Optimization of Mixed-Model Multi-Manned Assembly Lines for Fuel–Electric Vehicle Co-Production Under Workstation Sharing

Abstract

With the rapid transformation of the automotive industry towards electric vehicles, how to achieve efficient mixed-line production of electric vehicles and fuel vehicles has become a key challenge for modern assembly systems. This study investigated the balancing problem of a mixed-model multi-manned assembly line, considering workstation sharing (MMuALBP-WS), and developed a deterministic multi-objective model that integrates the heterogeneity of tasks and the coordination of shared workstations. An improved genetic algorithm was proposed, whose decoding mechanism enables different types of electric vehicle and fuel vehicle tasks to achieve dynamic collaboration within the shared workstations. A real case study from the chassis assembly line of Company W demonstrated the effectiveness of the proposed method, achieving a 25% reduction in the number of workstations, a 27% decrease in the total number of workers, and a 23.56% increase in average workstation utilization. The results confirmed that the workstation sharing mechanism significantly improved production balance, labor utilization, and flexibility, providing a practical and scalable optimization framework for the mixed-model assembly system in the era of the transition from electric vehicles to fuel vehicles. In addition to its practical significance, this study enhances the understanding of mixed-model multi-manned line balancing by incorporating workstation-sharing logic into both the mathematical modeling and optimization process, offering a theoretical basis for future extensions to more complex production environments.

1. Introduction

Agency (IEA) [1], global electric vehicle (EV) sales are projected to exceed 25 million units in 2025, accounting for nearly one-third of total new vehicle sales. The increasing demand for EVs has prompted automobile manufacturers to consider the transformation of their production lines. The market demand for fuel vehicles (FVs) indicates that FVs and EVs will coexist for a long time. This industrial transformation has prompted automotive manufacturers to focus on flexible production and resource sharing, enabling them to simultaneously meet the demands of both types of products.

As the global automotive industry accelerates its transformation towards new energy and intelligence, the collaborative production of FVs and EVs has become a trend for the flexible development of the automotive manufacturing industry. In recent years, the production of new energy vehicles has grown rapidly, while traditional FVs still occupy a considerable market share. This has prompted automotive manufacturing enterprises to simultaneously produce various models under limited factory space and equipment conditions, to reduce renovation costs and improve production flexibility. Against this backdrop, the mixed-model assembly line (MAL) has become the main production mode for automotive manufacturing enterprises. Automotive manufacturing enterprises assemble different models on the same production line, achieving sharing of equipment, workstations, and human resources, thereby enhancing production efficiency and economy [2].

However, due to the significant differences in power structure, component layout, and assembly processes between FVs and EVs, the task time, sequence of processes, and cycle constraints are inconsistent, and the imbalance problem of workstations becomes more prominent. The complexity of balancing optimization for the assembly line significantly increases [3]. To meet the demands of high-speed and high-complexity automotive assembly, manufacturing enterprises generally adopt the “multi-man per station” (Multi-Manned Station) operation mode, where two or more workers are assigned to the same workstation to complete tasks together. This mode can effectively shorten the critical process time and reduce idle time at the workstation [4,5]. After the introduction of the multi-man per station mechanism, the complexity of task allocation, worker assignment, and assembly line balancing problems (ALBP) has sharply increased [6]. Especially in the mixed production environment of fuel vehicles and electric vehicles, the heterogeneity of tasks among different vehicle models makes traditional models unable to simultaneously consider beat balance, worker coordination, and space constraints, further increasing the difficulty of problem-solving.

Although relevant research has been continuously enriched, most of them still assume that each workstation is used independently. For heterogeneous tasks of different vehicle models, how to complete them on the same workstation has not been discussed in any research. In the mixed production environment of FVs and EVs, tasks of different vehicle models are often executed alternately on the same workstation. Workstation sharing has become an important strategy for achieving flexible manufacturing. The workstation sharing mechanism can improve the utilization rate of the assembly line and promote multi-model collaborative production without increasing the investment in space and equipment. The introduction of the workstation sharing mechanism makes the problems of task allocation and worker scheduling more complex. Traditional intelligent algorithms cannot simultaneously satisfy the constraints of cycle time and workstation sharing during the decoding process, resulting in low assembly line efficiency. Therefore, establishing a mathematical model considering the workstation sharing mechanism and developing an improved algorithm with targeted decoding process is an important direction for the research on MALB.

Based on the above issues, this paper takes the mixed-model assembly line of FVs and EVs of a certain automobile manufacturing enterprise as the research background and proposes an MMuALBP-WS and its intelligent solution method. The innovation of this research lies in the following three aspects: First, a mathematical model considering vehicle heterogeneity, multiple people sharing the same workstation, and workstation sharing is constructed, and the goals are minimizing the number of workstations, the number of workers, and the smoothness of load. Second, an IGA based on the dynamic decoding mechanism of shared workstations is proposed. A double-layer sequence encoding structure (task sequence and workstation assignment sequence) is adopted. In the decoding stage, dynamic matching rules are introduced to allocate tasks to shared workstations based on vehicle attributes, process duration, and cycle constraints. Combined with the penalty repair mechanism and dictionary order fitness comparison method, global search and local optimization are balanced. Third, the model and algorithm are verified using real production data, and the effectiveness and robustness of the analysis method are analyzed based on indicators such as the number of workstations, the number of workers, and the worker utilization rate. This research provides an optimization framework for the mixed FV-EV assembly system and offers practical insights for the transition from traditional automotive manufacturing to electric vehicle manufacturing during co-line production.

To clarify the research focus, this study will address the following research questions:

(1)

How can the workstation sharing between EVs and FVs be balanced in a mixed-vehicle, multi-operator environment?

(2)

How can the genetic algorithm be improved to make it suitable for the constraints of shared workstations?

(3)

Compared with the traditional model without workstation sharing, what improvements can be achieved in terms of the number of workstations, human resource utilization, and workload balance?

These questions provide guidance for the proposed mathematical model and the development of IGA. The relevant content will be elaborated in the subsequent chapters.

2. Literature Review

The rapid development of mixed-model and multi-manned operations in automotive assembly has brought new complexity to balancing problems. To clarify the theoretical foundation and research context of the proposed MMuALBP-WS model, this section reviews the evolution of assembly line balancing, advances in mixed-model and multi-manned systems, relevant production-system principles, and recent methodological trends. This provides the basis for identifying the research gap addressed in this study.

