Document Type : Original Article
Author
Department of Industrial Engineering and management, Shahrood University of technology, Shahrood, Iran.
Abstract
The two-stage assembly flowshop scheduling problem has been studied in this research. Suppose that a number of products of different kinds are needed to be produced. Each product is consists of several parts. There are m uniform machines in the first stage to manufacture the components (parts) of products and there is one assembly station in the second stage to assembled parts into products. Setup operation should be done when a machine starts processing a new part and setup times are treated as separate from processing times. Two objective functions are considered: (1) minimizing the completion time of all products (makespan) as a classic objective, and (2) minimizing the cost of energy consumption as a new objective. Processing speed of each machine is adjustable and the rate of energy consumption of each machine is dependent of its processing speed. At first, this problem is described with an example, and then needed parameters and decision variables are defined. After that, this problem is modeled as a mixed integer linear programming (MILP) and GAMS software is applied to solve small problems. To solve this bi-objective model, Epsilon Constraint algorithm is used on some test problems obtained standard references. Data of test problems were obtained from previous references and new parameters have been adjusted for considered problem. Conflicting of two considered objective functions has been valid through the result. In additional, result of solving test problems and sensitivity analysis show that how we can reduce energy consumption by adjusting completion times.
Keywords
Al-Anzi, F. S., and Allahverdi, A., (2009). "Heuristics for a two-stage assembly flowshop with bicriteria of maximum lateness and makespan", Computers & Operations Research, Vol. 36, No. 9, pp. 2682–2689. https://doi.org/10.1016/J.COR.2008.11.018
Allahverdi, A., and Al-Anzi, F. S., (2009). "The two-stage assembly scheduling problem to minimize total completion time with setup times", Computers & Operations Research, Vol. 36, No. 10, pp. 2740–2747. https://doi.org/10.1016/J.COR.2008.12.001
Arroyo, J. E. C., and Armentano, V. A., (2005). "Genetic local search for multi-objective flowshop scheduling problems", European Journal of Operational Research, Vol. 167, No. 3, pp. 717–738. https://doi.org/10.1016/J.EJOR.2004.07.017
Biel, K., and Glock, C. H., (2016). "Systematic literature review of decision support models for energy-efficient production planning", Computers & Industrial Engineering, Vol. 101, pp. 243–259. https://doi.org/10.1016/J.CIE.2016.08.021
Cheng, T. C. E., and Wang, G., (1999). Scheduling the fabrication and assembly of components in a two-machine flowshop.
Chircop, K., and Zammit-Mangion, D., (2013). "On-constraint based methods for the generation of Pareto frontiers", Journal of Mechanics Engineering and Automation, Vol. 3, pp. 279–289.
Cummings, D. H., and Egbelu, M. P. J., (1998). "Minimizing production flow time in a process and assembly job shop", International Journal of Production Research, Vol. 36, No. 8, pp. 2315–2332. https://doi.org/10.1080/002075498192922
Dooren, D. Van Den, Sys, T., Toffolo, T. A. M., Wauters, T., and Berghe, G. Vanden., (2017). "Multi-machine energy-aware scheduling", EURO Journal on Computational Optimization, Vol. 5,pp. 285–307. https://doi.org/10.1007/s13675-016-0072-0
Du, B., Chen, H., Huang, G. Q., and Yang, H. D. (2011). "Preference Vector Ant Colony System for Minimising Make-span and Energy Consumption in a Hybrid Flow Shop", In Multi-objective Evolutionary Optimisation for Product Design and Manufacturing (pp. 279–304). London: Springer London. https://doi.org/10.1007/978-0-85729-652-8_9
Fattahi, P., Hosseini, S., Jolai, F., and safi Samghabadi, A. (2014). "Multi-objective scheduling problem in a three-stage production system", IInternational Journal of Industrial Engineering & Production Research, Vol. 25, No. 1, pp. 1–12.
