Optimisation of the Logistics System in an Electric Motor Assembly Flowshop by Integrating the Taguchi Approach and Discrete Event Simulation

Abstract

An electric motor assembly flowshop (EMAF) is a type of classical mixed-product assembly line that uses automatic guided vehicle (AGV) systems for material handling. To optimise the logistics system configuration and alleviate the impact of the AGV parameters on the efficiency of the EMAF, a modelling and optimisation method based on discrete event simulation (DES) combined with Taguchi orthogonal experimental design was proposed. A DES model of the entire production process for the EMAF was constructed using the Tecnomatix Plant Simulation software package. After optimisation of the principal layout in the DES model, the number of assembly stations was decreased from 13 to 9, and the balance ratio was increased from 65.08% to 84.65%. In addition, the combination of the Taguchi method with the DES model was further developed to achieve the optimal parameter combination of the AGVs in order to allow the AGVs to operate more efficiently under various states. The final overall theoretical throughput was increased from 134 to 295 units within the seven-hour observation period.

1. Introduction

According to Rekiek et al. [1], an electric motor assembly flowshop (EMAF) is a type of classical mixed-product assembly line (MPAL) that uses automatic guided vehicle (AGV) systems for material handling. MPALs are used extensively in numerous manufacturing systems [1,2,3]. The logistics system determines the working rhythm and production balance of the EMAF. Moreover, the allocations of the production resources for MPALs are variable. Modifications to MPALs require in-depth modelling and analysis to improve production performance and determine the main production configuration [4].

Various methods have been used to optimise the production performance. To date, many different algorithms, such as the new colony optimisation algorithm [5], the hybrid genetic algorithm [6], the multi-objective artificial bee colony algorithm [7], and the hybrid multi-objective dragonfly algorithm [8], have been designed and employed by researchers to solve line balancing and sequencing problems for MPALs and to obtain good overall productivity. In addition to these optimisation algorithms, production coordination [9,10,11] and the concept of nimble organisations [12,13,14] have been used to cope with changes in production. Moreover, visualisation support has been proposed to improve the design of the manufacturing systems [15,16,17].

Based on the above literature, some conclusions can be drawn. Few researchers have optimised the overall performance of a factory through simulation, particularly for logistics systems. In addition, most of the previous studies only simulated and optimised certain production factors independently. Moreover, the traditional optimisation experimental method is a one-factor-at-a-time (OFAT) experiment, i.e., one factor is varied at different levels while the remaining factors are fixed. Although this method is simple to apply, it ignores the possible interactions between the factors. The statistical design of experiment (DOE) method uses a simpler experimental configuration than that of the OFAT experiment to test the influence of each factor. The DOE method is a systematic approach for determining the optimal factors and levels to optimise the throughput of a process or design. Full factorial design means that the experiment considers all the possible combinations of factors and levels; fractional factorial design considers part of the entire experiment owing to the limitations of cost [18,19]. However, parameter design is an offline quality control technique. Machines must be turned off during experiments, which can significantly affect the production schedule. Additionally, the experiments are time-consuming. Thus, we suggest that the number of experiments performed should be as small as possible.

In an effort to overcome these shortcomings, a modelling and optimisation method based on discrete event simulation (DES) combined with the Taguchi orthogonal experimental design was proposed. DES is a discrete-state and event-driven method for dynamic systems whose behaviour is characterised by abrupt changes in the value of its state [20]. DES can efficiently evaluate different production configuration alternatives and production strategies to support decision-making [15,21,22]. DES methods for optimisation have been applied from the initial general process languages, such as Fortran, to simulation-based languages, such as SIMAN, and then to the use of object-oriented language analysis software, such as Witness [23,24], Flexsim [25,26], Lekin [27], AnyLogic [28], etc. The simulation and optimisation literature on production, logistics systems, and inverse logistics with the DES software package has mainly focused on validation and optimisation. Validation refers to the analysis of the proposed strategies or algorithms, while optimisation refers to the improvements and implementations of measures to production layouts, logistics strategies, inverse logistics, line balancing, scheduling, production configurations, etc. Therefore, DES has been widely applied to optimise and verify production and logistics systems [19,23,24,25,27,28,29,30,31,32,33]. Moreover, the Taguchi method is a systematic and efficient method for conducting experiments to determine the optimal values [18,32,34,35]. Using orthogonal arrays, the Taguchi method searches in the parameter space with a small number of experiments [36,37].

