Modeling and Optimization of a Mixed-Model Two-Sided Assembly Line Balancing Problem Considering a Workstation-Sharing Mechanism

Abstract

In the context of the rapid development of the new energy vehicle industry, how to achieve the mixed production of fuel vehicles and electric vehicles has become an important issue for the transformation and flexible manufacturing of automotive production lines. This paper addresses the balance problem of the mixed assembly line for electric vehicles and fuel vehicles and proposes a mathematical modeling method based on the product structure differences and workstation sharing. An improved genetic algorithm is designed for optimization. The established optimization model includes mathematical models of process priority relationships, cycle time constraints, synchronization constraints, and exclusive process co-placement constraints, with the optimization goals of minimizing workstation quantity and balancing workstation load. To solve such models, the decoding process of the genetic algorithm is redesigned in the algorithm design. The improved genetic algorithm can be well used to solve the workstation-sharing model. A case study of the chassis assembly line of an automotive manufacturing enterprise is used for verification. The results show that the method considering workstation sharing can effectively reduce the number of workstations, improve the distribution of workstation loads, and increase the utilization rate of the production line, while ensuring the cycle time constraints. The conclusions of this study expand the theoretical framework of the balance problem of mixed assembly lines and provide practical references for the transformation of fuel vehicle production lines into new energy vehicles.

1. Introduction

Over the past decade, the automobile sector has experienced a substantial transformation driven by technological innovation and electrification. The accelerating adoption of new energy vehicles (NEVs) has become a defining trend that is reshaping the structure of the global automotive market. According to statistics from the International Energy Agency, global electric vehicle (EV) sales exceeded 17 million units in 2024, accounting for more than 20% of total vehicle sales worldwide, with nearly half contributed by the Chinese market [1]. Meanwhile, the annual production of fuel vehicles (FVs) in China has decreased from 29 million in 2017 to less than 18 million in 2024. These changes have led to overcapacity in traditional FV production lines, and the construction of new pure EV production lines requires significant investment of capital and resources. How to achieve flexible transformation based on the existing production capacity has become a strategic issue that automotive manufacturing enterprises urgently need to address.

In this context, the mixed-model assembly line has become a common solution for automotive manufacturing enterprises [2,3]. By producing both FVs and EVs on the same assembly line simultaneously, enterprises can meet the diverse market demands while avoiding redundant investments and enhancing the flexibility of the production line. Compared with the traditional single-model assembly line, the mixed-model assembly line can maintain production continuity and economy in the case of rapid changes in product types [4,5]. However, mixed-model production also brings higher complexity. In the automotive final assembly line, due to significant process differences and task time differences among different vehicle models, the large number of components makes the task allocation and workstation balance more difficult [2,6].

Overall, although the existing research has made significant progress in model and algorithm design, there are still some shortcomings. First, most studies simplify the problem by weighing time and integrating priority relation graphs, ignoring the structural differences in process complexity between EV and FV, and thus cannot truly reflect its actual characteristics; the consideration of practical constraints is insufficient. Second, although some studies have involved worker skill differences and space limitations, the explicit modeling of synchronous constraints and workstation sharing constraints is still limited. Third, there is a lack of case studies that combine with actual automotive manufacturing enterprises, resulting in insufficient industrial application value of the research results.

Based on the above research deficiencies, this paper mainly conducts research from three aspects. A new mathematical model for the mixed production mode of EVs and FVs has been developed, clearly distinguishing the task sets of EVs and FVs, and introducing the workstation sharing mechanism. Considering the workstation sharing mechanism, a specific decoding strategy has been designed for IGA. During the decoding process, when tasks belonging to the shared workstation set are selected, the synchronous allocation of tasks from other vehicle types is made to the same workstation. A real chassis assembly line case from an automotive manufacturing enterprise was selected for research to verify the proposed model and algorithm. This study provides practical insights into the transformation of traditional FV production lines to EV manufacturing. In response to the demand for co-production of EVs and FVs, a comprehensive modeling and optimization framework has been formulated, providing theoretical support for flexible manufacturing systems.

Therefore, this study focuses on the following key questions:

RQ1: Given the significant structural differences between EVs and FVs, how can the assembly line be effectively balanced?

RQ2: How can the workstation sharing mechanism be considered in the modeling process to enhance production flexibility and resource utilization?

RQ3: How can an improved IGA be designed to solve multi-objective models?

Solving these problems will help to build a practical and feasible optimization framework for the mixed-model assembly system in the automotive industry.

In response to these questions, the main contributions of this study are as follows:

C1: A mathematical model is developed that distinguishes ET/FT/PT task sets and incorporates workstation sharing under precedence and synchronization constraints.

C2: A decoding-enhanced Improved Genetic Algorithm (IGA) is designed to embed EV–FV interaction logic and support efficient scheduling.

C3: A real chassis assembly case verifies the feasibility and managerial implications of the proposed approach.

2. Literature Review

Before developing the proposed model and algorithm, it is necessary to review the major developments in assembly line balancing theory and related optimization techniques. This section reviews the major studies on assembly line balancing, mixed-model configurations, and metaheuristic optimization approaches. The evolution from traditional SALBP to advanced MTALBP solutions is first introduced, followed by a discussion of algorithmic developments and industrial applications. Additionally, relevant cross-disciplinary insights are summarized to emphasize the importance of considering heterogeneous task characteristics and workstation-sharing mechanisms. These studies provide key references and reveal the research gaps that motivate the present work.

