Document Type : Original Article


1 Industrial Engineering Department, Engineering Faculty, Islamic Azad University, Tehran North Branch, Tehran, Iran.

2 Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran.

3 School of Strategy and Leadership, Faculty of Business and Law, Coventry University, Coventry, UK.

4 Industrial Engineering and Management Department, Shahrood University of Technology, Shahrood, Iran.


This paper aims to confront the uncertainties in the flexible job shop scheduling (FJSS) problem by considering the tax regulations of energy consumption and timely delivery. Uncertainties include all unexpected disruptions such as machine breakdowns, modifications or cancellation of the orders, and receiving new orders that lead to failure in initial scheduling. Two strategies with the energy-saving approach have been proposed based on scheduling repair. Two considered objective functions are to minimize the tax cost on surplus energy consumption and to minimize total cost of jobs tardiness. The problem is described with the parameters and decision variables clearly in the form of MIP model. Moreover, the proposed model is investigated using data of a real case study in a company based on casting processes. Since the problem is well known strongly NP-hard, a new approach is introduced based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) to find proper solutions for decision-makers. The computational results show that the proposed model and solution approach repairs properly the original scheduling and could improve the Pareto front comparing with the original scheduling. Due to the result, two proposed strategies could reduce total cost of jobs tardiness more than 47.56% compared with the original scheduling in eight different cases. It could also improve the second objective more than 56.91%. This approach will help the manufacturing industry managers, especially in make-to-order (MTO) systems with high-powered machines to respond rapidly to unexpected disruptions with the lowest energy consumption and tardiness penalty.