This study aims to establish an effective DES model and determine the main optimal logistics parameters for an EMAF through an integrated DOE approach, combining the Taguchi method and DES. The DES model of the EMAF provides a virtual online manufacturing environment for studying the impact of the logistics system on the production of the entire flowshop. The Taguchi method is used to determine the important AGV parameters to obtain better performance.

The remainder of this paper Is organised as follows. Section 2 provides the framework for the simulation modelling in Tecnomatix Plant Simulation based on the DES method. The Taguchi orthogonal experimental design of the main AGV parameter settings and the analysis of variance (ANOVA) are presented in Section 3. In Section 4, validation and comparison experiments are conducted. The conclusions and future work are presented in Section 5.

2. Modelling of an Electric Motor Assembly Flowshop

2.1. Design of a General DES Modelling Method for an EMAF

The typical 15 kW electric motor shown in Figure 1 is the main product of Jinfei Holding Group Co., Ltd., and the corresponding assembly flowshop design is shown in Figure 2.

The EMAF design in Figure 2 is the initial scheme, and the subsequent DES modeling and optimisation are carried out on this basis. The EMAF assembles eight types of semi-manufactured parts (as shown in Figure 1) into the final electric motor. The primary equipment and technology of the EMAF include processes such as inserting magnetic steel into the steel core, the assembly of the motor stator, and the insertion of the motor rotor into the motor stator, etc. The details of the EMAF process and the corresponding times for performing each task are presented in

Table 1. Electric motor assembly process and corresponding station allocation.

No.	Operation Name	Time [s]	Predecessor	Initial Sequence	Station (Initial)	Final Sequence	Station (Optimised)
1	Coating rotor core	20	/	1	1	1	1
2	Insertion of magnet steel	32	1	2	2	2	1
3	Steel core assembly	15	2	3	3	3	2
4	Rotor surface magnetic detection	30	3	4	4	4	2
5	Rotor dynamic balancing detection	60	4	5	5	5	3
6	Stator induction heating	20	/	6	6	6	4
7	Pressing stator into the motor casing	5	6	7	6	7	4
8	Coating the back cover and detection	25	7	8	7	8	4
9	Installation of the back cover	17	8	9	7	9	5
10	Drying semi-product 1	20	9	10	7	10	5
11	Rotor and semi-product 1 assembly	10	5, 10	11	8	11	5
12	Coating the front cover and detection	25	11	12	9	12	6
13	Installation of the front cover	17	12	13	9	13	6
14	Drying semi-product 2	20	13	14	9	14	7
15	Spin variable stator assembly	10	14	15	10	15	7
16	Wiring box assembly	22	15	16	11	16	7
17	Performance detection	60	16	17	12	17	8
18	Wiring box cover assembly	17	17	18	13	18	9
19	Performance review	10	18	19	13	19	9

.

The DES model of the EMAF consists of the workstations and the logistics. The production logistics include transportation requests, vehicle movement, loading and unloading, and workstation operations. To realise such complex operations in the DES model, the AGV allocation strategy, the ordinary and urgent delivery strategies, and the optimal route search strategy are designed to assign the AGVs and the delivery tasks. According to the delivery request, an AGV is assigned to the corresponding delivery task. The path of the AGV is optimised according to the shortest path principle. Finally, the proposed logistics control strategy is realised by using the SimTalk2.0 programming language in Tecnomatix Plant Simulation. The flow chart of the proposed DES modelling method for the EMAF is shown in Figure 3.

2.2. Mathematical Description for EMAF Rebalancing Model

According to Table 1, it is obvious that there is a significant difference in the time required between some stations in the initial production settings, which will cause accumulation and reduce the production efficiency of the EMAF. Therefore, it is necessary to redistribute the stations in the initial process sequence, form a new combination of stations, and shorten the time difference between the stations so as to rebalance the EMAF.