2.1. From SALBP to MTALBP

The Assembly Line Balancing Problem (ALBP) has been a key research direction in the field of production and manufacturing since it was proposed in the 1960s. The initial research focused on the single-model assembly line balancing problem (SALBP), whose goal was to reasonably allocate a set of assembly tasks to each workstation, while ensuring process priority constraints and production cycle times, and minimizing the number of workstations or maximizing production efficiency [7]. As market demand became more diverse, research gradually expanded to the mixed-model assembly line balancing problem (MALBP), which requires handling assembly tasks of multiple product models on the same production line. This significantly increases the complexity of the problem. To improve space utilization and production efficiency, scholars proposed the two-sided assembly line balancing problem (TALBP) [8,9,10] and developed the mixed-model two-sided assembly line balancing problem (MTALBP) [11]. In the final assembly stage of the automotive industry, bilateral assembly lines are widely used due to convenient material transportation and improved space efficiency, but they also require additional synchronization constraints and workstation orientation constraints, making the problem more complex [12,13,14].

2.2. Metaheuristic Approaches in ALBP

Kim et al. first applied genetic algorithms (GAs) to the TALBP, proving the applicability of intelligent optimization methods in complex constraints [10]. Özcan and Toklu established a mathematical model for the MTALBP and used the simulated annealing algorithm (SA) to solve it, achieving good results in medium-scale instances [11].

In terms of solutions, as the problem scale expands and the constraints become more complex, intelligent optimization algorithms have gradually become the research focus. Simaria and Vilarinho applied the ant colony algorithm (ACO) to the multi-model assembly line balancing problem, verifying the effectiveness of intelligent algorithms in complex optimization [15]. Chutima and Chimklai used particle swarm optimization (PSO) to handle the multi-objective mixed-model assembly line problem, improving the search performance, but the algorithm was prone to getting stuck in local optima [12]. Yuan et al. proposed a hybrid GA based on a bee colony, achieving a balance between global search and local development, improving the quality of the solution. However, it mainly focused on workstation quantity optimization and did not consider the load balance between workstations [16]. Duan et al. combined the migratory bird optimization (MBO) with multi-neighborhood search (VNS), improving the solution efficiency for large-scale MTALBP; however, their research lacked industrial case verification [17]. Delice et al. improved the PSO to achieve dual optimization of workstation quantity and load balance, and the numerical experimental results showed that its effect was superior to traditional methods [13].

In recent years, more studies have begun to integrate real-world constraints and multi-objective optimization. Kucukkoc and Zhang proposed a proxy-based ant colony algorithm, capable of handling complex parallel MALB [14]. Yadav and Agrawal proposed an improved genetic algorithm (IGA), improving the proportion of feasible solutions and search efficiency [18]. Huang et al. proposed a heuristic algorithm that takes weighted time as working hours to balance workstation quantity and balance rate [19]. Liao et al. introduced worker skill differences and spatial constraints into the model based on the multi-neighborhood search method, making the results closer to actual production, but did not consider the scenario of new energy vehicles [20]. Wang proposed a genetic-tabu search hybrid algorithm for optimizing the mixed-model hydraulic pump assembly line, aiming to minimize cycle time and workload imbalance. It improved workstation utilization and smoothed performance. However, this study is targeted at similar tasks and does not consider product diversity, so it is not very suitable for assembly lines of hybrid vehicle models combining EVs and FVs [21].

From 2020 to 2024, researchers began to incorporate more realistic industrial constraints into the solutions for MTALBP and related assembly line problems. Lin et al. integrated ergonomic risk indicators into the balancing model, reflecting realistic operational restrictions in assembly environments [22]. Tanhaie proposed a multi-objective PSO to simultaneously improve mixed-model line balancing and sequencing performance and improve load balance [23]. Belkharroubi and Yahyaoui developed a hybrid reactive GRASP metaheuristic to solve the type-I mixed-model assembly line balancing problem with complex precedence relationships [24]. Didden et al. introduced a GA-based decision support system for an automotive assembly line, that accounts for mixed-model production, sequence-dependent setup times and multi-operator workstations, addressing the challenges faced by traditional balancing approaches [25]. Li et al. formulated a mixed-model assembly line balancing problem that jointly considers learning effects and uncertain demand and proposed a mixed-integer programming–based heuristic and a variable neighborhood search algorithm to handle tight operational conditions [26], while Çimen et al. developed an assembly line rebalancing and worker assignment approach that considered ergonomic risks and workload evaluation in multi-manned settings [27]. But EV- and FV-specific task characteristics were not explicitly addressed.

2.3. The Issue of Balancing EVs and FVs from a Cross-Disciplinary Perspective

Although the automotive sector is the primary application domain of MTALBP, similar challenges of heterogeneous task structures and energy-based configurations arise in other transportation and manufacturing fields. For instance, in aviation fuel estimation, Khan et al. developed a self-organizing neural network to predict aircraft trip fuel consumption based on flight data [28], while Khan et al. proposed a covariance bidirectional extreme learning machine for jointly modeling aircraft trajectories and fuel usage. These studies demonstrate that variability in energy requirements directly affects production resource allocation and operational planning [29].

In the supply chain domain, Ullah et al. [30] examined how categorizing non-reworkable defective items can prevent delay propagation and improve profit in multi-stage production systems. This approach highlights the importance of minimizing incompatible task combinations—analogous to EV–FV heterogeneity in assembly line balancing. Together, these cross-domain insights emphasize the need for intelligent task allocation and shared-resource mechanisms when handling heterogeneous product types, reinforcing the motivation for adopting workstation-sharing strategies in EV–FV mixed-model assembly lines.

2.4. Summary

The relevant literature provides a valuable theoretical foundation for production line balancing and the optimization of mixed vehicle models. Various meta-heuristic methods have been applied to address the increasingly complex industrial demands, especially in the automotive production sector. However, practical applications still require a modeling framework that can handle different types of electric vehicles and fuel vehicles tasks, workstation sharing, and actual operational constraints. Therefore, the next section will introduce the proposed mathematical model to address these challenges.

3. Mathematical Model

This section establishes the mathematical formulation of the proposed mixed-model assembly line balancing problem. First, the problem description and task classification for EV–FV co-production are introduced. Then, the decision variables and modeling assumptions are defined. Finally, the objective functions and the associated precedence, synchronization, and workstation-sharing constraints are formulated.

