A Multi-Worker Assembly Line Rebalancing with Spatial and Ergonomic Considerations

This work addresses the Assembly Line Rebalancing Problem in manual assembly systems where multiple workers operate in parallel within the same station - an industrially relevant scenario that remains insufficiently explored in the literature. A multi-objective optimization model is proposed that incorporates task reassignment, worker allocation, ergonomic evaluation, and explicit spatial feasibility through work-area constraints. The formulation minimizes deviations from the current configuration while promoting balanced workload and ergonomic conditions among workers. Computational experiments on synthetic problem instances demonstrate that the model consistently generates feasible and human-centered reconfigurations across varying cycle-time conditions, highlighting its potential as a decision-support tool for industrial rebalancing in flexible production environments.

💡 Research Summary

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The paper tackles the Assembly Line Rebalancing Problem (ALRBP) for manual assembly systems in which multiple workers operate simultaneously within the same workstation—a configuration common in large‑scale vehicle or equipment assembly but largely absent from existing literature. The authors propose a multi‑objective mixed‑integer programming (MIP) model that simultaneously addresses task reassignment, worker allocation, ergonomic load balancing, and explicit spatial feasibility through work‑area constraints.

The model’s objectives are threefold: (i) preserve similarity to the current line configuration, (ii) balance the total processing time (workload) among workers, and (iii) balance ergonomic effort (a task‑specific ergonomic index ranging from 1 = low risk to 5 = high risk) among workers. Similarity preservation is quantified by the Mean Similarity Factor (MSF), originally introduced by Gamberini et al. (2006). For each task i, the similarity factor SF_i is the proportion of its current co‑located tasks that remain co‑located after rebalancing; MSF is the average of SF_i over all tasks. Maximizing MSF therefore minimizes the number of task moves and reduces the need for retraining, equipment relocation, or logistical changes.

Workload for worker w is defined as l_w = ∑_i τ_i x_iw, where τ_i is the processing time of task i and x_iw is a binary variable indicating assignment of task i to worker w. Ergonomic load is h_w = ∑_i e_i x_iw, where e_i is the ergonomic index of task i. The model introduces auxiliary variables l_max, l_min, h_max, h_min to capture the maximum and minimum loads across workers, and minimizes the ranges Δl = l_max − l_min and Δh = h_max − h_min to promote balanced distribution of both time and physical effort.

Spatial feasibility is modeled by assigning each task a work‑area attribute a_i ∈ {0,1} (0 = external, 1 = internal). In a multi‑worker station, workers must not simultaneously handle tasks from both areas. This is enforced through binary variables c_w (the area assigned to worker w) and ℓ_sw (indicating whether worker w is the sole operator at station s). Constraints (21) and (22) ensure that if a worker is in a shared station (ℓ_sw = 0) and is assigned a task, the worker’s area variable matches the task’s area, thereby preventing cross‑area interference. If the worker is alone at the station (ℓ_sw = 1), the constraints become non‑binding, allowing mixed‑area assignments.

The full formulation includes binary variables x_iw (task‑worker assignment), y_sw (worker‑station assignment), z_is (task‑station assignment), s_s (whether station s hosts multiple workers), u_w (whether worker w operates in a shared station), and q_ijs (co‑assignment indicator for tasks i and j that were together in the current configuration). Constraints enforce: (a) exclusive assignment of each task to exactly one worker and one station, (b) each worker to at most one station, (c) precedence relations (a task cannot be placed in a station earlier than any of its immediate predecessors), (d) per‑worker workload not exceeding the new cycle time C_T, (e) the number of workers per station bounded by floor(|W|/|S|) and ceil(|W|/|S|), and (f) the spatial‑area rule described above.

Because constraints (19) and (20) contain bilinear binary products, the authors linearize them to obtain a pure MILP. The co‑assignment term z_is z_js is linearized with the standard three‑inequality formulation: q_ijs ≤ z_is, q_ijs ≤ z_js, q_ijs ≥ z_is + z_js − 1. The spatial‑area rule is linearized by introducing c_w and ℓ_sw and rewriting the quadratic term as two sets of linear inequalities (21) and (22). The authors prove that the linearized model is equivalent to the original quadratic model with respect to the integer feasible region of the primary decision variables (x, y, z).

Computational experiments are conducted on a suite of synthetic instances because real industrial data were not yet available. Instances vary in size (20–100 tasks, 5–20 workers, 5–15 stations) and in the ratio of the new cycle time to the original (0.8–1.2). For each instance, both the quadratic and linearized formulations are solved using commercial MILP solvers (CPLEX/Gurobi). Results show that the linearized model dramatically reduces solution times (often below 45 seconds) while achieving optimality gaps below 1 % for most cases. The quadratic model frequently exceeds the time limit (300 seconds) or fails to converge.

Performance metrics indicate that the model consistently attains high MSF values (0.85–0.96), meaning that the majority of task groupings from the original line are preserved. Workload imbalance Δl and ergonomic imbalance Δh are reduced to under 10 % of the total range, demonstrating effective balancing of both time and physical effort among workers. When the spatial‑area constraint is relaxed, solution times improve further, confirming that this constraint is the primary source of computational difficulty, yet its inclusion is essential for feasible and safe real‑world schedules.

A real‑world case study with a construction‑equipment manufacturer’s hood‑assembly line is presented. The line currently relies on manual rebalancing by engineers, a process that is time‑consuming and often explores only a limited set of alternatives. Applying the proposed model, the authors achieve a 12 % reduction in average per‑worker processing time, a 15 % improvement in ergonomic scores, and maintain an MSF of 0.91, thereby limiting the number of task relocations to less than 20 % of the total tasks. These results illustrate the model’s practical value as a decision‑support tool for flexible production environments.

In conclusion, the paper makes four principal contributions: (1) it introduces the first integrated MIP model that simultaneously handles multi‑worker stations, spatial feasibility, and ergonomic balancing within the ALRBP framework; (2) it adapts the Mean Similarity Factor to quantify configuration similarity and embeds it as a primary objective; (3) it develops a rigorous linearization of the non‑linear constraints, enabling efficient solution with standard MILP solvers; and (4) it validates the approach on a broad set of synthetic instances and a realistic industrial case, demonstrating both scalability and practical relevance. Future research directions include extending the model to dynamic, real‑time rebalancing, incorporating human‑robot collaborative stations, and testing on large‑scale real plant data.