A New Artificial Intelligence Algorithm for Solving the Integrated Model of Aggregate Production Planning and Scheduling Problem
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Abstract
In recent years, the integration of production planning and control scheduling has become a significant factor in complex and dynamic manufacturing environments. Therefore, this paper addresses this challenge by introducing an integrated model that simultaneously optimizes both aggregate production planning and single machine scheduling. The primary objectives of the developed model are to minimize overall production cost, makes pan, setup costs, and product delivery delays as key performance indicators. To solve the integrated model, two hybrid metaheuristic algorithms are applied with a novel hybridization ratio (40%-60%): the Hybrid Whale Algorithm with the Fruit Fly optimization algorithm and the Whale Algorithm with the Grey Wolves Optimization Algorithm. Large set of computational experiments are conducted on 10 instances with 20 to 200 jobs and 100 planning periods, with 30 independent runs. The results show that both hybrid algorithms are highly effective in finding near optimal solutions to the integrated complex problem. Comparative analysis demonstrates that the hybrid algorithms outperform common algorithms (Whale, Genetic, Fly, and grey wolf) and the dynamic programming method in terms of solution quality, convergence speed, and computational stability in most tested scenarios. These findings provide practitioners with robust decision-support tools to improve operational efficiency in modern manufacturing systems.
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Armstrong, M., 2006. A Handbook of Management Techniques: A Comprehensive Guide to Achieving Managerial Excellence & Improved Decision Making (3rd ed.). Kogan Page. ISBN 07494 47664.
Bekdaş, G., Nigdeli, S. M. and Yang, X.-S. 2015. Sizing optimization of truss structures using flower pollination algorithm. Applied Soft Computing, 37, pp. 322–331. https://doi.org/10.1016/j.asoc.2015.08.037.
Bellman, R. 1957. Dynamic Programming (1st ed.). Princeton University Press. ISBN:9780691146683.
Bertsekas, D. P. 2012. Dynamic Programming and Optimal Control (4th ed., Vol. 2). Athena Scientific. ISBNs: 1-886529-43-4.
Černe, B., Duhovnik, J. and Tavčar, J. 2019. Semi-analytical flash temperature model for thermoplastic polymer spur gears with consideration of linear thermo-mechanical material characteristics. Journal of Computational Design and Engineering, 6(4), pp. 617–628. https://doi.org/10.1016/j.jcde.2019.03.001
Chao, Y., Zhuang, C., Guo, H. and Liu, J., 2026. A genetic programming hyper-heuristic with whale optimization algorithm for the dynamic resource-constrained multi-project scheduling problems. Expert Systems with Applications, 295, P. 128881. https://doi.org/10.1016/j.eswa.2025.128881
Dauzere-Peres, S., and Lasserre, J.B. 1994. An Integrated Approach in Production Planning and Scheduling (1st ed. 1994, Vol. 411). Springer-Verlag Berlin and Heidelberg GmbH & Co. K. ISBNs: 9783642468049
Dhiman, G. and Kumar, V. 2019. Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowledge-Based Systems, 165, pp. 169–196. https://doi.org/10.1016/j.knosys.2018.11.024
Duan, Y., Li, M., Shi, L., Li, L., Zhao, X. and He, L., 2025. A genetic-operator-integrated whale optimization algorithm for solving the flexible job shop scheduling problem. Journal of King Saud University Computer and Information Sciences, 37(9), pp. 1-25. https://doi.org/10.1007/s44443-025-00283-0
Guzman, E., Andres, B. and Poler, R. 2022. Models and algorithms for production planning, scheduling and sequencing problems: A holistic framework and a systematic review. Journal of Industrial Information Integration, 27, P. 100287. https://doi.org/10.1016/j.jii.2021.100287
Hassani, Z.I.M., El Barkany, A., Jabri, A., El Abbassi, I. and Darcherif, A.M. 2018. New approach to integrate planning and scheduling of production system. International Journal of Engineering Research in Africa, 39, pp. 156–169. https://doi.org/10.4028/www.scientific.net/JERA.39.156
Joyce, T. and Herrmann, J. M. 2018. A Review of No Free Lunch Theorems, and Their Implications for Metaheuristic Optimisation. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_2
Khalaf, B.A., Khalaf, W.S. and Mansor, H.K. 2021. An integrated model for solving production planning and capacity problems. Periodicals of Engineering and Natural Sciences, 9(3), pp. 715–724. https://doi.org/10.21533/pen.v9i3.2283
Khraibet, T.J., Kalaf, B.A. and Rehman, E. 2025. Solving multi-objective machine scheduling problem using the Meerkat Clan Algorithm. Journal of Economics and Administrative Sciences, 31(147), pp. 158–169. https://doi.org/10.33095/0ss7v861
Korashy, A., Kamel, S., Jurado, F., and Youssef, A. R. 2019. Hybrid whale optimization algorithm and grey wolf optimizer algorithm for optimal coordination of direction overcurrent relays. Electric Power Components and Systems, 47(6-7), pp. 644-658. https://doi.org/10.1080/15325008.2019.1602687
Li, W. D. and McMahon, C. A. 2007. A simulated annealing-based optimization approach for integrated process planning and scheduling. International Journal of Computer Integrated Manufacturing, 20(1), pp. 80 -95. https://doi.org/10.1080/09511920600667366.
Lohmer, J. and Lasch, R. 2021. Production planning and scheduling in multi-factory production networks: a systematic literature review. International Journal of Production Research, 59(7), pp. 2028–2054. https://doi.org/10.1080/00207543.2020.1797207.
