Modeling and Optimization of Cost-Based Hybrid Flow Shop Scheduling Problem using Metaheuristics


  • Wasif Ullah Faculty of Manufacturing and Mechatronics Engineering Technology, Universiti Malaysia Pahang Al- Sultan Abdullah, 26600 Pekan, Pahang, Malaysia
  • Mohd Fadzil Faisae Ab. Rashid Faculty of Mechanical and Automotive Engineering Technology, Universiti Malaysia Pahang Al-Sultan Abdullah, 26600 Pekan, Pahang, Malaysia
  • Muhammad Ammar Nik Mu’tasim Faculty of Mechanical and Automotive Engineering Technology, Universiti Malaysia Pahang Al-Sultan Abdullah, 26600 Pekan, Pahang, Malaysia



Hybrid flow shop, Cost optimization, Metaheuristics


The cost-based hybrid flow shop (CHFS) scheduling has been immensely studied due to its huge impact on productivity. For any profit-oriented organization, it is important to optimize total production costs. However, few researchers have studied hybrid flow shops (HFS) with total production cost utilization. This paper aims to develop a computational model and test the exploration capability of metaheuristics algorithms while optimizing the CHFS problem. Carlier and Neron defined three hypothetical benchmark problems for computational experiments. The popular optimization algorithms PSO, GA, and ACO were implemented on the CHFS model with ten optimization runs. The experimental results proven that ACO performed well regarding mean fitness value for all benchmark problems. Besides this, CPU time for PSO was very high compared to other algorithms. In the future, other optimization algorithms will be tested for the CHFS model, such as Teaching Learning Based Optimization (TLBO) and the Crayfish Optimization Algorithm (COA).


Anghinolfi, D., Paolucci, M., & Ronco, R. (2021). A bi-objective heuristic approach for green identical parallel machine scheduling. European Journal of Operational Research, 289(2), 416–434.

Behnamian, J., & Fatemi Ghomi, S. M. T. (2011). Hybrid flowshop scheduling with machine and resource-dependent processing times. Applied Mathematical Modelling, 35(3), 1107–1123.

Brabazon, A., O’Neill, M., & McGarraghy, S. (2015). Genetic Algorithm. In Report submitted at IIT Bombay (pp. 21–42).

Carlier, J., & Neron, E. (2000). An Exact Method for Solving the Multi-Processor Flow-Shop. RAIRO - Operations Research, 34(1), 1–25.

Dabiri, M., Yazdani, M., Naderi, B., & Haleh, H. (2022). Modeling and solution methods for hybrid flow shop scheduling problem with job rejection. Operational Research, 22(3), 2721–2765.

Deng, W., Xu, J., Song, Y., & Zhao, H. (2021). Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem. Applied Soft Computing, 100(3), 106–724.

Dong, J., & Ye, C. (2022). Green scheduling of distributed two-stage reentrant hybrid flow shop considering distributed energy resources and energy storage system. Computers & Industrial Engineering, 169(7), 108–146.

Fakhrzad, M. B., & Heydari, M. (2008). A Heuristic Algorithm for Hybrid Flow-Shop Production Scheduling to Minimize the Sum of the Earliness and Tardiness Costs. Journal of the Chinese Institute of Industrial Engineers, 25(2), 105–115.

Fanjul-Peyro, L. (2020). Models and an exact method for the Unrelated Parallel Machine scheduling problem with setups and resources. Expert Systems with Applications: X, 5(4), 10–22.

Fei, H., Meskens, N., & Chu, C. (2010). A planning and scheduling problem for an operating theatre using an open scheduling strategy. Computers & Industrial Engineering, 58(2), 221–230.

Geng, K., Ye, C., Dai, Z. hua, & Liu, L. (2020). Bi-Objective Re-Entrant Hybrid Flow Shop Scheduling considering Energy Consumption Cost under Time-of-Use Electricity Tariffs. Complexity, 31(12), 1469–1480.