2.1. Evolution of Assembly Line Balancing Research

Since Bryton [7] proposed the assembly line balancing problem, the research on this issue has evolved from single-model (SALB) to mixed-model (MALB), and then to multi-manned shared stations (MuALBP) and mixed-model multi-manned shared stations (MMuALBP). The research on SALB aimed to minimize the number of workstations or the cycle time. As the complexity of the problem increased, researchers gradually introduced heuristic algorithms and intelligent algorithms to solve the model, such as genetic algorithms (GA), ant colony algorithms (ACO), particle swarm algorithms (PSO), and simulated annealing (SA), which improved the solution efficiency under complex constraints [3,8,9]. Thomopoulos [10] proposed the comprehensive priority relationship method for mixed-flow assembly lines, and Roberts [11] and Vilarinho et al. [12] improved load balancing through integer programming and probability weighting methods. Kang et al. [13] achieved multi-objective mixed-model balancing optimization by improving genetic algorithms and hybrid heuristic algorithms, leading to the development of MALB towards flexible manufacturing.

2.2. Multi-Manned and Mixed-Model Multi-Manned Assembly Line Balancing

In the field of multi-person concurrent stations, Dimitriadis [4] proposed the definition and solution framework of MuALBP, and Fattahi et al. [6] presented a mixed integer programming model and used the artificial bee colony algorithm to optimize and solve the model; Kazemi and Sedighi [14] proposed a mathematical programming model with cost as the objective, and Kellegöz [15] considered the number of workstations, the number of workers, and the smoothing index, and used the variable neighborhood search algorithm to solve; Lopes et al. [16] and Michels et al. [17] introduced worker skill ability constraints and workstation space constraints to make the model closer to actual production. With the widespread application of mixed-model production methods in automotive assembly lines, research gradually developed towards the balanced problem of mixed-flow multi-person concurrent assembly lines (MMuALBP). Roshani and Ghazi Nezami [18] proposed a mathematical model for MMuALBP concurrent stations and used the SA to solve it. El Machouti [19] used GA for multi-objective optimization, Şahin and Kellegöz [20] considered resource constraints in the model, and used PSO. Lopes et al. [16] optimized the flexible layout through the Variable Workstation Boundary (VSB) method. Rosanini et al. [21] proposed a hybrid adaptive VNS method to solve the multi-pass assembly line balance problem, aiming to minimize the cycle time. Compared with traditional methods, their approach effectively improved computational efficiency. However, the structural differences in products and the workstation sharing among different models were not considered, reducing their applicability in mixed assembly systems.

2.3. Theoretical Background

Apart from the recent studies on mixed-model and multi-manned assembly line balancing, the development of the workstation sharing mechanism in this paper has also been inspired by broader principles in production system engineering. The foundational system engineering literature [22] emphasizes the importance of understanding how resources are allocated and how trade-offs must be made when multiple performance goals need to be considered. These concepts are closely related to the need to balance the number of workstations, worker loads, and smoothness in heterogeneous assembly environments.

The classic production system theory [23] further provides insights into how bottlenecks, blocking/hunger behaviors, and throughput losses occur in unbalanced lines. These mechanisms help explain why combining PT with specific model tasks on shared workstations can reduce local bottlenecks and improve overall assembly line efficiency. Similarly, concepts from manufacturing system design [24], such as workflow coordination and production line configuration, are consistent with the motivation to reorganize multi-station tasks to better utilize available labor capacity.

Recent research on cycle-overrun analysis [25] also provides a useful perspective, helping to understand why smoothness and cycle time feasibility are crucial when there are significant differences in duration between EV-specific and FV-specific tasks. Their research results further emphasize the importance of considering changes in task workload when evaluating the performance of mixed-model production lines.

Incorporating these theoretical perspectives helps to place the proposed MMuALBP-WS model within a broader production system engineering context and clarify how workstation sharing can be an effective strategy to alleviate imbalance issues in actual multi-model assembly environments.

2.4. Recent Research Trends

Recent studies have highlighted that coordination among multiple resources significantly affects assembly line performance. In human–robot collaborative settings, differences in operator skills and collaboration patterns influence cycle-time feasibility and task allocation efficiency [26], indicating that synchronization challenges are not unique to EV–FV co-production. At the methodological level, multi-objective and bi-level optimization models have been widely used to capture interactions among balancing decisions. For example, integrating ALB with part-feeding through a bi-level GA improves overall line performance [27], while fuzzy–stochastic multi-manned models simultaneously optimize stations, workers, and workload smoothness under uncertain task times [28].

Advances in meta-heuristic design have further improved solution stability. Hybrid GA–PSO approaches enhance convergence robustness in reconfigurable assembly environments [29], and flexible meta-heuristic frameworks show that algorithm effectiveness is highly sensitive to task-time patterns and precedence structures—supporting the use of customized decoding strategies in heterogeneous EV–FV systems. Genetic algorithms also remain effective in structurally constrained lines. Multi-objective GA applications in two-sided ALB demonstrate strong performance under complex spatial and precedence constraints [13], while time–space multi-manned studies show that spatial feasibility and worker motion directly affect station-level operability [30]. Real mixed-model automotive assembly lines further confirm that GA-based decision support effectively handles sequence-dependent operations and model-specific requirements [31]. Finally, research on synchronous mixed-model two-sided lines shows that model variation can threaten cycle-time feasibility unless supported by dedicated task-allocation strategies [32]—a finding that reinforces the motivation for the workstation-sharing mechanism in EV–FV co-production.

3. Mathematical Model

The mathematical model constructed in this research is a deterministic model. It is based on the framework proposed by Roshani and Ghazi Nezami [18] and has been expanded. The new model considers workstation sharing based on the structural differences between EVs and FVs. Constraints on workstation sharing are added to the constraints. New binary variables are introduced to clearly define the shared workstations. A hierarchical multi-objective structure is established to optimize the number of workstations, the number of workers, and the worker load separately. This improved model can reflect the situation of mixed-type production lines with structural differences, providing a basis for the allocation of workloads among shared workstations.