Consider an EMAF with $m$ stations, $G=\left(E,P\right)$ represents a joint precedence diagram without loops, which means that the assembly process of the product unit can be disassembled into a combination of $E$ tasks. $P$ similar models are to be assembled in an intermixed product sequence. Each product unit requires the execution of $n$ tasks (indivisible elements of process) in the EMAF. For product unit $j$, the processing time of task $i$ is $t_{i,j}$. The loading and unloading time of candidate station $k$ is $t_k$. Therefore, the EMAF rebalancing problem concerns how to reassign the $n$ tasks to the candidate stations under the constraint of the cycle time $C$ in order to minimise the following two objectives:

(a)

The number of stations used (vertical balancing);

(b)

The processing time variation for different models at each station (horizontal balancing).

The EMAF rebalancing problem is also to solve the division of the node set $E$, that is, $E={\cup }_{j=1}^P{S}_j$, so that the objectives are optimised and certain constraints are met; it is formulated as follows:

(1)

$S_i\cap S_j=\varphi ,\left(i\ne j;i,j\in 1,2,3,\dots ,n\right)$: each common task for different units should be assigned to a single station;

(2)

$\cup S_k=E$: all tasks of the product unit should be assigned to candidate stations;

(3)

$T\left(S_k\right)\le C,\left(k\in 1,2,3,\dots ,m\right)$: the total time of the tasks at each candidate stations in the EMAF should be under the constraint of the cycle time $C$;

(4)

$P={\left(P_{ij}\right)}_{n\times n}$: assembly tasks priority relationship matrix, when $P_{ij}=1,i\in S_x,j\in S_j$, then $x\le y$.

The notation used for the formulation of the problem is summarised as follows:

• $i,t$: index of assembly tasks, $i,t=1,\dots ,n$;
• $j$: index of product unit, $j=1,\dots ,p$;
• $k$: index of candidate stations, $k=1,\dots ,n$;
• $n$: number of tasks;
• $m$: number of stations;
• $p$: number of units to be assembled on the EMAF;
• $C$: required cycle time;
• $w_j$: the weight of unit $j$ in total production,
• $j=1,\dots ,p$; $0<w_j<1$ and ${\displaystyle {\sum }_j{w}_j}=1$;
• $t_{i,j}$: processing of task i for unit j in total production,
• $t=1,\dots ,n;j=1,\dots ,p$;
• $x_{i,k}=\{\begin{array}{l}1,\mathrm{if}\mathrm{task}i\mathrm{is}\mathrm{assigned}\mathrm{to}\mathrm{station}i\\ 0,\mathrm{otherwise}\end{array}$.

In this study, the balance ratio (BR) indicates the degree of balance in the distribution of each task at the candidate stations. The function (Fitness) with smoothness index (SI) and machine station index (MI) is generally used to evaluate the fitness of the entire assembly line by observing the distribution of each candidate station’s time relative to the cycle time. The weights of two coefficients $({\eta }_1=0.8;{\eta }_1=0.2)$ are chosen experimentally in order to meet the two objectives. The greater the BR and the less the Fitness factor, the better the performance of the EMAF. They are formulated as follows:

$$BR=\frac{{\displaystyle {\sum }_{k=1}^m{\displaystyle {\sum }_{j=1}^P{w}_j\left(t_k+{\displaystyle {\sum }_{i=1}^n{t}_{i,j}{x}_{i,k}}\right)}}}{m\times C}\times 100\%$$

(1)

$$SI=\sqrt{\frac{{\displaystyle {\sum }_{k=1}^m{\displaystyle {\sum }_{j=1}^P{w}_j{\left(C-t_k-{\displaystyle {\sum }_{i=1}^n{t}_{i,j}{x}_{i,k}}\right)}^2}}}{m}}$$

(2)

$$MI=\frac{{\displaystyle {\sum }_{k=1}^m{\displaystyle {\sum }_{j=1}^P{w}_j}\left(C-t_k-{\displaystyle {\sum }_{i=1}^n{t}_{i,j}{x}_{i,k}}\right)}}{m}$$

(3)

$$Fitness={\eta }_{1}SI+{\eta }_{2}MI$$

(4)

2.3. Optimisation of EMAF Principal Layout

To obtain the optimal principle of the EMAF layout, a simulation model for the layout was developed based on the DES modelling method. In this study, a genetic algorithm (GA) was used to assign the assembly tasks to the best candidate stations according to the principle and to optimise the balance performance of the EMAF. The GA adopts a coding form based on the expression of the processing order. The length of a chromosome is equal to the number of tasks, with each task expressed by a number, and the order of storage represents the order of processing. Then, the tasks are assigned to the stations according to the processing order, ensuring that the times of each station are not greater than the production cycle time.