Istokovic, D., Perinic, M., Vlatkovic, M., & Brezocnik, M. (2020). Minimizing Total Production Cost in a Hybrid Flow Shop: a Simulation-Optimization Approach. International Journal of Simulation Modelling, 19(4), 559–570.

Janiak, A., Kozan, E., Lichtenstein, M., & Oğuz, C. (2007). Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion. International Journal of Production Economics, 105(2), 407–424.

Jiang, S., Liu, M., Hao, J., & Qian, W. (2015). A bi-layer optimization approach for a hybrid flow shop scheduling problem involving controllable processing times in the steelmaking industry. Computers & Industrial Engineering, 87(9), 518–531.

Li, X., Tang, H., Yang, Z., Wu, R., & Luo, Y. (2020). Integrated Optimization Approach of Hybrid Flow-Shop Scheduling Based on Process Set. IEEE Access, 8(14), 223782–223796.

Lian, X., Zheng, Z., Wang, C., & Gao, X. (2021). An energy-efficient hybrid flow shop scheduling problem in steelmaking plants. Computers & Industrial Engineering, 162(12), 107–683.

Luo, H., Du, B., Huang, G. Q., Chen, H., & Li, X. (2013). Hybrid flow shop scheduling considering machine electricity consumption cost. International Journal of Production Economics, 146(2), 423–439.

Marini, F., & Walczak, B. (2015). Particle swarm optimization (PSO). A tutorial. Chemometrics and Intelligent Laboratory Systems, 149(15), 153–165.

Moazami Goodarzi, R., Ahmadizar, F., & Farughi, H. (2021). Integrated hybrid flow shop scheduling and vehicle routing problem. Journal of Industrial and Systems Engineering, 13(2), 223–244.

Ruiz, R., & Vázquez-Rodríguez, J. A. (2010). The hybrid flow shop scheduling problem. European Journal of Operational Research, 205(1), 1–18.

Shao, W., Shao, Z., & Pi, D. (2022). A network memetic algorithm for energy and labor-aware distributed heterogeneous hybrid flow shop scheduling problem. Swarm and Evolutionary Computation, 75(12), 101–190.

Songserm, W., & Wuttipornpun, T. (2019). MIP-based heuristic algorithm for finite capacity MRP problem in hybrid flow shop with unrelated parallel machines. International Journal of Industrial and Systems Engineering, 33(2), 181–203.

Sukkerd, W., Latthawanichphan, J., Wuttipornpun, T., & Songserm, W. (2021). Non-population Metaheuristics with a New Fitness Evaluation to Minimise Total Penalty Costs for a Hybrid Flow Shop with Assembly Operations Scheduling Problem. 2021 Research, Invention, and Innovation Congress: Innovation Electricals and Electronics (RI2C), 340–346.

Wang, M., Zhong, R. Y., Dai, Q., & Huang, G. Q. (2016). A MPN-based scheduling model for IoT-enabled hybrid flow shop manufacturing. Advanced Engineering Informatics, 30(4), 728–736.

Wang, Y., Tang, J., Pan, Z., & Yan, C. (2015). Particle swarm optimization-based planning and scheduling for a laminar-flow operating room with downstream resources. Soft Computing, 19(10), 2913–2926.

Zheng, X., Zhou, S., Xu, R., & Chen, H. (2020). Energy-efficient scheduling for multi-objective two-stage flow shop using a hybrid ant colony optimisation algorithm. International Journal of Production Research, 58(13), 4103–4120.

Zohali, H., Naderi, B., Mohammadi, M., & Roshanaei, V. (2019). Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems. Computers & Operations Research, 104(4), 127–138.




How to Cite

Ullah, W., Rashid, M. F. F. A., & Mu’tasim, M. A. N. (2023). Modeling and Optimization of Cost-Based Hybrid Flow Shop Scheduling Problem using Metaheuristics. International Journal of Global Optimization and Its Application, 2(4), 244–254.
Abstract viewed = 240 times