In mixed-model FV–EV assembly systems, task heterogeneity refers to the structural and operational differences between assembly tasks belonging to different product types. These differences include (1) task exclusivity, where certain operations exist only in EVs (e.g., battery packaging, HV cable installation) or only in FVs (e.g., fuel tank mounting); (2) processing-time variability of common tasks, where EV and FV versions of the same operation require different durations; and (3) model-specific precedence structures, where the sequencing of tasks differs across product types. Such heterogeneity significantly increases the complexity of allocating tasks to workers and workstations.

3.1. Model Assumptions

The model is established under the following assumptions:

(1)

The priority relationship constraints among tasks are known.

(2)

The same assembly work needs to be assigned to the same workstation.

(3)

The transportation time of the product between workstations is not considered.

(4)

The switching time between different model products is not considered.

(5)

One task can only be assigned to one workstation.

(6)

The standard time for completing the operation is scientifically determined and fixed.

(7)

The equipment is movable, and any operation can be assigned to any workstation.

(8)

The completion time of the operation does not change due to the assignment to a workstation.

(9)

Workers at all workstations possess identical skill levels and are capable of performing any assigned task.

(10)

The time required by different workers to complete the same task element is assumed to be identical.

(11)

The cumulative processing time of tasks allocated to an individual worker must not exceed the specified cycle time.

(12)

The maximum number of workers permitted at each workstation is predefined.

(13)

Each worker remains fixed at the assigned workstation during one production cycle.

(14)

Within a workstation, workers may move freely to support other operations if idle time occurs after completing their assigned tasks.

It should be noted that some of the above assumptions (e.g., identical worker skills, deterministic task times, and negligible switching time) represent an idealized production environment. These assumptions are commonly adopted in the first stage of assembly line balancing research to ensure model tractability and to isolate the influence of workstation sharing. In real production, short model-switching operations are often absorbed by buffered workstations or included in the predetermined standard time provided by the industrial engineering department of Company W.

Therefore, the current model can be regarded as an initial deterministic planning framework that focuses on structural heterogeneity and workstation sharing. Future extensions of this research will incorporate stochastic processing times, worker skill variability and model-switching delays to improve adaptability under highly dynamic production scenarios.

3.2. Notation Description

Table 1. Symbolic Representation.

Symbol	Meaning
$i,h,p$	Represent task $i,h,p\in I$
$j,g$	Represent workstations $j,g\in J$
$m$	Product type indicator, $m=1$ for FV, $m=2$ For EV.
$I$	Task set $I=\left\{\mathrm{1,2},\dots i\dots ,nt\right\}$
$J$	Workstation set $J=\left\{\mathrm{1,2},\dots j\dots ,nms\right\}$
$W$	Set of workers assigned to stations, $W=\left\{\mathrm{1,2},\dots ,nw\right\}$
$ET$	Set of EV-specific tasks
$FT$	Set of FV-specific task
PT	Set of shared tasks
$P\left(i\right)$	Set of immediate predecessor tasks of task i
$P_a\left(i\right)$	Set of all predecessor tasks of task i
$P_0$	Set of tasks with no predecessors, $P_0=\left\{i\in I|P\left(i\right)=\varnothing \right\}$
$Q_{max}$	Upper bound on the number of workers allowed per workstation.
$t_{im}$	Operation time of task i for product type m
$t_{im}^s$	Operation time of task i for product type m
$t_{im}^f$	Finish time of task i for product type m
$T_w$	Total assembly time of worker w
$\overline{T}$	Average completion time of all workers
$c_i$	Completion time associated with task i
$CT$	Cycle time of the production line
$\delta$	A sufficiently large positive constant
$y_{iw}$	Binary variable equal to 1 when task i is handled by worker w, and otherwise, 0.
$x_{ij}$	Binary variable equal to 1 when task i is assigned to workstation j; otherwise, 0.
$v_{wj}$	Binary variable taking value 1 if worker w operates at workstation j; otherwise, 0.
Oih	Indicator variable equal to 1 when tasks i and h share the same worker, with i preceding h in sequence.
$Z_{ip}$	Binary indicator that equals 1 if, within the same station, task i is processed before p.
$U_j$	Utilization flag for workstation j; 1 if active, 0 otherwise.
$K_w$	Worker assignment flag: 1 if worker w performs at least one task.
$b_j$	Binary variable: equals 1 if workstation j is a shared (mixed) workstation; otherwise, 0.
$E_j$	Binary variable: 1 if workstation j contains tasks belonging to ET; otherwise, 0.
$F_j$	Binary variable: 1 if workstation j contains tasks belonging to FT; otherwise, 0.

Note: In this model, the cycle time $CT$ and the upper bound of workers per workstation $Q_{max}$ are treated as predefined parameters rather than decision variables. Based on practical production settings and preliminary experiments, the typical value range of $CT$ lies between 80–200 s, and that of $Q_{max}$ between 2–5 workers. In the case study, we adopted $CT=150\mathrm{s}$ and $Q_{max}=3$, which provides a realistic workload level. In addition, both $CT$ and $Q_{max}$ directly influence convergence behavior during decoding: a tighter $CT$ or a smaller $Q_{max}$ increases the frequency of station expansion and constraint violations, thereby enlarging the search space and slowing convergence; conversely, moderate values (as used in the case study) help stabilize the decoding process and improve GA convergence efficiency.

lists the notation and symbols used in this paper.

3.3. Objective Functions

In this research, a hierarchical multi-objective strategy is adopted in the genetic algorithm: the first level minimizes the number of starting workstations $S_1$, the second level minimizes the number of starting workers $S_2$, and the third level minimizes the load smoothing index $S_3$.

Equation (1): Minimizes the number of workstations, minimizes the space utilization rate.

Equation (2): Minimizes the total number of workers, improves labor efficiency.