3.1. Problem Statement

The subject of this study is the assembly line balance problem for the mixed production of EVs and FVs on the same bilateral assembly line. Due to the significant differences in the process flow and operation requirements of the two types of products, their tasks are all subject to priority relationship constraints. It is necessary to reasonably allocate the assembly tasks of the two types of products to each workstation and ensure that the operation time at each workstation does not exceed the production cycle. Priority relationships and cycle constraints need to be satisfied, and the goal is to minimize the number of workstations and achieve assembly line balance.

To facilitate description, the priority relationships between tasks can be represented by a priority relationship diagram, as can be seen in Figure 1. The nodes in the figure represent tasks, the numbers in the circles are task numbers, the values in the parentheses indicate operation times, and the letters L, R, and E represent that the task must be completed at the left, right, or any side workstation. The arrows reflect the priority order between tasks.

Based on the characteristics of this problem, a deterministic mathematical model is established in this study. During the modeling process, it is assumed that all task times, worker operation times, equipment resources, and production cycle time are known and fixed parameters. Random disturbances such as equipment failures, worker operation fluctuations, or demand variations are not considered. Therefore, under identical input conditions, the optimization algorithm will produce the same task allocation scheme and assembly line balancing solution, providing reliable decision support for production optimization.

3.2. Model Assumptions

In the modeling process of this article, the following assumptions were made:

(1)

The priority relationships of all tasks are known and remain unchanged.

(2)

Each task can only be assigned to a unique workstation and cannot be divided.

(3)

Any task can theoretically be assigned to any workstation (without considering space limitations).

(4)

The additional time consumption during the workstation switching for different product models is not considered.

(5)

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

(6)

The standard operation time for all tasks is a fixed value that has been scientifically determined in advance.

(7)

The completion time of the task does not vary depending on the workstation or the worker.

(8)

The assembly line workers have consistent proficiency and can complete all types of tasks.

(9)

The time required for different workers to complete the same task is the same.

(10)

The total working hours allocated to each worker for their tasks must not exceed the cycle time.

(11)

One worker is assigned to each side of each workstation, and they respectively complete all the tasks assigned to their respective sides.

The above assumption simplifies the problem to a certain extent, but it can reflect the core constraints of the operation of the MTALB, providing a theoretical basis for model construction.

3.3. Mathematical Formulation

The mathematical model developed in this study is based on the fundamental research results of Özcan and Toklu [11] and has been expanded upon. Considering the heterogeneity of EVs and FVs, and considering the workstation sharing mechanism, relevant constraints for workstation sharing have been added. The objective function not only considers the minimum number of workstations but also incorporates an optimal smoothness index as a secondary objective, which is used to improve the workload balance among workstations.

3.3.1. Notation Description

Table 1. Symbolic Representation.

Symbol	Meaning
$i,h,p,r,e,f$	Indices representing task operations
$j,g$	Indices representing workstations
$m$	Index representing the product type
$d,k$	Indices representing sides of the workstation
$\left(j,d\right)$	A paired workstation j operating on side d
$I$	Set all tasks, $I=\left\{\mathrm{1,2},\dots i\dots ,nt\right\}$
$J$	Set of all paired workstations, $J=\left\{\mathrm{1,2},\dots j\dots ,nms\right\}$
M	Set representing the two product types (FV and EV), $M=\left\{\mathrm{1,2}\right\}$
D	Set indicating assembly directions (left and right sides), $D=\left\{\mathrm{1,2}\right\}$
$t_{im}$	Processing time of task i for product type m.
$t_{im}^s$	Starting time of task i for product type m
$t_{im}^f$	Finishing time of task i for product type m
$CT$	Cycle time of the assembly line
$c_i$	Completion time of task i
$A_L$	Set of tasks that must be assigned to the left side, ${ A}_L\in I$
$A_R$	Set of tasks that must be assigned to the right side, $A_R\in I$
$A_E$	Set of tasks that can be assigned to either side, $A_E\in I$
$P\left(i\right)$	Set of immediate predecessors of task i
$P_a\left(i\right)$	Set of all predecessors of task i.
$P_0$	Set of tasks without predecessors $P_0=\left\{i\in I|P\left(i\right)=\varnothing \right\}$
$\delta$	A sufficiently large positive constant (Big-M)
$x_{ijd}$	Binary variable: equals 1 if task i is assigned to workstation j on side d; otherwise, 0.
$F_j$	Binary variable: equals 1 if workstation j is used; otherwise, 0.
$b_j$	Binary variable: equals 1 if workstation j is a shared (mixed) workstation; otherwise, 0.
$SC$	Set of synchronous task pairs that must be executed simultaneously on both sides, $SC=\left\{\left(i,h\right),\dots \left(p,r\right)\right\}$
$ET$	Set of EV-exclusive tasks $ET=\left\{1,\dots e\dots \right\}$
$FT$	Set of FV-exclusive tasks $FT=\left\{1,\dots f\dots \right\}$

lists the notation and symbols used in this paper.

3.3.2. Model Formulation

This model takes into account two levels of objectives. The primary objective is to minimize the total number of production positions, reducing the number of positions set up and lowering the input of resources. The secondary objective is to minimize the smoothing index and improve the balance of the production line.

$$min{W}_1=\sum _{j\in J}{F}_j$$

(1)

During the actual algorithm optimization process, there are often multiple solutions with the same number of workstations. To facilitate the selection of the better solution, a secondary objective can be used for distinction. To distinguish solutions with the same number of workstations, a smoothing index is introduced.

