For manufacturing processes to meet evolving market demands, they must be executed in the most efficient manner while maintaining flexibility against unanticipated disruptions. Often, traditional scheduling methods overlook dynamic variability and real-time interruptions. An inverse scheduling framework for a multi-machine flowshop system is proposed in this research with the primary objective of makespan minimisation. Several issue situations are analysed to validate the algorithmic efficacy, and metaheuristic techniques are used to obtain near-optimal solutions. Additionally, to handle unforeseen disruptions, a predictive–reactive scheduling paradigm is developed by incorporating idle buffers within processing intervals. Disruptions are simulated and characterised according to their frequency and repair time using fuzzy set theory. When disruptions reach predefined tolerance criteria, rescheduling begins.The model also takes work location effects and learning phenomena into account when predicting processing time. Furthermore, a model for scheduling fuzzy multi-objective parallel machines is introduced and compared to deterministic approaches. Weighted tardiness, earliness, flow time, and machine deterioration cost are all reduced at the same time.To further illustrate the advantages of the suggested method, comparative performance indicators such as convergence rate, solution stability, and computational efficiency are investigated. Sensitivity analysis is used to assess how learning parameters and the severity of disruptions affect scheduling performance. The findings demonstrate that in complex manufacturing settings, the combined fuzzy and metaheuristic framework greatly increases system resilience, lowers operating costs, and boosts decision-making reliability.

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1. Ahuja R. K. and Orlin, J. B. “Inverse optimization,” Operations Research, Vol. 49, No. 5, pp. 771-783, 2001
2. Martorell, S., Sánchez, A., Carlos, S., et al., 2002. Comparing effectiveness and efficiency in technical specifications and maintenance optimization. Reliability Engineering & System Safety, 77(3):281-289. [doi:10.1016/S0951-8320(02)00061- 3].
3. Wang L. and Zheng D. Z., 2003, “An effective hybrid heuristic for flow shop scheduling”, International Journal of Advanced Manufacturing Technology, 21, No. 1, pp. 38-44, 2003.
4. Heuberger, C. “Inverse combinatorial optimization: a survey on problems, methods, and results,” Journal of Combinatorial Optimization, Vol. 8, No. 3, pp. 329-361,
5. Koulamas, C. “Inverse scheduling with controllable job parameters”, International Journal of Services and Operations Management, Vol. 1, pp. 35-43, 2005.
6. Chen R. J., Chen F., and. Chun, T. G “Inverse problems of a single machine scheduling to minimize the total completion time,” Journal of Shanghai Second Polytechnic University, Vol. 22, No. 2, pp. 1-7, 2005.
7. Liu and Zhang, J. “Inverse maximum flow problems under the weighted Hamming distance,” Journal of Combinatorial Optimization, Vol. 12, No. 4, pp. 395-408, 2006.
8. Liu L., Ng, C. T. and Cheng, T. C. E. “Bi criterion scheduling with equal processing times on a batch processing machine,” Computers & Operations Research, Vol. 36, No. 1, pp. 110-118, 2009.
9. Chen R. J. and Tang, G. C. “Inverse problems of supply chain scheduling and flowshop scheduling,” Operations Research and Management Science, Vol. 18, No. 2, pp. 80-84, 2009.
10. P. and Shakhlevich, N. V., “Inverse scheduling with maximum lateness objective,” Journal of Scheduling, Vol. 12, No. 5, pp. 475-488, 2009.
11. Berrichi A., Amodeo L., Yalaoui F., Chatelet E., & Mezghiche M. (2009). “Bi- objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem”, Journal of Intelligent Manufacturing, 20, pp. 389-400.
12. Fattahi P. and Fallahi, A. “Dynamic scheduling in flexible jobshop systems by considering simultaneously efficiency and stability,”CIRP Journal of Manufacturing Science and Technology, Vol. 2, No. 2, pp. 114-123, 2010.
13. Moradi E., & Zandieh M. (2010). “Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm”, Intelligent Journal of Advanced Manufacturing Technology, 51 pp. 829-
14. P. and Shakhlevich, N. V. “Inverse scheduling: two machine flow-shop problem,” Journal of Scheduling, Vol. 14, No. 3, pp. 239-256, 2011.
15. Pham H. and Lu X., “Inverse problem of total weighted completion time objective with unit processing time on identical parallel machines”, Journal of East China University of Science and Technology, Vol. 38, No. 6, pp. 757-761, 2012.
16. Ahmad, R., Kamaruddin, S., 2012. An overview of time-based and condition-based maintenance in industrial application, Computers & Industrial Engineering, 63(1):135-149.
17. Aissi , Bazgan C., and Vanderpooten, D. “General approximation schemes for min- max (regret) versions of some (pseudo-)polynomial problems,” Discrete Optimization, Vol. 7, No. 3, pp. 136-148, 2010.
18. Ganesan T., Elamvazuthi I., Shaari, K. Z. K and Vasant P.,“ Swarm intelligence and gravitational search algorithm for multi-objective optimization of synthesis gas production,” Applied Energy, Vol. 103, pp. 368-374, 2013.
19. Vasant, P. “Hybrid LS-SA-PA methods for solving fuzzy nonlinear programming problems”, Mathematical and Computer Modelling, Vol. 57, No. 1-2, pp. 180-188,
20. Kim B. S. and. Joo C. M, “Single-machine total completion time scheduling with position-based deterioration and multiple rate-modifying activities,” Industrial Engineering Management Systems, Vol. 10, No. 4, pp. 247-254, 2011.
21. Liu P. and Tian X., “Two-agent single-machine scheduling with resource-dependent starting times,” Mathematical Problems in Engineering, Vol. 2013, Article ID 805261, 5 pages, 2013.
22. Li C., Hsu P.-H., and. Chang C.-C, “A genetic algorithm based approach for single- machine scheduling with learning effect and release time,” Mathematical Problems in Engineering, Vol. 2014, Article ID249493, 12 pages, 2014.
23. Hongtruong P and Xiwen L 2014, “The inverse parallel machine scheduling problem with minimum total completion time”, Vol. 10, No. 2, pp. 613-620.
24. Wang & Liu M., (2014). “Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method”, International Journal of Production Research, 52(5) pp. 1495-1508.
25. Cui, W.W., Lu, Z., and Pan, E. (2014). “Integrated production scheduling and maintenance policy for robustness in a single machine”, Computers & Operations Research, 47 pp. 81-91.
26. Batun and Azizolu M., “Single machine scheduling with preventive maintenances,” International Journal of Production Research, Vol. 47, No. 7, pp. 1753-1771, 2009.
27. Elamvazuthi, Vasant P., and Ganesan, T. “Hybrid optimization techniques for optimization in a fuzzy environment,” Intelligent Systems Reference Library, Vol. 38, pp. 1025-1046, 2013.Glover F., Tabu seacrh,
28. ORSA Journal on Computing 1989, Vol. 1, No. 3. Reeves. C. A genetic algorithm for flow shop sequencing. Computers and Operations Research, 1995, 22: 5-13.

