Development of a Mathematical Model Based on Ordered Load for Production and Assembly Line Balancing
Keywords:
Assembly line balancing, Ordered load, Mathematical optimization, Heuristic algorithm, Production efficiency, Demand variabilityAbstract
This study aims to develop and validate a mathematical assembly line balancing model based on ordered load to improve workload equity, reduce idle time, and enhance productivity in order-driven production environments. The study adopted an applied, quantitative research design using real operational data collected from multiple industrial production and assembly lines characterized by heterogeneous orders and mixed-model production. Ordered load was defined as the effective workload imposed on each workstation as a function of order quantity, product mix, and processing requirements. A mixed-integer mathematical programming model was formulated to minimize workload imbalance and idle time under precedence and capacity constraints. The model was solved using an exact optimization approach (Gurobi) to obtain benchmark solutions, and a heuristic algorithm implemented in MATLAB to address scalability and computational efficiency. Model validation was conducted through numerical experiments, cross-factory comparison, and sensitivity analysis under ±10% and ±20% ordered load variations. Exact optimization results showed substantial improvements in line balance index across all factories, accompanied by significant reductions in idle time and workload variance. Productivity increased consistently without additional resources, indicating more effective utilization of existing capacity. The heuristic algorithm achieved solution quality exceeding 97% of the exact optimum while reducing computation time by over 90%, demonstrating strong scalability. Sensitivity analysis confirmed that the model maintained stable balance performance under demand fluctuations, with mid-line stations identified as structurally critical but effectively controlled through load redistribution. The findings confirm that incorporating ordered load into assembly line balancing provides a more realistic and robust representation of demand-driven workload, leading to superior balance, efficiency, and adaptability compared to traditional time-based approaches.
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Copyright (c) 2026 Behzad Bararzadeh (Author); Alireza Irajpour; Reza Ehtesham Rasi (Author)
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