Equation (2) represents the minimization of the smoothness index, where CT denotes the cycle time and $2\sum _{j\in J}{F}_j$ represents the total number of active workstation sides (both left and right). The load time of workstation $j$ on side $d$ is defined in Equation (3). Here, $x_{ijd}$ is the task assignment indicator variable, and $t_{im}$ represents the processing time of task $i$ for product type $m$. A smaller smoothness index indicates a more balanced distribution of workload across all workstations.

$${minW}_2=\sqrt{{\displaystyle \frac{\sum _{j\in J}\sum _{d\in D}{\left(T_{jd}-CT\right)}^2}{2\sum _{j\in J}{F}_j}}}$$

(2)

where

$$T_{jd}={\sum }_{i=1}^n{x}_{ijd}\times t_{im}$$

(3)

3.3.3. Model Constraints

This mathematical model incorporates multiple sets of constraints to ensure that the task allocation plan adheres to priority order, cycle time limits, synchronization requirements, and workstation sharing regulations.

Equation (4) Task Assignment Constraint.

Ensure that each task is assigned to only one workstation station within a workstation group.

$${\sum }_{j\in J}{\sum }_{d\in D\left(i\right)}{x}_{ijd}=1 \forall i\in I$$

(4)

Equations (5) and (6) Precedence Constraints.

Equation (5) ensures that each job can be assigned to the current workstation under the condition that all the preceding jobs of this job have already been assigned to the previous or the same workstation.

$${\sum }_{g\in J}{\sum }_{d\in D\left(h\right)}g\times x_{hgd}\le {\sum }_{j\in J}{\sum }_{d\in D\left(i\right)}j\times x_{ijd} \forall i\in I-P_0,h\in P\left(i\right)$$

(5)

Equation (6) ensures that task $h$ and its immediate successor task $i$ can only start after task $h$ is completed.

$$\begin{gathered} t_{im}^s-t_{hm}^s+\delta \left(1-\sum _{d\in D\left(h\right)}{x}_{hjd}\right)+\delta (1-\sum _{d\in D\left(i\right)}{x}_{ijd})\ge t_{hm} \\ \forall i\in I-P_0,h\in P\left(i\right),j\in J,m\in M \end{gathered}$$

(6)

Equation (7) indicates that the start operation time of any task for each product must be greater than or equal to 0.

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

(7)

Equation (8) Cycle Time Constraint represents the cycle time constraint. The maximum completion time for each workstation on both sides should not exceed the production cycle.

$$\max \left({\sum }_{i=1}^n{x}_{ijd}\times t_{im}\right)\le CT \forall j\in J,m\in M,d\in D(i)$$

(8)

Equation (9) Synchronization Constraint.

For each synchronous task pair $(h,i)\in SC$, tasks $h$ and $i$ must be assigned to opposite sides of the same workstation, and all product types must start simultaneously. This restriction ensures that paired tasks can be executed concurrently on both sides of the workstation.

$$\begin{gathered} x_{hjk}-x_{ijd}=0 \forall \left(i,h\right)\in SC,j\in J,d\in D\left(h\right),k\in D\left(i\right),d\ne k \\ t_i^s-t_h^s=0 \forall (i,h)\in SC \end{gathered}$$

(9)

Equation (10) Workstation-Sharing Constraint.

This constraint defines the conditions under which a workstation can be shared by exclusive tasks of FVs and EVs.

The binary parameter $b_j$ indicates whether workstation $j$ is configured as shared.

When $b_j=1$, both EV-exclusive and FV-exclusive tasks must be assigned to that workstation within the allowable upper limit $\delta$.

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

(10)

This formulation guarantees that once a workstation is designated as shared, both FV and EV exclusive tasks are allocated. EV-exclusive and FV-exclusive tasks may be assigned to the same workstation when sharing is allowed, thereby improving line flexibility and workstation utilization across mixed-model production.

3.4. Model Summary and Discussion

The mathematical model proposed in this study considers the possibility of the co-production of EVs and FVs. Compared with the traditional single model or the same-structured MALB model, this model distinguishes the dedicated tasks for EV-exclusive tasks (ET) and FV-exclusive tasks (FT), and considers the workstation sharing constraints, allowing the dedicated tasks of EVs and FVs to be assigned to the same workstation when feasible. This allocation method, considering the workstation sharing mechanism, can increase the utilization rate of the workstations, providing theoretical support for automotive manufacturers in their transition from traditional FV production to EV production. Additionally, this model adopts dual-objective optimization. While minimizing the number of workstations, it also considers minimizing the smoothing index. In cases where the number of workstations is the same, hierarchical optimization can prioritize the scheme with a smaller smoothing index, improving the balance rate of the assembly line.

4. Algorithm Design

In recent years, genetic algorithms have often been applied to solve complex combinatorial and multi-objective optimization problems in manufacturing [25,31,32]. Due to their powerful global search capability, GAs have demonstrated outstanding performance in balancing and scheduling applications. To enhance the convergence speed and the quality of the solutions, researchers have proposed several improved and hybrid GAs, such as the dual-population GA [33] and the hybrid algorithm of GA and tabu search [26], which combine local search and adaptive mutation mechanisms. This study designs an IGA framework to solve the assembly line scheduling problem of EVs and FVs, considering structural differences. The proposed IGA is not a completely new one, but rather an adaptive adjustment to the specific problems of the classical GA framework. This algorithm designs a decoding mechanism for workstation sharing to ensure the synchronization between the task set of EVs and that of FVs.

4.1. Algorithm Procedure

In this subsection, the overall procedure of the Improved Genetic Algorithm (IGA) is presented. First, the chromosome representation and decoding mechanism are described, followed by the initialization of the population. Then, the fitness evaluation scheme is introduced to assess candidate solutions under the proposed multi-objective framework.

4.1.1. Encoding

The essence of the balanced problem for the MTAL is to assign all the operation elements on the assembly line to various workstations for assembly tasks to maximize the optimization of the balance objective function. This study aims to minimize the number of workstations, that is, under the premise of a limited production cycle, to reduce the total number of workstations. It adopts a natural number encoding method based on the priority order of processes, according to the assembly relationship of the processes, and in accordance with the sequence of each process being assigned to the workstation, the operation sequence numbers are arranged in a column, corresponding to each gene position of the chromosome, and the resulting gene sequence is a coded chromosome. This encoding method avoids the drawback of a large computational load caused by base conversion. As shown in Figure 2.

