Hybrid optimization of production scheduling and maintenance using mathematical programming and NSGA-II meta-heuristic method

Document Type : Research Paper


1 Department of Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Management, University of Tehran, Tehran, Iran



This paper presents an integrated hybrid optimization problem for production and maintenance scheduling within a comprehensive system using overall cost and reliability. The total cost consists of three parts: production costs, inventory costs, and workforce costs. This integration aims to simultaneously find the optimal value of the function in a period. Using mixed-integer linear programming, the optimal values ​​are minimized over a limited horizon in the various samples considered for different numbers of workers and machines. In order to evaluate the model in larger dimensions, the NSGA-II metaheuristic method has been used. Given that the error rate of the developed mathematical model with the results of the meta-heuristic method in small dimensions can be neglected, so this meta-heuristic method has been used to perform sensitivity analysis in larger dimensions of the problem. In general, the results of this paper provide valuable information about changes in the number of workers and machines simultaneously to prevent interruptions and save on production to managers and analysts in the field of production planning.


Aghezzaf, E.-H. and Najid, N. M. (2008). "Integrated production planning and preventive maintenance in deteriorating production systems." Information Sciences 178(17): 3382–3392.
Babaeinesami, A., & Ghasemi, P. (2020). Ranking of hospitals: A new approach comparing organizational learning criteria. International Journal of Healthcare Management, 1-9.
Bahria, N., Dridi, I. H., Chelbi, A., & Bouchriha, H. (2020). Joint design of control chart, production and maintenance policy for unreliable manufacturing systems. Journal of Quality in Maintenance Engineering.
Behnezhad, A. R., & Khoshnevis, B. (1988). "The effects of manufacturing progress function on machine requirements and aggregate planning problems." The International Journal of Production Research 26(2): 309-326.
Bensmain, Y., Dahane, M., Bennekrouf, M., & Sari, Z. (2019). Preventive remanufacturing planning of production equipment under operational and imperfect maintenance constraints: A hybrid genetic algorithm based approach. Reliability Engineering & System Safety, 185, 546-566.
Berrichi, A., Amodeo, L., Yalaoui, F., & Mezghiche, M. (2010). "Bi-objective ant colony optimization approach to optimize production and maintenance scheduling, Computers & Operations Research 37(9): 1584-1596.
Berrichi, A., Amodeo, L., Yalaoui, F., Châtelet 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(40): 389-400.
Duffuaa, S., Kolus, A., Al-Turki, U., & El-Khalifa, A. (2020). An integrated model of production scheduling, maintenance and quality for a single machine. Computers & Industrial Engineering, 142, 106239.
Ettaye, G., El Barkany, A., & El Khalfi, A. (2017). Modeling and optimization a production/maintenance integrated planning. In International Journal of Engineering Research in Africa (Vol. 28, pp. 169-181). Trans Tech Publications Ltd.
Fitouhi, M.-C., & Nourelfath, M. (2014). Integrating noncyclical preventive maintenance scheduling and production planning for multi-state systems. Reliability Engineering & System Safety 121: 175-186.
Gajpal, Y., & Nourelfath, M. (2015). Two efficient heuristics to solve the integrated load distribution and production planning problem. Reliability Engineering & System Safety 144: 204–214.
Ghasemi, P., & Babaeinesami, A. (2019). Estimation of relief supplies demands through fuzzy inference system in earthquake condition. Journal of Industrial and Systems Engineering, 12(3), 154-165.
Ghasemi, P., & Talebi Brijani, E. (2014). An integrated FAHP-PROMETHEE approach for selecting the best flexible manufacturing system. European Online Journal of Natural and Social Sciences, 3(4), pp-1137.
Ghasemi, P., Mehdiabadi, A., Spulbar, C., & Birau, R. (2021). Ranking of Sustainable Medical Tourism Destinations in Iran: An Integrated Approach Using Fuzzy SWARA-PROMETHEE. Sustainability, 13(2), 683.