Equation (3): The minimum worker load smoothing index, which balances the workload of each worker.

$$min{S}_1={\sum }_{j\in J}{U}_j\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{U}_j=\left\{\begin{array}{c}1, if{\sum }_{i\in I}{x}_{ij}\ge 1\hfill \\ 0,otherwise\hfill \end{array}\right.$$

(1)

$$min{S}_2={\sum }_{w\in W}{K}_w\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{K}_w=\left\{\begin{array}{c}1, if{\sum }_{i\in I}{y}_{iw}\ge 1\hfill \\ 0,otherwise\hfill \end{array}\right.$$

(2)

$$min{S}_3=\sqrt{{\displaystyle \frac{1}{W}}{\sum }_{w\in W}{\left(T_w-\overline{T}\right)}^2}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\overline{T}={\displaystyle \frac{1}{W}}{\sum }_{w\in W}{T}_w$$

(3)

Suppose there are $w$ workers. The completion time for each worker’s task is $T_w$, and the average completion time is $\overline{T}$.

3.4. Constraints

Allocation constraints: Equation (4) ensures that each task can only be assigned to one workstation. Equation (5) indicates that each task can only be assigned to one worker.

$$\sum _{j\in J}{x}_{ij}=1 \forall i\in I$$

(4)

$$\sum _{w\in W}{y}_{iw}=1 \forall i\in I$$

(5)

Equation (6) Priority Constraint: The priority constraint ensures that each job can be assigned to the current workstation under the condition that all the preceding jobs of this job have been assigned to a previous or the same workstation.

$$\sum _{g\in J}g\times x_{hg} \le \sum _{j\in J}j\times x_{ij} \forall i\in I-P_0,h\in P(i)$$

(6)

Equation (7) guarantees the temporal feasibility of the model by requiring that each task begins at a non-negative time instance.

$$t_{im}^s\ge 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\forall i\in I,m\in M$$

(7)

Equations (8)–(10) further refine the task sequencing relationships.

Equation (8) enforces the direct precedence between tasks h and i.

$$\begin{gathered} t_{im}^s-t_{hm}^s+\delta \left(1-x_{hj}\right)+\delta (1-x_{ij})\ge t_{hm} \\ \forall i\in I-P_0,h\in P\left(i\right),j\in J,m\in M \end{gathered}$$

(8)

Equations (9) and (10) describe sequencing rules for tasks without precedence relations when assigned to the same workstation, ensuring that task execution order remains feasible.

$$\begin{gathered} t_{pm}^s-t_{im}^s+\delta \left(1-x_{ij}\right)+\delta \left(1-x_{pj}\right)+\delta (1-Z_{ip})\ge t_{im} \\ \forall i\in I,m\in M,p\in I-P_a\left(i\right),j\in J \end{gathered}$$

(9)

$$\begin{gathered} t_{im}^s-t_{pm}^s+\delta \left(1-x_{ij}\right)+\delta \left(1-x_{pj}\right)+\delta Z_{ip}\ge t_{pm} \\ \forall i\in I,m\in M,p\in I-P_a\left(i\right),j\in J \end{gathered}$$

(10)

Equation (11) introduces the workstation-sharing constraint, a key feature of the proposed model. It enables the co-location of EV-specific and FV-specific operations at the same workstation to improve cycle time utilization and model coordination. A binary variable $b_j$ is introduced to indicate whether workstation j operates as a shared (hybrid) station, ensuring that both EV and FV models have executable tasks at any active workstation.

$$\begin{gathered} \sum _{i\in ET}{x}_{ij}\mid \ge \mid b_j,\sum _{i\in FT}{x}_{ij}\mid \ge \mid b_j,\sum _{i\in ET}{x}_{ij}\mid \le \mid \delta \mid b_j,\sum _{i\in FT}{x}_{ij}\mid \le \mid \delta \mid b_j \\ {b}_j\in \left\{\mathrm{0,1}\right\},\forall j\in J \end{gathered}$$

(11)

Equation (12): A worker can only handle one process at a time and cannot handle two processes simultaneously; that is to say, the two processes assigned to the same worker must satisfy the sequence constraint.

$$c_i\le c_h-t_h+\delta \left(1-O_{ih}\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\forall i,h\in I$$

(12)

Equations (13) and (14) represent a time constraint. The completion time of worker w is equal to the end time of the latest completed process among all the processes he assembles. The maximum completion time of all workers does not exceed the cycle time.

$$T_w=\underset{i\in I_w}{\max }{t}_{im}^f\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\forall m\in M,w\in W$$

(13)

$$T_w\le CT\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}w\in W$$

(14)

Equation (15): The actual number of staff working at the workstation does not exceed the maximum number of staff that the workstation can accommodate.

$$\sum _{w\in W}{v}_{wj}\le Q_{max}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\forall j\in J$$

(15)

Equation (16): The tasks assigned to the same worker must be assigned to the same workstation.

$$\begin{gathered} \sum j\ast x_{ij}\le \sum j\ast x_{hj}+\delta \left(2-y_{iw}-y_{hw}\right) \\ \forall \left(i,h\right)\in I,i\ne h,\forall w\in W \\ \sum j\ast x_{hj}\le \sum j\ast x_{ij}+\delta \left(2-y_{iw}-y_{hw}\right) \\ \forall \left(i,h\right)\in I,i\ne h,\forall w\in W \end{gathered}$$

(16)

4. Algorithm Design

Based on the MMuALBP-WS mathematical model proposed in this paper, the following introduces the implementation of IGA specifically designed to consider workstation sharing. Through the proposed decoding mechanism for workstation sharing, the classic GA framework is expanded. IGA can generate feasible and near-optimal solutions for MMuALBP. Different from algorithm improvements that aim for general performance enhancement, the IGA optimization design in this paper is carried out in response to the new decision variables and constraints introduced by the workstation sharing mechanism. The following will detail the steps, operations, and evaluation mechanism.

4.1. Encoding and Decoding Mechanism

Before detailing the decoding process, the encoding strategy used to represent task sequences and workstation assignments is first introduced.

4.1.1. Encoding Strategy

When representing individual entities, a natural number encoding method based on the priority order of process topologies is adopted. Each gene position corresponds to a process number, and the entire chromosome represents the allocation sequence of assembly line tasks. This approach can avoid the increase in computational complexity caused by base conversion. The encoding method is shown in Figure 1.