4.1.2. Decoding

To obtain a feasible solution, a specific decoding method must be adopted on the basis of the above operation sequence. According to the encoding and the characteristics of the two-sided assembly line, the following decoding process is carried out for the i-th gene $o_i$, so that the job elements meet all the constraints.

Step 1: Open a new paired workstation and add all unassigned job elements $o_i$ to the candidate set $P$.

Step 2: Find the job element $o_i$ with the highest priority in the task candidate set $P$. Search for the job element $o_i$ in all constraint sets. If it exists in the synchronization constraint set $PC$, proceed to Step 3; otherwise, proceed to Step 5.

Step 3: In the synchronization constraint set, find the other job element $o_h$ associated with the job element $o_i$. Search for the job element $o_h$ in the candidate task set. If it exists in the candidate task set and meets the beat constraint, proceed to Step 4; otherwise, remove the job element $o_i$ and its subsequent tasks from the candidate set and proceed to Step 8.

Step 4: Substitute the job elements $o_i$ and oh and related data into the cycle time constraint formula. If the remaining time on both sides of the workstation is greater than the operation time on both sides, assign the job elements oi and oh to the two sides of the paired workstation $j$ according to their operation orientation attributes $d_i$ and $d_h$, and proceed to Step 6. Otherwise, open a new paired workstation $j+1$ for task assignment, and proceed to Step 8.

Step 5: Substitute the data related to the job element $o_i$ into the cycle time constraint formula. If it holds true, assign the job element $o_i$ to one side of the paired workstation $j$ according to its operation orientation attribute $t_i$, and proceed to Step 6. Otherwise, open a new paired workstation $j+1$ for task assignment, and proceed to Step 8.

Step 6: Search for the job element $o_i$ in the dedicated process set. If it exists in the dedicated process set E or F, proceed to Step 7; otherwise, proceed to Step 8.

Step 7: In the dedicated process set F or E, find the job element $o_i$ with the highest priority. Search for the job element $o_i$ in all constraint sets. If it exists in the synchronization constraint set, proceed to Step 4; otherwise, proceed to Step 5.

Step 8: Check the task candidate set. If the job set is empty, proceed to Step 9; if there are still elements in the job set that have not been assigned, proceed to Step 2 and repeat the cycle.

Step 9: End.

The detailed decoding flow is illustrated in Figure 3.

4.1.3. Population Initialization

This paper generates the initial population based on the priority order constraints of the job elements using a random search method based on topological sorting. The specific process is as follows:

(1)

In the job element set $I$, find the job elements without preceding job elements or whose preceding job elements have been assigned, and name them $P.$

(2)

Randomly select one job element $O_i$ from set $P$ to form a chromosome sequence, and remove the job element $O_i$ from the set $P.$

(3)

Repeat the above steps until all job elements in I have been assigned, completing the initialization of one complete chromosome.

(4)

According to the population size $NP$, repeat the above operation NP times, then initialize and form $NP$ chromosomes.

4.1.4. Fitness Evaluation

For the balancing problem of the MTALB, this paper constructs a method based on hierarchical dictionary order for fitness evaluation. Firstly, the total number of workstations is taken as the first-level optimization objective to ensure that the decoding result can minimize the number of workstations in the assembly line. Secondly, to further distinguish the superiority and inferiority of solutions with the same number of workstations, the minimum smoothing index is used as the second-level objective to measure the deviation between workstation load and cycle time. The smaller the smoothing index, the more balanced the distribution of the assembly line. Moreover, for infeasible solutions, a penalty term is introduced:

$$P=M_1{V}_{prio}$$

(11)

where $V_{\mathrm{prio}}$ represents the number of violations of the priority relationship, and $M_1$ is the larger penalty coefficient. Since the synchronization constraints and side constraints have been strictly guaranteed during the decoding process, the penalty is mainly targeted at violations of the priority constraints.

Finally, the lexicographic fitness evaluation is expressed as:

$$K=\left(P,W_1-W_1^{min},W_2\right)$$

(12)

Here, $W_1^{min}$ represents the minimum number of workstations for feasible solutions in the current population. During individual comparison, the ranking is based on penalty values, workstation numbers, and smoothness indicators in sequence.

4.2. Genetic Operators

In this subsection, the genetic operators of the IGA are introduced. To maintain feasibility and diversity during evolution, three operators are employed: selection, crossover, and mutation.

4.2.1. Selection Operator

The selection operation adopts a method combining the elite retention strategy and the roulette wheel selection. First, the population individuals are sorted in descending order of fitness values, and only the top 10% individuals are retained as elite individuals; then, using the roulette wheel method, some individuals are selected from the parent population to generate the offspring population, the fitness values of the new population are calculated and arranged in descending order; finally, the individuals with the lower fitness values in the offspring population are replaced by the individuals with the higher fitness values in the original parent population. This method can maximize the retention of excellent genes while maintaining the diversity of the population.

4.2.2. Crossover Operator

This paper adopts the sequential crossover method. Based on the specified crossover probability, it selects the individuals that need to undergo crossover operations. The individuals are paired two by two for the crossover operation, and new offspring individuals are generated. The operation is as follows:

Let the two parent individuals that need to be crossed be $F_1$ and $F_2$, and the offspring individuals generated after crossover are $S_1$ and $S_2$. For the parent individual $F_1$, two crossover point positions $C_1$ and $C_2$ are randomly generated, and then all the genes in the parent individual $F_1$ except $[C_1,C_2]$ are deleted, only the genes within $[C_1,C_2]$ are retained and inherited unchanged to the offspring S_1. The genes contained in $[C_1,C_2 ]$ of the parent individual $F_2$ are removed, and the remaining genes of the parent individual $F_2$ are successively supplemented to the missing gene positions of the offspring $S_1$, thereby generating offspring $S_2$. The process of generating $S_2$ is the same as that of $S_1$. The schematic diagram of the crossover process is shown in Figure 4.

