation Conference (WSC) (pp. 3420-3431). IEEE.‏
  • Rocholl, J., Mönch, L., & Fowler, J. (2020). Bi-criteria parallel batch machine scheduling to minimize total weighted tardiness and electricity cost. Journal of Business Economics, 90(9), 1345-1381.
  • Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.
  • Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.
Journal of Industrial Engineering Research in Production Systems
Volume 10, Issue 21
January 0
Pages 107-117