In this study, the parameters (population size = 100, maximal generation = 10, crossover probability = 0.8, and mutation probability = 0.1) used in the GA are chosen experimentally in order to obtain a satisfactory solution quality in an acceptable time span. The average loading and unloading time of a candidate station is 8 s, and the cycle time of the EMAF is 76 s; the EMAF simulation model with nine stations and the application of the GA is shown in Figure 4. On the premise of satisfying the production process, a smaller station time fluctuation and a higher EMAF balance rate are taken as the optimisation goals of the EMAF rebalancing problem. As shown in the figure, the final result of the simulation is that the optimal solution is reached when the number of stations is nine, and the processes assigned to the stations are stored in the table and are named Jobs. After optimisation, the total number of production stations was reduced from 13 to 9. The balance ratio was increased from 65.08% to 84.65%, which is 30% greater than that before the optimisation. The details of each process are listed in Table 1.

2.4. Optimisation of EMAF Principal Layout

The DES model of the entire EMAF production process was established based on the optimal layout principle. As shown in Figure 5, the DES model includes the following modules: pre-storage, workstations, AGV pool, robots, scheduling strategy, and statistical analysis.

In the EMAF simulation model, the key to the creation of the model was to design the AGV’s control and scheduling strategy. It mainly includes the AGV’s loading and unloading strategy, urgent delivery, conventional delivery, execution strategy, delivery request, etc. When the EMAF starts operation, the exit control of the buffer will calculate whether the existing material in the buffer is lower than the minimum inventory. The buffer will send a request to the center of the AGV pool to ask for distribution from the pre-storage when it does not meet the requirement. The AGV executes the distribution task according to the above scheduling strategy; it first sends a pick-up KanBan to the corresponding raw material staging area (PreStore) and removes the corresponding amount of materials. It passes through the sensor position of the track along the designed buffer and triggers the unloading strategy method. Robots then transport the piece of product to the corresponding station for assembly.

The production process for a particular series of electric motors operates during the observed period for seven hours per day. After the discrete event simulation, the throughput was 134 units. The buffer occupancy, robot utilisation, and workstation efficiencies are shown in Figure 6A,C,E, respectively. Further analysis revealed that the buffer was idle most of the time, and the work efficiency of each robot and workstation could be further improved. Therefore, the AGV configuration needed to be optimised.

3. Taguchi Orthogonal Experiments

According to the above analysis, the flowshop production process was optimised through the optimisation of the layout principle. In addition, the Taguchi method was applied to study the parameters that affect the throughput of the production line to determine the optimal parameters of the AGVs and to allow the AGVs to operate more efficiently under various states.

The Taguchi design consists of four main steps. In the problem formulation step, a parameter diagram is used to classify the variables associated with the product into noise, control, signal (input), and response (throughput) factors. Next, the ideal function and signal/noise (S/N) ratio are defined, and experiments are designed that change the control, noise, and signal factors systematically using orthogonal arrays. S/N is an index of quality that was introduced by Taguchi to determine the optimal combination in a series of experiments. In the experiment/data collection step, the experiments are conducted using hardware or through simulations according to the OA developed in the previous step. In this study, the experiments are carried out in the DES model built in the previous step. In the parameter analysis step, the effects of the control factors are calculated using Minitab 17, and the results are analysed to determine the excellent settings of the control factors. In the prediction step, the performance of the system is predicted under the baseline and the excellent settings of the parameters. Then, confirmation experiments under these conditions are carried out in the DES model. Finally, the best parameter combination is obtained through comprehensive verification and analysis to realise the optimised production effects and the improved production performance.