4.1.2. Decoding Strategy

The coding sequence reflects the relative order of the processes. The decoding process converts each chromosome into an effective configuration of task, worker and workstation allocation, ensuring compliance with priority relationships and cycle time constraints. Considering the characteristics of mixed production of fuel and electric vehicles, multi-workers sharing the same workstation, and workstation sharing, the decoding steps are as follows:

Step 1: Topology initialization, generating candidate set

Perform topological sorting on the processes. Any jobs whose pre-requisite tasks have been assigned will be added to the candidate set C. Based on the vehicle type attributes, the tasks are classified into electric vehicle-specific tasks (ET), fuel vehicle-specific tasks (FT), and general tasks (PT). Initialize the first workstation and the worker set $W_1$.

Step 2, Candidate set update and task selection

To promote workstation sharing, the decoder explicitly considers task heterogeneity during selection. When the current workstation contains only ET or only FT, the decoder gives priority to tasks of the opposite category (FT or ET) to fill the idle capacity of the station. If both types of specific tasks already exist in the station, task selection will follow priority in the chromosome sequence. This mechanism transforms task-type heterogeneity into an opportunity for workstation sharing, instead of treating it as a conflict.

Step 3: Worker allocation and takt time check

The worker with the least current load in the station is selected. For each EV/FV scenario, the effective load is computed as max (PT + ET, PT + FT). The current task is assigned only if the worst-case load does not exceed the cycle-time limit CT.

Otherwise, Step 4 will be triggered.

Step 4: Workstation expansion and shared station repair

If the number of workers has not reached the upper limit $Q_{max}$, a new worker will be added, and task assignments are re-evaluated. If the station is full, the decoder checks whether the station contains only ET or only FT. In such cases, a “shared-station repair” procedure is activated: tasks of the missing category are searched and allocated to the station whenever the worst-case load remains feasible. This process converts single-class stations into shared stations, ensuring a stronger utilization of workstation capacity. If no complementary task is feasible, the station will be closed and the next workstation will be initialized.

Step 5: Iteration and termination

Repeat the above process until all tasks are allocated.

Fitness comparison uses the strict lexicographic method: first compare the number of workstations, if they are the same, then compare the number of workers, if they are still the same, then compare the smoothing index.

The decoding process is depicted in Figure 2.

Workstation sharing is only permitted when two conditions are satisfied:

(1)

The required fixture or geometric position for EV- and FV-specific tasks is compatible.

(2)

The combined workload of both task types does not exceed the cycle time CT.

If either condition is violated, the task is assigned to a new workstation, ensuring that workstation sharing does not lead to cycle-time delays or operator overload. This reflects the actual assembly rules of Company W, where model switching is allowed only when tooling compatibility and safety constraints are fulfilled. Therefore, workstation sharing in this paper is not arbitrary, but a restricted strategy embedded into the decoding mechanism to improve resource utilization in heterogeneous assembly environments.

4.2. Parameter Selection Justification

The parameter configuration adopted in this study was determined based on literature. The parameters used in the improved genetic algorithm are as follows: population size is 60, crossover probability is 0.90, mutation probability is 0.20, elite rate is 20%, and the maximum number of iterations is 200. According to the literature discussed in the assembly line balance research [31], the recommended population size is usually between 50 and 100 to ensure sufficient genetic diversity while avoiding excessive computational burden [8,32]. The crossover probability is generally set between 0.8 and 0.95, as it can accelerate the combination process of promising partial solutions, and the mutation rate is considered appropriate within the range of 0.05 to 0.30 [13]. The upper limit of 200 iterations was determined based on the preliminary run results. The preliminary run results showed that the target value had stabilized before reaching this upper limit, indicating that further iterations would not bring significant benefits.

These observations are consistent with the recognized behavior of genetic algorithms. In this algorithm, a moderate population size, a high crossover rate, and a controllable mutation level are conducive to achieving stable convergence. The preliminary test of the case study also confirmed that minor adjustments based on these settings would not have a substantial impact on the final number of stations or workers, while the convergence speed and computing time remained stable. Therefore, the selected parameter configuration is considered suitable for the mixed model FV-EV assembly line balance problem discussed in this study.

4.3. Generation of Initial Population

To ensure the feasibility and diversity of individuals, this paper adopts a random initialization algorithm based on topological sorting to generate the initial population. The specific steps are as follows:

(1)

Extract tasks without predecessors or whose predecessors have been completed from task set I, forming a candidate set P;

(2)

Randomly select task $o_i\in P$ and add it to the chromosome sequence, then remove it from P;

(3)

Update the candidate set P and repeat the operation until all tasks are assigned.

(4)

Repeat the above process NP times to obtain an initial population containing NP feasible chromosomes.

4.4. Fitness Evaluation

In genetic algorithms, the fitness function is used to evaluate the quality of individual solutions and serves as the core basis for algorithm selection operations. For the balanced problem of MMuALBP, to reflect the multi-level optimization concept, this paper adopts the hierarchical lexicographical order method for fitness evaluation.

Firstly, the total number of workstations is set as the first-level optimization objective to ensure that the decoding result can minimize the number of workstations on the assembly line as much as possible. Secondly, the total number of workers is used as the second-level optimization objective to ensure that the decoding result can minimize the number of workers on the assembly line. Finally, to further distinguish the superiority and inferiority of solutions with the same number of workstations and workers, the minimum worker smoothing index is used as the third-level objective to measure the deviation between worker loads. During individual comparison, the sorting criteria are successively the workstation number level, the worker number level, and the smoothing index.

4.5. Genetic Operators

This subsection describes the genetic operators adopted in the IGA. To keep the evolving population feasible and diverse, the algorithm applies three key operators: selection, crossover, and mutation.

4.5.1. Selection Operator Design

The selection operator determines the way of inheriting superior genes. In this paper, a strategy combining elite retention and roulette wheel selection is adopted. Firstly, the individuals are sorted in descending order of fitness value, and the top 20% are retained as elites. Then, using the roulette wheel method, a portion of individuals from the parent population is selected to generate the offspring population. The fitness value of the new population is calculated and sorted in descending order. Finally, 20% of the individuals with the lowest fitness value in the offspring are replaced by the elites from the parent population to balance the global search and local exploration capabilities. This method considers the genetic nature of the global optimal solution and the diversity of the population, which helps to prevent the algorithm from getting stuck in a local optimum.

4.5.2. Crossover Operator Design

This article adopts the sequential cross-over method, and the process is as follows:

Two parent chromosomes $F_1$ and $F_2$ are randomly selected, and two crossover points $c_1$ and $c_2$ are determined ($c_1<c_2$). The segment between $[c_1,c_2]$ in $F_1$ is copied to the same position in offspring $S_1$, while the remaining genes are filled from $F_2$ in their original order. The same process is applied symmetrically to produce $S_2$.