4.2.3. Mutation Operator

The variation is mainly aimed at enhancing the diversity of the population, and through this variation, a better new population can be obtained. The variation process is as follows:

(1)

Randomly determine the variation point $a_1$ of the individual and traverse all the direct predecessors and successors of operation $i$ at position $a_1$ in the matrix $P$, and determine their positions in the new chromosome.

(2)

Let the gene position of the last operation among all the immediate predecessors of operation $i$ be $b_1$, and the gene position of the first operation among all the immediate successors be $b_{2.}$

(3)

Randomly insert the gene at $a_1$ into any position within the interval $[b_1,b_2]$, generating a new individual.

4.3. Termination Criteria

Since the chromosomes obtained after the genetic mechanism may have some cases where the priority order relationships between the chromosomes are not consistent, the consideration of adjusting the priority order relationship sequence is added.

Let $t$ be the current evolution generation of the GA, and T be the maximum evolution generation of the GA. If $t\le T$ then set $t=t+1$, and use the new population as the initial population to perform iterative operations in a loop; if $t>T$ then output the individual with the best fitness value obtained during the evolution process, that is, the optimal objective function value, and terminate the algorithm operation.

4.4. Rationale for GA Component Selection

The rationale behind each component choice is briefly explained based on evolutionary optimization principles and the requirements of EV–FV co-production. The precedence-feasible encoding is generated using randomized topological sorting, which ensures that chromosomes satisfy precedence constraints from the beginning and avoids excessive penalty values in early generations—an approach also adopted in recent studies such as Yadav & Agrawal [26] and Huang et al. [27]. The decoding mechanism is the core innovation of this study, as it explicitly distinguishes EV-exclusive, FV-exclusive and shared tasks (ET/FT/PT) and dynamically executes workstation sharing, embedding real production rules during chromosome interpretation. Fitness evaluation follows a hierarchical structure that simultaneously minimizes station quantity and workload smoothness (W₂), with penalties assigned to infeasible solutions—a common practice in ALBP studies. Order-based crossover is used to preserve task precedence relationships, while neighborhood-insertion mutation allows local adjustment without destroying feasible solution structures. Elitism is applied to preserve high-quality individuals, as confirmed effective in previous MTALBP studies [23,25]. Parameter setting follows ranges commonly used in MTALBP literature (e.g., Pc = 0.7–0.9, Pm = 0.1–0.2) and were validated by ensuring convergence stability during preliminary runs on real production data.

4.5. Pseudocode

To clearly illustrate the entire calculation process, the following presents the concise pseudocode of the proposed IGA. The complete decoding logic for implementing workstation sharing and EV-FV task interaction is elaborated in detail in Appendix A.

Input:   I           : set of tasks with precedence constraints   ET, FT, PT   : EV-exclusive, FV-exclusive, and shared task sets   SC          : set of synchronous task pairs   CT          : cycle time   GA params : PopSize, MaxGen, Pc, Pm, EliteRate Output:   BestSol    : best decoded workstation assignment   BestFit    : best fitness value (penalty, #stations, smoothness) ----------------------------------------------------------- 1:  // Initialization 2: Generate an initial population Pop of size PopSize. 3: t ← 0, BestFit ← +∞, BestSol ← ∅ 4: // Main GA loop 5: while t < MaxGen do 6:   for each chromosome χ in Pop do 7:     Sol ← DecodeSolution(χ, CT, SC, ET, FT, PT) 8:     Fit(χ) ← EvaluateFitness(Sol) 9:    end for 10:   Sort Pop by Fit(χ) in ascending order 11:   if Fit(Pop(1)) < BestFit then 12:     BestFit ← Fit(Pop(1)) 13:     BestSol ← decoded solution of Pop(1) 14:   end if 15:   EliteNum ← round(EliteRate × PopSize) 16:   EliteSet ← first EliteNum chromosomes of Pop 17:   ParentSet ← roulette-wheel selection of (PopSize − EliteNum) parents 18:   Offspring ← ∅ 19:   while |Offspring| < (PopSize − EliteNum) do 20:     Select parents p1, p2 21:     With probability Pc, apply order-based crossover (c1, c2) 22:     Otherwise, c1 ← p1, c2 ← p2 23:     With probability Pm, apply neighborhood insertion mutation to c1 and c2 24:     Offspring ← Offspring ∪ {c1, c2} 25:   end while 26:   Truncate Offspring to required size if needed 27:   Pop ← EliteSet ∪ Offspring 28:   t ← t + 1 29: end while 30: return BestSol, BestFit -----------------------------------------------------------

5. Case Study

In this section, a real-world automotive chassis assembly line is used to verify the effectiveness of the proposed model and algorithm. The case background, model implementation, and optimization results are presented and analyzed.

5.1. Case Background

Based on the proposed mathematical model and the IGA, this study selected the chassis assembly line of W automobile manufacturing enterprise as the research object. Due to changes in automotive market demand, the company adjusted its production plan and planned to increase EV production. However, due to the overcapacity of the production capacity of FVs, the enterprise planned to assemble an EV on the existing FV assembly line. This EV model was based on the chassis of the fuel vehicle. Since the chassis assembly processes of the two types of vehicles are different, for example, the installation of the battery pack of the EV is different from the installation of the fuel tank of the FV. The task allocation of the existing production line needs to be adjusted.