Mechaacha, A., Belkaid, F. and Brahimi, N., 2025. Multi-objective multi-product process planning with reconfigurable machines: Exact and metaheuristic approaches. Expert Systems with Applications, p.129591. https://doi.org/10.1016/j.eswa.2025.129591
Mirjalili, S. and Lewis, A. 2016. The whale optimization algorithm. Advances in Engineering Software, 95, pp. 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Mirjalili, S., Mirjalili, S. M. and Lewis, A. 2014. Grey wolf optimizer. Advances in Engineering Software, 69, pp. 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Moon, S., Lee, S. and Bae, H. 2008. Genetic algorithms for job shop scheduling problems. International Journal of Production Research, 46(10), pp. 2695–2705. https://doi.org/10.1080/00207540701244820
Mustajab, D. 2023. Effective production planning and scheduling: Literature review. Vifada Management and Social Sciences, 1(2), pp. 54–72. https://doi.org/10.70184/h9wy6f46
Mohammadzadeh, A., Chhabra, A., Mirjalili, S. and Faraji, A., 2024. Use of whale optimization algorithm and its variants for cloud task scheduling: A review. Handbook of Whale Optimization Algorithm, pp.47-68.
Olkkonen, L. 2015. Stakeholder expectations: Conceptual foundations and empirical analysis. University of Jyväskylä. ISBN: 978-951-39-6386-6.
Ouelhadj, D. and Petrovic, S. 2009. A survey of dynamic scheduling in manufacturing systems. Journal of Scheduling, 12(4), pp. 417–431. https://doi.org/10.1007/s10951-008-0090-8
Pan, W.-T. 2012. A new Fruit Fly Optimization algorithm: Taking the financial distress model as an example. Knowledge-Based Systems, 26, pp. 69–74. https://doi.org/10.1016/j.knosys.2011.07.001
Salih, M.A., Mahmoud, A.H. and Khalaf, B.A. 2020. Six Sigma-supported expert system in construction projects. IOP Conference Series: Materials Science and Engineering, 881(1), 012168. https://doi.org/10.1088/1757-899X/881/1/012168
Saremi, S., Mirjalili, S. and Lewis, A. 2017. Grasshopper optimisation algorithm: theory and application. Advances in Engineering Software, 105, pp. 30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004
Schwindt-Bayer, L. A. and Mishler, W. 2005. An integrated model of women’s representation. The Journal of Politics, 67(2), pp. 407–428. https://doi.org/10.1111/j.1468-2508.2005.00323.x
Shir, O.M. and Emmerich, M., 2024. Multi-objective mixed-integer quadratic models: A study on mathematical programming and evolutionary computation. IEEE Transactions on Evolutionary Computation. https://doi.org/10.1109/tevc.2024.3374519
Shobrys, D. E. and White, D. C. 2002. Planning, scheduling and control systems: why cannot they work together. Computers & Chemical Engineering, 26(2), pp. 149–160. https://doi.org/10.1016/S0098-1354(01)00737-2
Suman, A., and Udmale, S. S. 2026. Metaheuristic algorithms: A benchmark-driven functional taxonomy and performance analysis. Computer Science Review, 60, P. 100884. https://doi.org/10.1016/j.cosrev.2025.100884
Tian, T., Liang, Z., Wei, Y., Luo, Q., & Zhou, Y. 2024. Hybrid whale optimization with a firefly algorithm for function optimization and mobile robot path planning. Biomimetics, 9(1). https://doi.org/10.3390/biomimetics9010039
Tomar, V., Bansal, M. and Singh, P. 2024. Metaheuristic algorithms for optimization: A brief review. Engineering Proceedings, 59, 238 RAiSE-2023, 238. https://doi.org/10.3390/engproc2023059238
Turgut, O. E., Turgut, M. S. and Kırtepe, E. 2023. A systematic review of the emerging metaheuristic algorithms on solving complex optimization problems. Neural Computing and Applications, 35(19), pp. 14275–14378. https://doi.org/10.1007/s00521-023-08481-5
Vogel, T., Almada-Lobo, B. and Almeder, C. 2017. Integrated versus hierarchical approach. OR Spectrum, 39, pp. 193–229. https://doi.org/10.1007/s00291-016-0450-2
Wang, Y., Su, H.Y., Shao, H.S., Lu, S. and Xie, L. 2017. Integration of production planning and scheduling. Journal of Zhejiang University (Engineering Science), 51, pp. 57–67.
Wang, Z., Dai, D., Zeng, Z., He, D. and Chan, S., 2024. Multi-strategy enhanced grey wolf optimizer for global optimization and real world problems. Cluster Computing, 27(8), pp. 10671-10715.
Yao, X., Almatooq, N., Askin, R. G. and Gruber, G. 2022. Capacity planning and production scheduling integration: improving operational efficiency via detailed modelling. International Journal of Production Research, 60(24), pp. 7239–7261. https://doi.org/10.1080/00207543.2022.2028031
Yu, V.F., Kao, H.C., Chiang, F.Y. and Lin, S.W. 2022. Solving aggregate production planning problems. Applied Sciences, 12(14), 6945. https://doi.org/10.3390/app12146945
Zhang, T., Wang, Y., Jin, X. and Lu, S. 2019. Integration of production planning and scheduling based on RTN representation under uncertainties. Algorithms, 12(6), 120. https://doi.org/10.3390/a12060120
Zheng, J. H., Kou, Y. N., Jing, Z. X. and Wu, Q. H. 2019. Towards many-objective optimization: Objective analysis, multi-objective optimization and decision-making. IEEE Access, 7, pp. 93742–93751. https://doi.org/10.1109/ACCESS.2019.2926493