After the crossover, a precedence-checking and repair procedure is performed to ensure feasibility by adjusting task orders that violate precedence constraints. The process of the crossover operation is illustrated in Figure 3.

4.5.3. Mutation Operator Design

To prevent premature convergence and enhance population diversity, a topology-constrained insertion mutation is applied. A task a₁ is randomly selected for mutation, and its direct predecessors and successors are identified to determine their positions in the chromosome. Let b₁ denote the last position among its predecessors and b₂ the first position among its successors. The selected gene a₁ is then reinserted at a random position within the interval [b₁, b₂], forming a new feasible sequence. This mutation strategy preserves topological feasibility while improving the algorithm’s global search ability and its capacity to escape local optima.

4.6. Termination Criteria

Let t represent the current generation index and T the predefined generation limit. After completing selection, crossover, and mutation operations in each iteration, the algorithm proceeds to the next generation when t < T. If no improvement in the best fitness value is detected over several successive iterations, or the generation limit is reached, the evolutionary process terminates. The chromosome exhibiting the highest fitness is then considered the final optimal solution.

4.7. Summary

The IGA framework proposed in this paper is an improvement on the classical GA. It achieves this improvement by introducing a workstation-sharing decoding mechanism specifically for heterogeneous vehicle models. Although it does not introduce a completely new algorithm structure, the IGA can effectively adapt to the new decision variables and constraints related to workstation sharing, thereby increasing the utilization rate of the production line without increasing equipment costs.

The proposed workstation-sharing mechanism serves as the main strategy to mitigate the negative effects of task heterogeneity. By enabling EV- and FV-specific tasks to co-exist within the same workstation when feasible, the model reduces idle time caused by model-exclusive operations, improves workstation utilization, and increases the flexibility of task deployment. Furthermore, the decoding procedure in the IGA prioritizes complementary EV/FV tasks during assignment, allowing heterogeneous workloads to be balanced dynamically across workers. These strategies help maintain line balance even under significant cross-model task differences.

Therefore, the improvement proposed in this paper emphasizes that the term “improvement” refers to the adaptability of the algorithm in a specific context, rather than a traditional advancement of the algorithm. In the next section, this paper will demonstrate the practicality of the proposed method and algorithm through case studies and experiments.

5. Case Study and Experimental Validation

To evaluate the effectiveness and practical relevance of the proposed MMuALBP-WS model and the associated IGA, a real mixed-model automotive assembly line is used as the basis for empirical validation. This section presents the case description, experimental setup, and result analysis, demonstrating how workstation sharing influences station utilization, worker allocation, and overall line performance.

5.1. Assembly Line Data

Company W is a small car manufacturing enterprise. Due to changes in the automotive market, the company plans to increase the production volume of EVs. Due to the adjustment of the production plan, the production capacity of the FV assembly line is overcapacity. The company is considering placing the assembly of an EV based on the FV chassis on the FV assembly line for production.

According to the production data provided by the enterprise, this study takes Chassis Assembly Line 1 of W Automobile Company as the research case. Extracted 58 assembly tasks; each task is assigned a standard operation time and a precedence relationship. The cycle time is set to 150 (s). Among these tasks, 17 are EV-specific operations (ET), 19 are FV-specific operations (FT), and the remaining 22 are common tasks (PT) shared by both vehicle models. The EV-specific tasks mainly involve battery pack mounting, high-voltage cable routing, and thermal management module installation, whereas the FV-specific tasks include fuel tank assembly, exhaust system installation, and engine-related connections.

The precedence relationships are represented in the form of a directed graph to ensure the logical consistency of the process sequence. All data is derived from on-site investigations and standard time measurements provided by the enterprise, accurately reflecting the actual production situation.

The assembly task data for the FV and EV Chassis Assembly Line 1 are shown in

Table 2. Detailed task data of the mixed-model chassis assembly line.

Task ID	Task	Task Time (s)	Immediate Predecessors	Task Set
0	Chassis positioning and initial alignment	20	-	PT
1	Tighten the engine	60	0	FT
2	Fasten the drive motor	40	0	ET
3	Place the motor on both left and right mounts	12	2	ET
4	Install the left hover	48	3	ET
5	Install the right mount	64	3	ET
6	Install the left mount to the subframe end	30	4	ET
7	Install the right mount to the subframe end	30	5	ET
8	After installation, mount it onto the drive motor	48	6, 7	ET
9	After installation, mount it to the subframe end	30	8	ET
10	Install the left suspension bracket of the engine	30	0	FT
11	Install the mount on the right side of the engine	48	10	FT
12	Install the left suspension of the engine	40	11	FT
13	Install the right-side mount of the engine	40	12	FT
14	The gearbox is rear mounted onto the gearbox	38	1	FT
15	The transmission is rear mounted onto the vehicle body	15	14	FT
16	Install the transmission to the engine	20	15	FT
17	Install the transmission to the engine	20	15	FT
18	Place the three-way catalytic converter assembly	20	16	FT
19	Install the three-way catalytic converter assembly	20	17	FT
20	Install the vacuum tank assembly	22	0	PT
21	Install the small bracket assembly of the vacuum pump	26	20	PT
22	Tighten the bolts of the vacuum pump bracket	20	21	PT
23	Connect the front wiring harness	15	22	PT
24	Place the brake pedal assembly	50	0	PT
25	Install the brake pedal assembly	50	24	PT
26	Install the pin shaft and lock pin	15	25	PT
27	Apply lubricating grease	8	26	PT
28	Place the three-way catalytic converter assembly	40	1	FT
29	Install the three-way catalytic converter assembly	40	1	FT
30	Install the parking brake control assembly	40	28	FT
31	Connect the wiring harness	40	29	FT
32	Place the handbrake cable assembly onto the front floor	64	30, 31	FT
33	Install the handbrake cable assembly to the front floor	64	32	FT
34	Place the handbrake cable assembly on the rear floor	64	33	FT
35	Install the handbrake cable assembly to the rear floor	64	33	FT
36	Install the charging and distribution system	55	0	ET
37	Place the power battery	40	36	ET
38	Lift the power tray	40	36	ET
39	Place the bolts for the power battery	48	37	ET
40	Pre-tighten the bolts of the power battery	48	38	ET
41	Tighten the bolts of the left power battery	10	39	ET
42	Tighten the bolts of the right power battery	10	40	ET
43	Connect the grounding bolt	48	41, 42	ET
44	Connect the front wiring harness	48	43	ET
45	Add the brake fluid reservoir cap	32	34, 35, 18, 19, 44	PT
46	Arrange the rear brake hard pipe assembly	52	9, 13, 23, 27	PT
47	After installation, brake the hard pipe assembly	60	46	PT
48	Connect the front brake hard pipe assembly	40	47	PT
49	Tighten the brake hard pipe assembly before fastening	20	48	PT
50	Place the brake master cylinder booster assembly	50	45	PT
51	Connect the brake master cylinder booster assembly	40	50	PT
52	Connect the brake master cylinder	25	51	PT
53	Tighten the brake master cylinder	50	52	PT
54	Install the ABS module assembly onto the bracket	30	51	PT
55	Install the ABS bracket assembly onto the vehicle body	15	54	PT
56	Place the rear wheel speed sensor	40	49, 53, 55	PT
57	Install the rear wheel speed sensor	25	56	PT