5.2. Data Description

This article extracted a total of 58 assembly tasks from the production data of the enterprise, including common tasks shared by both vehicle models, ET and FT. Each task includes standard operation time, priority relationship, and workstation attributes (left side, right side, or either side). The production cycle time is set at 60 s. All data are from on-site investigations and standard time measurements, accurately reflecting the actual production situation. The detailed task data are listed in

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

Task ID	Operation Side	Task Time (s)	Immediate Predecessors	Task Set	Task ID	Operation Side	Task Time (s)	Immediate Predecessors	Task Set
0	$E$	5	-	$PT$	29	$R$	20	1	$FT$
1	$E$	30	0	$FT$	30	$L$	20	28	$FT$
2	$E$	20	0	$ET$	31	$R$	20	29	$FT$
3	$E$	6	2	$ET$	32	$E$	32	30, 31	$FT$
4	$L$	24	3	$ET$	33	$E$	32	32	$FT$
5	$R$	32	3	$ET$	34	$L$	32	33	$FT$
6	$L$	15	4	$ET$	35	$R$	32	33	$FT$
7	$R$	15	5	$ET$	36	$E$	28	0	$ET$
8	$E$	24	6, 7	$ET$	37	$L$	20	36	$ET$
9	$E$	15	8	$ET$	38	$R$	20	36	$ET$
10	$E$	15	0	$FT$	39	$L$	24	37	$ET$
11	$E$	24	10	$FT$	40	$R$	24	38	$ET$
12	$E$	20	11	$FT$	41	$L$	5	39	$ET$
13	$E$	20	12	$FT$	42	$R$	5	40	$ET$
14	$E$	19	1	$FT$	43	$E$	24	41, 42	$ET$
15	$E$	5	14	$FT$	44	$E$	24	43	$ET$
16	$L$	10	15	$FT$	45	$E$	16	34, 35, 18, 19, 44	$PT$
17	$R$	10	15	$FT$	46	$E$	26	9, 13, 23, 27	$PT$
18	$L$	10	16	$FT$	47	$E$	36	46	$PT$
19	$R$	10	17	$FT$	48	$E$	20	47	$PT$
20	$E$	11	0	$PT$	49	$E$	10	48	$PT$
21	$E$	13	20	$PT$	50	$E$	25	45	$PT$
22	$E$	10	21	$PT$	51	$E$	20	50	$PT$
23	$E$	7	22	$PT$	52	$L$	13	51	$PT$
24	$E$	27	0	$PT$	53	$L$	25	52	$PT$
25	$E$	24	24	$PT$	54	$R$	15	51	$PT$
26	$E$	8	25	$PT$	55	$R$	5	54	$PT$
27	$E$	3	26	$PT$	56	$E$	20	49, 53, 55	$PT$
28	$L$	20	1	$FT$	57	$E$	12	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 corresponding priority relationships are shown in Figure 5. The process data of the first line of the chassis for FVs and EVs are shown in Table 2, and the comprehensive priority relationships are shown in Figure 5.

The set of synchronous task pairs in this case study is defined as follows:

$$SC=\left\{\right(\mathrm{4,5}),(\mathrm{6,7}),(\mathrm{16,17}),(\mathrm{18,19}),(\mathrm{28,29}),(\mathrm{30,31}),(\mathrm{34,35}),(\mathrm{37,38}),(\mathrm{39,40}),(\mathrm{41,42}\left)\right\}$$

5.3. Experimental Results and Analysis

The experiment was implemented using MATLAB programming (MATLAB R2019a, MathWorks, Natick, MA, USA), and the running platform was an Intel i7-12700 CPU with 16 GB of memory and a Windows 10 system. The parameters for the GA were set as follows: population size 60; maximum number of iterations 250; crossover probability 0.85; mutation probability 0.2; elite proportion 10%; all experiments were run 20 times to obtain the optimal result to ensure the stability and reliability of the results. The production cycle was 60 s.

First, considering heterogeneity and the co-location of workstations, based on the model proposed in this paper and the GA process, 20 runs were conducted, and the 20 running results obtained are shown in

Table 3. Results of 20 Experimental Runs.

Run	Stations	Idle Sum	Best Fitness
1	9	60	906,014.8235
2	9	60	906,013.0588
3	8	65	806,516.3292
4	8	83	808,319.0958
5	9	102	910,213.4118
6	9	48	904,804.8235
7	9	71	907,111.7026
8	9	105	910,520.0294
9	9	88	908,816.8105
10	9	90	909,015.1765
11	9	64	906,405.2026
12	8	77	807,714.8292
13	9	78	907,816.9412
14	9	87	908,722.8529
15	9	81	908,113.4412
16	9	82	908,215.4379
17	9	79	907,918.9575
18	9	105	910,515.9118
19	9	74	907,418.3399
20	8	66	806,614.5167

.

The selection is made in the order of the smallest number of workstations, the shortest idle time, and the smallest optimal fitness value. The third run was selected as the best solution obtained in the experimental run. The third fitness curve graph (Figure 6) and workstation allocation graph (Figure 7) were output.

For comparison with the product differences not being considered, the workstation allocation scheme obtained by applying the method based on a GA according to the reference model in article [11] is shown in Figure 8.

Based on the workstation allocation diagrams shown in Figure 7 and Figure 8, a detailed analysis was conducted on the task allocation results of the EV and FV models at each workstation. The corresponding workload distribution and idle time data are summarized in

Table 4. Detailed task allocation and workload distribution results for Model 1 (reference) and Model 2 (proposed).

Station	EV (Model 1)	FV (Model 1)	EV (Model 2)	FV (Model 2)
Station1L	35	20	53	55
Station1R	52	0	58	58
Station2L	37	28	52	47
Station2R	26	41	48	59
Station3L	28	25	57	45
Station3R	34	29	53	59
Station4L	47	37	59	35
Station4R	20	30	57	20
Station5L	24	30	39	60
Station5R	54	30	24	60
Station6L	32	47	47	55
Station6R	35	35	26	58
Station7L	50	26	56	56
Station7R	24	32	55	55
Station8L	46	46	50	50
Station8R	20	52	45	45
Station9L	16	48	-	-
Station9R	25	57	-	-
Station10L	58	58	-	-
Station10R	52	52	-	-
Idle time	485	477	181	143

Note: Model 1 represents the reference model without the workstation-sharing mechanism, while Model 2 refers to the proposed model that with the workstation-sharing. The same case data are used for both models for a performance comparison.