For manufacturing processes to meet evolving market demands, they must be executed in the most efficient manner while maintaining flexibility against unanticipated disruptions. Often, traditional scheduling methods overlook dynamic variability and real-time interruptions. An inverse scheduling framework for a multi-machine flowshop system is proposed in this research with the primary objective of makespan minimisation. Several issue situations are analysed to validate the algorithmic efficacy, and metaheuristic techniques are used to obtain near-optimal solutions. Additionally, to handle unforeseen disruptions, a predictive–reactive scheduling paradigm is developed by incorporating idle buffers within processing intervals. Disruptions are simulated and characterised according to their frequency and repair time using fuzzy set theory. When disruptions reach predefined tolerance criteria, rescheduling begins.The model also takes work location effects and learning phenomena into account when predicting processing time. Furthermore, a model for scheduling fuzzy multi-objective parallel machines is introduced and compared to deterministic approaches. Weighted tardiness, earliness, flow time, and machine deterioration cost are all reduced at the same time.To further illustrate the advantages of the suggested method, comparative performance indicators such as convergence rate, solution stability, and computational efficiency are investigated. Sensitivity analysis is used to assess how learning parameters and the severity of disruptions affect scheduling performance. The findings demonstrate that in complex manufacturing settings, the combined fuzzy and metaheuristic framework greatly increases system resilience, lowers operating costs, and boosts decision-making reliability.

🔒 This is a subscription article

Full text is available to subscribers and institutional members. Please choose an option below to access it.