Fattahi, P., Hosseini, S. M. H., and Jolai, F. (2013). "A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem", International Journal of Advanced Manufacturing Technology, Vol. 65. https://doi.org/10.1007/s00170-012-4217-x
Fattahi, P., Hosseini, S. M. H., Jolai, F., and Tavakkoli-Moghaddam, R. (2014). "A branch and bound algorithm for hybrid flow shop scheduling problem with setup time and assembly operations", Applied Mathematical Modelling, Vol. 38, No. 1. https://doi.org/10.1016/j.apm.2013.06.005
He, Y., Liu, F., Cao, H., and Li, C. (2005). "A bi-objective model for job-shop scheduling problem to minimize both energy consumption and makespan", Journal of Central South University of Technology, Vol. 12, No. 2, pp. 167–171. https://doi.org/10.1007/s11771-005-0033-x
Hosseini, S. M. H. (2016). "Modeling the Hybrid Flow Shop Scheduling Problem Followed by an Assembly Stage Considering Aging Effects and Preventive Maintenance Activities", International Journal of Supply and Operations Management, Vol. 3, No. 1, pp. 1215–1233. https://doi.org/10.22034/2016.1.07
Hosseini, S. M. H. (2019). "Modelling and solving the job shop scheduling Problem followed by an assembly stage considering maintenance operations and access restrictions to machines", Journal of Optimization in Industrial Engineering, Vol. 12, No. 1, 71–80. https://doi.org/10.22094/JOIE.2018.760.1484
Lee, C.-Y., Cheng, T. C. E., and Lin, B. M. T., (1993). "Minimizing the Makespan in the 3-Machine Assembly-Type Flowshop Scheduling Problem", Management Science. INFORMS. https://doi.org/10.2307/2632599
Lee, I. S., (2018). "Minimizing total completion time in the assembly scheduling problem", Computers & Industrial Engineering, Vol. 122, pp. 211–218. https://doi.org/10.1016/J.CIE.2018.06.001
Lee, J.-Y., and Bang, J.-Y., (2016). "A Two-Stage Assembly-Type Flowshop Scheduling Problem for Minimizing Total Tardiness", Mathematical Problems in Engineering, Vol. 2016, pp. 1–10. https://doi.org/10.1155/2016/6409321
Loukil, T., Teghem, J., and Tuyttens, D., (2005). "Solving multi-objective production scheduling problems using metaheuristics", European Journal of Operational Research, Vol. 161, No. 1, pp. 42–61. https://doi.org/10.1016/J.EJOR.2003.08.029
Maleki-Darounkolaei, A., Modiri, M., Tavakkoli-Moghaddam, R., and Seyyedi, I., (2012). "A three-stage assembly flow shop scheduling problem with blocking and sequence-dependent set up times", Journal of Industrial Engineering International, Vol. 8, No. 1, pp. 8-26. https://doi.org/10.1186/2251-712X-8-26
Mansouri, S. A., Aktas, E., and Besikci, U., (2016). "Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption", European Journal of Operational Research, Vol. 248, No. 3, pp. 772–788. https://doi.org/10.1016/J.EJOR.2015.08.064
Merkert, L., Harjunkoski, I., Isaksson, A., Säynevirta, S., Saarela, A., and Sand, G., (2015). "Scheduling and energy – Industrial challenges and opportunities", Computers & Chemical Engineering, Vol. 72, pp. 183–198. https://doi.org/10.1016/J.COMPCHEMENG.2014.05.024
Módos, I., Šůcha, P., and Hanzálek, Z. (2017). "Algorithms for robust production scheduling with energy consumption limits", Computers & Industrial Engineering, Vol. 112, pp. 391–408. https://doi.org/10.1016/J.CIE.2017.08.011
Mouzon, G., Yildirim, M. B., and Twomey, J., (2007). "Operational methods for minimization of energy consumption of manufacturing equipment", International Journal of Production Research, Vol. 45, pp. 4247–4271. https://doi.org/10.1080/00207540701450013
Plitsos, S., Repoussis, P. P., Mourtos, I., and Tarantilis, C. D. (2017). "Energy-aware decision support for production scheduling", Decision Support Systems, Vol. 93, pp. 88–97. https://doi.org/10.1016/J.DSS.2016.09.017
Potts, C. N., Sevast’janov, S. V., Strusevich, V. A., Van Wassenhove, L. N., and Zwaneveld, C. M., (1995). "The Two-Stage Assembly Scheduling Problem: Complexity and Approximation", Operations Research, Vol. 43, No. 2, pp. 346–355. https://doi.org/10.1287/opre.43.2.346
Salmasnia, A., Mousavi-Saleh, M., and Mokhtari, H., (2018). "A Multi-objective Competitive Location Problem within Queuing Fra", International Journal of Supply and Operations Management, Vol. 5, No. 1, pp. 42–65.
Shrouf, F., Ordieres-Meré, J., García-Sánchez, A., and Ortega-Mier, M., (2014). "Optimizing the production scheduling of a single machine to minimize total energy consumption costs ", Journal of Cleaner Production, Vol. 67, pp. 197–207. https://doi.org/10.1016/J.JCLEPRO.2013.12.024
Xiang Liu, Fengxing Zou, and Xiangping Zhang., (2008). Mathematical model and genetic optimization for hybrid flow shop scheduling problem based on energy consumption, In 2008 Chinese Control and Decision Conference (pp. 1002–1007). IEEE. https://doi.org/10.1109/CCDC.2008.4597463
Yahia, W. Ben, Felfel, H., Ayadi, O., and Masmoudi, F., (2015). Comparative Study for a Multi-objective MLCSP Problem Solved Using NSGA-II & E-Constraint (pp. 139–149). Springer, Cham. https://doi.org/10.1007/978-3-319-17527-0_14
Yi, Q., Li, C., Tang, Y., and Wang, Q., (2012). A new operational framework to job shop scheduling for reducing carbon emissions. In IEEE International Conference on Automation Science and Engineering (CASE) (pp. 58–63). IEEE. https://doi.org/10.1109/CoASE.2012.6386372
Yokoyama, M., and Santos, D. L., (2005). "Three-stage flow-shop scheduling with assembly operations to minimize the weighted sum of product completion times ", European Journal of Operational Research, 161(3), 754–770. https://doi.org/10.1016/j.ejor.2003.09.016
Zhang, L., Li, X., Gao, L., Zhang, G., and Wen, X. (2012). Dynamic scheduling model in FMS by considering energy consumption and schedule efficiency. In Proceedings of the 2012 IEEE 16th International Conference on Computer Supported Cooperative Work in Design (CSCWD) (pp. 719–724). IEEE. https://doi.org/10.1109/CSCWD.2012.6221898
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