Chan, D.Y.L., Huang, C.F., Lin, W.C., and Hong, G.B., (2014). "Energy efficiency benchmarking of energy-intensive industries in Taiwan", Energy Conversion and Management, Vol. 77, pp. 216–220. 
Li, K., and Lin, B., (2016). "Impact of energy conservation policies on the green productivity in China’s manufacturing sector: Evidence from a three-speed DEA model", Applied Energy, Vol. 168, pp. 351–363. 
Cassettari, L., Bendato, I., Mosca, M., and Mosca, R., (2017). "Energy resources intelligent management using on line real-time simulation: A decision support tool for sustainable manufacturing", Applied Energy, Vol. 190, pp. 841–851. 
The 13th five-year plan for economic and social development of the people’s republic of China, (2016). People's Daily, pp. 1e78.
Moon, W., Florkowski, W.J., Bruckner, B., (2002). "Willingness to pay for environmental practices: implications for eco-labeling", Land Econ., Vol. 78, No.1, 88e102.
Zhang, Linghong, Wang, J., and You, J., (2015). "Consumer environmental  awareness and channel coordination with two substitutable products", European Journal of Operational Research, Vol. 241, No. 1, pp. 63–73. 
Howes, R., Skea, J., Whelan, B., (2013). Clean and competitive: motivating environmental performance in industry, Routledge.
Herroelen, W., and Leus, R., (2005). "Project scheduling under uncertainty: Survey and research potentials", European Journal of Operational Research, Vol. 165, No. 2, pp. 289–306. 
Herroelen, W., and Leus, R., (2004). "Robust and reactive project scheduling: a review and classification of procedures", International Journal of Production Research, Vol. 42, No. 8, pp. 1599–1620. 
Sabuncuoglu, I., and Bayiz, M., (2000). "Analysis of reactive scheduling problems in a job shop environment", European Journal of Operational Research, Vol. 126, No. 3, pp. 567–586. 
Hatami, S., Ebrahimnejad, S., Tavakkoli-Moghaddam, R. et al., (2010). “Two meta-heuristics for three-stage assembly flowshop scheduling with sequence-dependent setup times”, The International Journal of Advanced Manufacturing Technology, 50, 1153–1164.
Ayyoubzadeh, B., Ebrahimnejad, S., Bashiri, M., Baradaran, V., and Hosseini, S.M.H., (2021). "Modeling and an improved NSGA-II algorithm for sustainable manufacturing systems with energy conservation under environmental uncertainties: a case study", International Journal of Sustainable Engineering, Vol. 14, No. 3, pp. 255-279.
Rahmani, D., and Ramezanian, R., (2016). "A stable reactive approach in dynamic flexible flow shop scheduling with unexpected disruptions : A case study", Computers & Industrial Engineering, Vol. 98, pp. 360–372. 
Kim, T., Kim, Y., and Cho, H., (2020). "A simulation-based dynamic scheduling model for curtain wall production considering construction planning reliability", Journal of Cleaner Production, 124922. 
Minguillon, F. E., and Stricker, N., (2020). ARTICLE IN PRESS CIRP Annals - Manufacturing Technology Robust predictive À reactive scheduling and its effect on machine disturbance mitigation. CIRP Annals - Manufacturing Technology, 00, 17–20. 
Goli, A., Tirkolaee, E. B., and Soltani, M., (2019). "A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors", Production & Manufacturing Research, Vol. 7, No. 1, pp. 294–315. 
Ayough, A., and Khorshidvand, B., (2019). "Designing a manufacturing cell system by assigning workforce", Journal of Industrial Engineering and Management, Vol. 12, No. 1, pp. 13-26.
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(18–19), pp. 4247–4271. 
Mouzon, G., and Yildirim, M. B., (2008). "A framework to minimise total energy consumption and total tardiness on a single machine", International Journal of Sustainable Engineering, Vol. 1, No. 2, pp. 105–116. 
Che, A., Wu, X., Peng, J., and Yan, P.,  (2017). "Energy-efficient bi-objective single-machine scheduling with power-down mechanism", Computers and Operations Research, Vol. 85, pp. 172–183. 
Dai, M., Tang, D., Giret, A., Salido, M. A., and Li, W.D., (2013). "Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm", Robotics and Computer-Integrated Manufacturing, Vol. 29, No. 5, pp. 418–429. 
Che, A., Lv, K., Levner, E., and Kats, V., (2015). "Energy consumption minimization for single machine scheduling with bounded maximum tardiness", In: ICNSC 2015 - 2015 IEEE 12th International Conference on Networking, Sensing and Control, pp. 146–150. 
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. 
Tirkolaee, E.B., Goli, A., and Weber, G.W., (2020). "Fuzzy Mathematical Programming and Self-Adaptive Artificial Fish Swarm Algorithm for Just-in-Time Energy-Aware Flow Shop Scheduling Problem With Outsourcing Option", IEEE Transactions on Fuzzy System, Vol. 28, No. 11, pp. 2772 - 2783. 
Fang, K., Uhan, N.A., Zhao, F., and Sutherland, J.W., (2013). "Flow shop scheduling with peak power consumption constraints", Annals of Operations Research, Vol. 206, No. 1, pp. 115–145. 
Dai, M., (2015). Research on Energy-efficient Process Planning and Scheduling. Doctor of Philosophy, Nanjing University of Aeronautics and Astronautics.
Zhang, R., and Chiong, R., (2016). "Solving the energy-efficient job shop scheduling problem: A multi-objective genetic algorithm with enhanced local search for minimizing the total weighted tardiness and total energy consumption", Journal of Cleaner Production, Vol. 112, pp. 3361–3375. 
Zhang, Liping, 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 2012, pp. 719–724. 
Pach, C., Berger, T., Sallez, Y., Bonte, T., Adam, E., and Trentesaux, D., (2014). "Reactive and energy-aware scheduling of flexible manufacturing systems using potential fields", Computers in Industry, Vol 65, No. 3, pp 434–448. 
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. 
Cheng, J., Chu, F., Liu, M., Wu, P., and Xia, W., (2017). "Bi-criteria single-machine batch scheduling with machine on/off switching under time-of-use tariffs", Computers and Industrial Engineering, Vol. 112, pp. 721–734. 
Chen, Der-San, Batson, Robert G., Dang, Y., (2010). Applied integer programming: modeling and solution, ISBN: 9780470373064.
Ho, N.B., and Tay, J.C., (2004). "GENACE: An efficient cultural algorithm for solving the flexible job-shop problem", In: Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004, 2, pp. 1759–1766. 
Wu, X., and Wu, S., (2017). "An elitist quantum-inspired evolutionary algorithm for the flexible job-shop scheduling problem", Journal of Intelligent Manufacturing, Vol. 28, No. 6, pp. 1441–1457. 
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., (2002). "A fast and elitist multiobjective genetic algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, Vol. 6, No. 2, pp. 182–197.