. Furthermore, based on these results, the overall assembly line performance of the two vehicle models under different modeling conditions can be evaluated, which provides a basis for the comprehensive comparison presented in

Table 5. Comparative results between the reference and proposed models for EV and FV.

Model Type	Vehicle Type	No. of Workstations	Total Idle Time (s)	Smoothness Index (W2, s)	Line Balance Rate (%)
Reference model (without workstation sharing)	EV	10	485	27.39	59.58
Reference model (without workstation sharing)	FV	10	477	27.58	60.25
Proposed model (with workstation sharing)	EV	8	181	15.32	81.15
Proposed model (with workstation sharing)	FV	8	143	13.80	85.10

.

As shown in Table 4, the task allocation schemes of Model 1 (the reference model without workstation sharing) and Model 2 (the proposed model with workstation sharing). Model 2 has fewer workstations and less idle time on both sides of the workstations. These results confirm that the IGA can effectively solve the balancing problem with heterogeneous task constraints. Table 5 compares the comprehensive key indicators of the two models (for EV and FV lines). It highlights the differences in total idle time, smoothing index (W₂), and production line balance rate, further demonstrating the practical advantages and necessity of the proposed model.

As shown in Figure 9, the workstation utilization rate of the proposed model has significantly improved compared to the baseline model. This indicates that the workstation sharing mechanism is effective in allocating tasks when balancing the mixed-model assembly line of EVs and fuel FVs.

Through a case study of the assembly line of the chassis, this paper verifies the applicability of the proposed MMuALBP-WS model. The model considers the structural differences in different types of products and implements a sharing mechanism for workstation allocation. The results show that this method can reduce the number of workstations while ensuring production cycle constraints, improve the balance of workstation loads, and increase the utilization rate of the production line. The results of the analysis validate the effectiveness of the proposed model. It provides decision support for enterprises to achieve flexible manufacturing in a mixed production environment of FVs and EVs, and offers theoretical references and practical guidance for the transformation of traditional production lines to NEV.

6. Conclusions and Future Directions

This section summarizes the main findings of the study and discusses their managerial implications. Based on the results of the case study, practical insights are provided for EV–FV mixed-model production. Furthermore, potential directions for future research are outlined.

6.1. Conclusion and Managerial Implications

This paper addresses the balancing problem of the mixed-model assembly line for EVs and FVs. It proposes a mathematical modeling method considering heterogeneity for the mixed-model assembly line balancing, constructs a model with task allocation and priority relationship constraints, and clarifies the multi-objective optimization direction, which is, under the conditions of meeting the cycle time constraints, synchronization constraints, and workstation sharing constraints, minimizing the number of workstations and achieving balanced workstation loads. In terms of algorithms, this paper improves the traditional GA by proposing a decoding method considering workstation sharing, introducing mechanisms such as elite retention, sequential crossover, neighborhood mutation, and penalty function. The IGA can effectively perform optimization.

Through the analysis of the actual case of the chassis assembly line of W Company, the effectiveness of the proposed model and algorithm is verified. The results show that the optimized scheme can reduce the number of workstations while ensuring the production cycle, reduce the human and equipment investment of the enterprise, and significantly improve the workstation load distribution, thereby enhancing the balance and utilization rate of the production line. In addition, the dedicated tasks for EVs and FVs can be placed in the same workstation, avoiding the idle problem caused by vehicle model differences, thus improving the flexibility and adaptability of the mixed-model production.

The research in this paper has certain theoretical significance and practical value. From a theoretical perspective, the model proposed in this paper breaks through the excessive simplification of the traditional weighted time method for the process differences in different vehicle models, more realistically depicting the heterogeneity characteristics of EV and FV mixed-model production and expanding the research framework of assembly line balancing problems. From a practical perspective, this paper provides a feasible optimization idea and decision support tool for enterprises in the transformation from FV production lines to EV production lines, helping to achieve efficient and flexible production under the conditions of capacity adjustment and investment constraints.

In addition, the workstation-sharing mechanism and decoding strategy provide valuable managerial implications. First, they enable flexible reconfiguration of existing FV assembly lines without heavy equipment investment, which is particularly beneficial for small- and medium-sized manufacturers. Second, the framework can be extended to other stages of automobile manufacturing, such as general assembly, dashboard installation, engine and transmission assembly, and battery module integration, provided that precedence and synchronization constraints are available. Third, the method is compatible with both semi-automated and manual production environments, where workstation sharing helps reduce idle time and stabilize cycle flows. Lastly, task coordination across EV and FV models may reduce unnecessary walking movements and simplify operator assignments, contributing to improved ergonomics and a better working environment.

6.2. Future Research Directions

Of course, this research still has certain limitations. In the modeling process, the model assumes that task times are fixed and worker proficiency is consistent, and does not consider random factors such as worker differences, equipment failures, and demand fluctuations in real production. In addition, this paper only uses a single case for verification. In the future, it is necessary to conduct empirical research by combining different types of production lines.

Future research can be carried out in the following aspects:

(1) Robust and stochastic modeling.

Introducing uncertainty factors to establish stochastic or robust optimization models to enhance the adaptability of the model. Incorporating realistic constraints such as worker skill differences, changeover times, etc., into the modeling to improve the operability of the results.

(2) Integration with Industry 4.0 and real-time decision-making.

In the future, it can be considered to combine this model with digital twin technology or online monitoring systems, so that the shared decision-making at the workstation can be dynamically adjusted, rather than being pre-planned only.

(3) Extension to different product types and production scales.

This framework can be adapted to suit bus, truck, electric vehicle power system modules, or battery pack assemblies by adjusting the task set and synchronization rules. For large-scale applications, hybrid methods such as NSGA-II or GA–MIP mathematical heuristic approaches can be employed to enhance the scalability of the solutions.

In conclusion, the EV-FV MTALB model and the IGA proposed in this paper not only enrich the research content of assembly line balancing problems theoretically but also provide valuable references for the production line transformation and flexible production of the new energy vehicle industry.