1. Ahuja R. K. and Orlin, J. B. “Inverse optimization,” Operations Research, Vol. 49, No. 5, pp. 771-783, 2001
2. Martorell, S., Sánchez, A., Carlos, S., et al., 2002. Comparing effectiveness and efficiency in technical specifications and maintenance optimization. Reliability Engineering & System Safety, 77(3):281-289. [doi:10.1016/S0951-8320(02)00061- 3].
3. Wang L. and Zheng D. Z., 2003, “An effective hybrid heuristic for flow shop scheduling”, International Journal of Advanced Manufacturing Technology, 21, No. 1, pp. 38-44, 2003.
4. Heuberger, C. “Inverse combinatorial optimization: a survey on problems, methods, and results,” Journal of Combinatorial Optimization, Vol. 8, No. 3, pp. 329-361,
5. Koulamas, C. “Inverse scheduling with controllable job parameters”, International Journal of Services and Operations Management, Vol. 1, pp. 35-43, 2005.
6. Chen R. J., Chen F., and. Chun, T. G “Inverse problems of a single machine scheduling to minimize the total completion time,” Journal of Shanghai Second Polytechnic University, Vol. 22, No. 2, pp. 1-7, 2005.
7. Liu and Zhang, J. “Inverse maximum flow problems under the weighted Hamming distance,” Journal of Combinatorial Optimization, Vol. 12, No. 4, pp. 395-408, 2006.
8. Liu L., Ng, C. T. and Cheng, T. C. E. “Bi criterion scheduling with equal processing times on a batch processing machine,” Computers & Operations Research, Vol. 36, No. 1, pp. 110-118, 2009.
9. Chen R. J. and Tang, G. C. “Inverse problems of supply chain scheduling and flowshop scheduling,” Operations Research and Management Science, Vol. 18, No. 2, pp. 80-84, 2009.
10. P. and Shakhlevich, N. V., “Inverse scheduling with maximum lateness objective,” Journal of Scheduling, Vol. 12, No. 5, pp. 475-488, 2009.
11. Berrichi A., Amodeo L., Yalaoui F., Chatelet E., & Mezghiche M. (2009). “Bi- objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem”, Journal of Intelligent Manufacturing, 20, pp. 389-400.
12. Fattahi P. and Fallahi, A. “Dynamic scheduling in flexible jobshop systems by considering simultaneously efficiency and stability,”CIRP Journal of Manufacturing Science and Technology, Vol. 2, No. 2, pp. 114-123, 2010.
13. Moradi E., & Zandieh M. (2010). “Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm”, Intelligent Journal of Advanced Manufacturing Technology, 51 pp. 829-
14. P. and Shakhlevich, N. V. “Inverse scheduling: two machine flow-shop problem,” Journal of Scheduling, Vol. 14, No. 3, pp. 239-256, 2011.
15. Pham H. and Lu X., “Inverse problem of total weighted completion time objective with unit processing time on identical parallel machines”, Journal of East China University of Science and Technology, Vol. 38, No. 6, pp. 757-761, 2012.
16. Ahmad, R., Kamaruddin, S., 2012. An overview of time-based and condition-based maintenance in industrial application, Computers & Industrial Engineering, 63(1):135-149.
17. Aissi , Bazgan C., and Vanderpooten, D. “General approximation schemes for min- max (regret) versions of some (pseudo-)polynomial problems,” Discrete Optimization, Vol. 7, No. 3, pp. 136-148, 2010.
18. Ganesan T., Elamvazuthi I., Shaari, K. Z. K and Vasant P.,“ Swarm intelligence and gravitational search algorithm for multi-objective optimization of synthesis gas production,” Applied Energy, Vol. 103, pp. 368-374, 2013.
19. Vasant, P. “Hybrid LS-SA-PA methods for solving fuzzy nonlinear programming problems”, Mathematical and Computer Modelling, Vol. 57, No. 1-2, pp. 180-188,
20. Kim B. S. and. Joo C. M, “Single-machine total completion time scheduling with position-based deterioration and multiple rate-modifying activities,” Industrial Engineering Management Systems, Vol. 10, No. 4, pp. 247-254, 2011.
21. Liu P. and Tian X., “Two-agent single-machine scheduling with resource-dependent starting times,” Mathematical Problems in Engineering, Vol. 2013, Article ID 805261, 5 pages, 2013.
22. Li C., Hsu P.-H., and. Chang C.-C, “A genetic algorithm based approach for single- machine scheduling with learning effect and release time,” Mathematical Problems in Engineering, Vol. 2014, Article ID249493, 12 pages, 2014.
23. Hongtruong P and Xiwen L 2014, “The inverse parallel machine scheduling problem with minimum total completion time”, Vol. 10, No. 2, pp. 613-620.
24. Wang & Liu M., (2014). “Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method”, International Journal of Production Research, 52(5) pp. 1495-1508.
25. Cui, W.W., Lu, Z., and Pan, E. (2014). “Integrated production scheduling and maintenance policy for robustness in a single machine”, Computers & Operations Research, 47 pp. 81-91.
26. Batun and Azizolu M., “Single machine scheduling with preventive maintenances,” International Journal of Production Research, Vol. 47, No. 7, pp. 1753-1771, 2009.
27. Elamvazuthi, Vasant P., and Ganesan, T. “Hybrid optimization techniques for optimization in a fuzzy environment,” Intelligent Systems Reference Library, Vol. 38, pp. 1025-1046, 2013.Glover F., Tabu seacrh,
28. ORSA Journal on Computing 1989, Vol. 1, No. 3. Reeves. C. A genetic algorithm for flow shop sequencing. Computers and Operations Research, 1995, 22: 5-13.