Note: ET denotes Electric Vehicle-specific tasks. FT denotes Fuel Vehicle-specific tasks. PT denotes Public (shared) tasks common to both models.

, and the comprehensive precedence relationships are illustrated in Figure 4.

5.2. Results and Discussion

The following analysis begins with the presentation of the experimental results, followed by comparative evaluations and verification of the workstation-sharing mechanism.

5.2.1. Experimental Results Presentation

Computational experiments were conducted in MATLAB R2019a, where the key parameters of the genetic algorithm were configured as follows: a population size of 60, 200 generations, crossover and mutation probabilities of 0.9 and 0.2, respectively, and an elitism rate of 20%. The production cycle time was fixed at 150 s, with no more than three operators assigned to each workstation.

Considering heterogeneity and the workstation-sharing mechanism, the best task assignment scheme was obtained from the experiments using the proposed model and decoding strategy. The assembly task allocation scheme and the worker load distribution are shown in Figure 5.

Without considering heterogeneity-based workstation sharing, the task allocation scheme obtained using the GA-based model proposed in Reference [20] is shown in Figure 6.

5.2.2. Comparative Analysis of Results

The comparison results are presented in

Table 3. Comparison of assembly line balancing results between models with and without workstation sharing.

Worker	EV (Model 1)	FV (Model 1)	EV (Model 2)	FV (Model 2)
Worker 1	110	110	137	138
Worker 2	60	138	128	138
Worker 3	142	0	126	135
Worker 4	30	103	133	133
Worker 5	0	138	134	124
Worker 6	0	144	144	124
Worker 7	130	55	73	137
Worker 8	138	50	132	132
Worker 9	71	87	72	136
Worker 10	20	128	135	135
Worker 11	144	0	140	140
Worker 12	142	112	–	–
Worker 13	107	147	–	–
Worker 14	125	125	–	–
Worker 15	135	135	–	–
Total Idle Time	896	778	296	178
Total Available Working Time	2250	2250	1650	1650
Overall Load Rate	60.18%	65.42%	82.06%	89.21%

Note: Model 1 corresponds to the baseline model proposed in Reference [18], which does not consider workstation sharing. Model 2 represents the proposed model in this study, which incorporates workstation sharing and a revised decoding mechanism to optimize task allocation among heterogeneous models (EV and FV).

.

By running the improved genetic algorithm, the main outcomes of the assembly line balancing optimization can be summarized as follows:

(1)

Number of Workstations: After optimization, the required number of workstations was reduced to four, representing a 25% decrease compared with the baseline model. This indicates an improvement in space efficiency and an enhancement in task grouping.

(2)

Number of workers: After optimization, the total number of workers decreased from 15 to 11, a reduction of 27%.

(3)

Smoothness index: The smoothness index dropped from 7.08 to 3.26, a decrease of nearly 50%, indicating a more balanced workload among workers.

(4)

Worker load efficiency: The average worker load rate increased from 63% to 86%, resulting in a 23% improvement in labor productivity and workload balance.

(5)

Task allocation rationality: Dedicated EV tasks and dedicated FV tasks are assembled on shared workstations, reducing idle workstations and enabling tasks with structural differences between EV and FV to share workstations.

5.2.3. Verification of the Workstation-Sharing Effect

This paper compares the working hours of EV and FV processing at the workstation under two models, verifying the effectiveness of the workstation sharing mechanism. This paper compares the usage of workstations and conducts statistics on idle time. In the baseline model (Model 1), since the workstation sharing was not considered, the dedicated processes of EV and FV occupied the workstations separately, resulting in significant idle time for the workstations. The detailed results are shown in

Table 4. Workstation utilization non-sharing model.

Workstation	Workers	Task Time per Worker (s)	Total Work Time (s)	Total Available Time (s)	Utilization
S1 (EV)	3	110, 60, 142	312	450	69.33%
S1 (FV)	3	110, 138, 0	248	450	55.11%
S2 (EV)	3	30, 0, 0	30	450	6.67%
S2 (FV)	3	103, 138, 144	385	450	85.56%
S3 (EV)	3	130, 138, 71	339	450	75.33%
S3 (FV)	3	55, 50, 87	192	450	42.67%
S4 (EV)	3	20, 144, 132	296	450	65.78%
S4 (FV)	3	128, 0, 112	240	450	53.33%
S5 (EV)	3	107, 125, 135	367	450	81.56%
S5 (FV)	3	147, 125, 135	407	450	90.44%
Average	-	-	-	-	62.58%

Note: The key algorithm parameters were configured as follows: a population size of 60, 200 generations, crossover and mutation probabilities of 0.90 and 0.20, respectively, and an elitism rate of 20%. The production cycle time was fixed at 150 s, with a maximum of three operators allowed at each workstation.

. The MMuALBP-WS model proposed in this paper (Model 2) considers workstation sharing, enabling EV and FV tasks to alternate execution within the same workstation, thereby improving the utilization efficiency of workstation resources. The detailed results are shown in

Table 5. Workstation utilization sharing model.