Jafari, L., & Makis, V. (2015). Joint optimal lot sizing and preventive maintenance policy for a production facility subject to condition monitoring, International Journal of Production Economics 169: 156-168.
Khalili-Damghani, K., Tavana, M., & Ghasemi, P. (2021). A stochastic bi-objective simulation–optimization model for cascade disaster location-allocation-distribution problems. Annals of Operations Research, 1-39.
Khalilzadeh, M., Ghasemi, P., Afrasiabi, A., & Shakeri, H. (2021). Hybrid fuzzy MCDM and FMEA integrating with linear programming approach for the health and safety executive risks: a case study. Journal of Modelling in Management.
Khanchehzarrin, S., Shahmizad, M., Mahdavi, I., Mahdavi-Amiri, N., & Ghasemi, P. (2021). A model for the time dependent vehicle routing problem with time windows under traffic conditions with intelligent travel times. RAIRO--Operations Research.
Kolus, A., El-Khalifa, A., Al-Turki, U.M., & Duffuaa, S.O. (2020), "An integrated mathematical model for production scheduling and preventive maintenance planning", International Journal of Quality & Reliability Management, Vol. 37 No. 6/7, pp. 925-937. https://doi.org/10.1108/IJQRM-10-2019-0335.
LaRoche-Boisvert, M., Dimitrakopoulos, R., & Ferland, J. A. (2021). Simultaneous production scheduling and transportation optimization from mines to port under uncertain material supply. Resources Policy, 73, 102150.‏
Liao, L. "Joint production and maintenance strategy for economic production quantity model with imperfect production processes," Journal of Intelligent Manufacturing, vol. 24, no. 6, pp. 1229-1240, 2013.
Lu, S., Pei, J., Liu, X., & Pardalos, P. M. (2021). A hybrid DBH-VNS for high-end equipment production scheduling with machine failures and preventive maintenance activities. Journal of Computational and Applied Mathematics, 384, 113195.‏
Moussavi-Haidar, L., Daou, H., & Khalil, K. (2021). Joint reserve stock and just-in-time inventory under regular preventive maintenance and random disruptions. International Journal of Production Research, 1-22.
Nourelfath, M., Nahas, N., & Ben-Daya, M., "Integrated preventive maintenance and production decisions for imperfect processes," Reliability Engineering & System Safety, vol. 148, pp. 21-31, 2016.
Saha, R., Azeem, A., Hasan, K. W., Ali, S. M., & Paul, S. K. (2021). Integrated economic design of quality control and maintenance management: Implications for managing manufacturing process. International Journal of System Assurance Engineering and Management, 12(2), 263-280.
Samimi, E., & Sydow, J. (2020). Human resource management in project-based organizations: revisiting the permanency assumption. The International Journal of Human Resource Management, 1-35.
Shafipour-omran, B., Khalili-Damghani, K., & Ghasemi, P. (2020). Solving a supply chain problem using two approaches of fuzzy goal programming based on TOPSIS and fuzzy preference relations. Journal of Industrial and Systems Engineering, 13(2), 27-48.
Shirazi, H., Kia, R., & Ghasemi, P. (2021). A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak. Applied Soft Computing, 112, 107725.
Tsao, Y.-C. "Combined production-maintenance decisions in situations with process deterioration," International Journal of Systems Science, vol. 44, no. 9, pp. 1692-1700, 2013.
Xiang, Y., Cassady, C. R., Jin, T. and Zhang, C. W. "Joint production and maintenance planning with machine deterioration and random yield," International Journal of Production Research, vol. 52, no. 6, pp. 1644-1657, 2014.
Yalaoui, A, Chaabi, K. and Yalaoui, F. "Integrated production planning and preventive maintenance in deteriorating production systems," Information Sciences, vol. 278, pp. 841-861, 2014.
Yang, H., Li, W., & Wang, B. (2021). Joint optimization of preventive maintenance and production scheduling for multi-state production systems based on reinforcement learning. Reliability Engineering & System Safety, 214, 107713.‏
Zhang, X., Xia, T., Pan, E., & Li, Y. (2021). Integrated optimization on production scheduling and imperfect preventive maintenance considering multi-degradation and learning-forgetting effects. Flexible Services and Manufacturing Journal, 1-32.‏
Zheng, J., Yang, H., Wu, Q., & Wang, Z. (2020). A two-stage integrating optimization of production scheduling, maintenance and quality. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 234(11), 1448-1459.