Workstation	Workers	Task Time per Worker (s)	Total Work Time (s)	Total Available Time (s)	Utilization
S1 (EV)	3	137, 128, 126	391	450	86.89%
S1 (FV)	3	138, 138, 135	411	450	91.33%
S2 (EV)	3	133, 134, 144	411	450	91.33%
S2 (FV)	3	133, 124, 124	381	450	84.67%
S3 (EV)	3	73, 132, 72	277	450	61.56%
S3 (FV)	3	137, 132, 136	405	450	90.00%
S4 (EV)	2	135, 140	275	300	91.67%
S4 (FV)	2	135, 140	275	300	91.67%
Average					86.14%

Note: This table reports the workstation utilization results under the workstation-sharing model (Model 2).

.

The relatively low utilization observed for S3 (EV) is mainly due to the model-exclusive operations located at the early stages of the chassis assembly process. Because these tasks cannot be shared between FV and EV models and must satisfy strict precedence constraints, opportunities for merging or reallocating tasks across models are limited. Potential improvements include re-sequencing preparatory tasks, inserting minor auxiliary operations to fill idle time, or enabling limited worker support between adjacent stations.

Figure 7 compares the workstation utilization rates between the baseline model (Model 1: Non-sharing) and the proposed model (Model 2: With sharing). The introduction of workstation sharing effectively increases the average utilization rate from 62.58% to 86.14%, demonstrating enhanced balance and resource efficiency across the assembly line.

Due to the introduction of the workstation sharing mechanism, the utilization rate of workstations has increased, enabling various tasks to make full use of space and human resources. This mechanism has improved the balance of the production line, production flexibility, and the responsiveness to the demand for mixed vehicle models.

Furthermore, in order to verify the necessity of the proposed model, we conducted a comparative analysis between the baseline model proposed by Roshani and Ghazi Nezami [18] and the proposed MMuALBP-WS model. The baseline model did not consider workstation sharing, which inevitably results in idle workers when only EV-specific or FV-specific tasks are available at a given workstation. This is a realistic phenomenon commonly observed in mixed assembly lines (see Table 4 and Figure 6)

In contrast, the proposed model integrates specific tasks for different types of EVs and FVs within the same workstation (Table 5 and Figure 5), thereby reducing the number of workstations by 25%, the total number of staff by 27%, and increasing the average utilization rate by 23.56%.

These findings confirm that the proposed workstation sharing mechanism has changed the direction of optimization, achieving a more stable workload distribution and better resource utilization under the same production constraints, thereby verifying the necessity and effectiveness of the proposed MMuALBP-WS model.

5.3. Summary of Case Findings

The case study of the chassis assembly line for hybrid vehicles of W Company verified the effectiveness of the proposed MMuALBP-WS model and IGA. The comparative experiment shown in Section 5.2 demonstrated that integrating the workstation sharing function significantly improved the balance, labor efficiency, and resource utilization of the production line. In conclusion, the experimental results confirmed that introducing the workstation sharing mechanism in a hybrid vehicle and multi-operator environment can enhance production flexibility and space utilization, providing reference opinions for automotive enterprises that aim to achieve co-production of FVs and EVs on the same production line.

6. Conclusions and Future Work

This section is divided into two parts: Section 6.1 summarizes the main findings of the study, and Section 6.2 outlines future research directions.

6.1. Conclusions

This research explores the MMuALBP-WS issue in the context of the automotive industry’s transition from FVs to EVs manufacturing. This paper develops a deterministic multi-objective mathematical model that considers the heterogeneity of assembly tasks for EVs and FVs, as well as the workstation sharing mechanism. An IGA with a specific decoding process is designed, and the algorithm decodes the workstation sharing mechanism proposed in the model to solve the proposed model. The case study of the chassis assembly line of W Company validates the feasibility and superiority of the proposed method. From a quantitative perspective, the proposed model and algorithm achieve performance improvement, with the number of workstations and labor demand reduced by approximately 25% and 27%, respectively, and the stability of worker load increased by nearly 50%, and the average workstation utilization rate increased by 23.56%. These results highlight the ability of this model to coordinate heterogeneous tasks, reduce idle resources, and enhance the flexibility of the entire assembly line. From a practical perspective, the workstation sharing mechanism can effectively allocate human and space resources, enabling EVs and FVs to share production processes. These research results provide theoretical support for enterprises that wish to transform traditional FV production lines into EV production lines.

The applicability of the workstation-sharing mechanism depends on several structural characteristics of the mixed-model assembly system. In particular, the proportion of model-specific tasks (ET and FV), the degree of task-time heterogeneity, and the upper limit of workers per station jointly determine whether sharing provides actual benefits. When model-specific operations dominate a workstation or when task durations are extremely unbalanced, the effectiveness of sharing may diminish. The present study focuses on validating the mechanism under the realistic conditions of the industrial case, while a systematic analysis of boundary conditions will be explored in future research.

6.2. Future Work

Although the proposed MMuALBP-WS model and IGA algorithm can optimize actual production, there are still directions that need further exploration. Future research can consider uncertainties and dynamic factors in the production process, such as task time uncertainty, worker skill differences, and equipment failures. An important goal is to investigate the applicability boundaries of the workstation sharing mechanism, and determine under which conditions EV–FV sharing becomes ineffective (e.g., extremely unbalanced model proportions or rigid precedence structures).

Additionally, for multi-objective planning models, more advanced meta-heuristic algorithms or hybrid algorithms (such as NSGA-II, MOEA/D, or GA–Tabu Search) can be adopted to improve it into a fully multi-objective optimization method. From a theoretical perspective, future extensions could incorporate concepts from production-systems engineering (e.g., bottleneck analysis, resource allocation and trade-off principles) to provide a more general system-level framework for mixed-model multi-manned balancing.

Another direction is to consider combining this model with digital twins and simulation software (such as FlexSim or Arena) to achieve real-time verification of the assembly process and adaptive reconfiguration. Moreover, the workstation sharing mechanism can be applied to more mixed production systems, including joint production lines of electric vehicles and plug-in hybrid vehicles, battery pack assembly, and intelligent component manufacturing, thereby supporting the digital transformation of the automotive industry.