3.1. Optimisation of EMAF Principal Layout

The flowshop performance is strongly influenced by the logistics parameter settings. Delegating variables to control the factor parameters is important in the Taguchi experimental design before the Taguchi approach is used to divide the parameters into several levels. Because the experimental method is expensive and time-consuming, it is critical to meet the requirements of the design goals with a minimum number of tests. Two or three levels are thus selected for each control, and noise factor parameters are set to cover the design region sufficiently. Therefore, the levels are designed carefully; five parameters with two- and three-level hybrid designs are used for the established inner arrays, and two factors with two levels are designed for the outer arrays.

First, the Taguchi methodology for robust parameter design was applied to determine the appropriate settings for the control factors. These control factors were selected based on the opinions of the technical engineers.

Table 2. Control factor parameters and their variables.

No.	Operation Parameters	Notation	Variables
P1	Safe boundary capacity for BF	BF_Safecap	Min.0 (number), Max.1 (number);
P2	Number of AGVs in EMAF	AGV_Num	Min.1 (number), Max.3 (number);
P3	Operation velocity of AGVs	AGV_Spd	$\mathrm{Min}.0.4(\mathrm{m}/\mathrm{s}$$),\mathrm{Max}.0.6(\mathrm{m}/\mathrm{s}$);
P4	Acceleration of AGVs	AGV_Ac	$\mathrm{Min}.0.1({\mathrm{m}/\mathrm{s}}^2$$),\mathrm{Max}.0.3({\mathrm{m}/\mathrm{s}}^2)$;
P5	Capacity of the buffer (BF)	BF_Cap	Min.2 (number), Max.4 (number);

and

Table 3. Control factor parameters and levels.

No.	Control Factor Parameters	Levels
		1	2	3
P1	BF_Safecap	0	1	/
P2	AGV_Num	1	2	3
P3	AGV_Spd	0.4	0.5	0.6
P4	AGV_Ac	0.1	0.2	0.3
P5	BF_Cap	2	3	4

list the factors to be investigated and the assignment of the corresponding levels. Furthermore, to reduce noise variability, two noise factors (as listed in

Table 4. Noise factor parameters and their variables.

No.	Operation Parameters	Notation	Variables
Q1	Safe boundary capacity for BF	Availability	Min.95 (%), Max.99 (%);
Q2	Mean time to repair the main assembly station	MTTR	Min.300 (s), Max.600 (s);

and

Table 5. Noise factor parameters and levels.

No.	Operation Parameters	Levels
		1	2
Q1	Availability	95%	99%
Q2	MTTR	300 s	600 s

) with two levels each were incorporated into the experiment: the availability of the main assembly station (factor Q1) and the mean time to repair the main assembly station (factor Q2).

The five control factors were assigned to the inner orthogonal array, L₁₈(2**1 3**4), whereas the two noise factors were assigned to the outer orthogonal array, L₄(2**2). The crossed array requires a total of 18 × 4 = 72 experimental runs, as indicated in

Table 6. Crossed array with output (7 h) as the response and larger-the-better $S/N_{p-LTB}$.

Control Factors(Column L18(2**1 3**4))							Noise Factors(Column L4(2**2))
						Q1	95%	95%	99%	99%
						Q2	300	600	300	600
No.	P1	P2	P3	P4	P5		Response				Mean	SNR
1	0	1	0.4	0.1	2		94	92	96	94	94.00	39.4596
2	0	1	0.5	0.2	3		171	168	175	171	171.25	44.6699
3	0	1	0.6	0.3	4		264	249	272	267	263.00	48.3848
4	0	2	0.4	0.1	3		273	255	284	276	272.00	48.6708
5	0	2	0.5	0.2	4		285	294	302	302	295.75	49.4110
6	0	2	0.6	0.3	2		258	243	268	262	257.75	48.2067
7	0	3	0.4	0.2	2		272	257	284	280	273.25	48.7120
8	0	3	0.5	0.3	3		286	296	303	303	297.00	49.4478
9	0	3	0.6	0.1	4		286	295	303	303	296.75	49.4404
10	1	1	0.4	0.3	4		145	145	146	142	144.50	43.1959
11	1	1	0.5	0.1	2		85	82	86	83	84.00	38.4810
12	1	1	0.6	0.2	3		135	134	137	135	135.25	42.6219
13	1	2	0.4	0.2	4		283	263	290	284	280.00	48.9252
14	1	2	0.5	0.3	2		172	167	175	172	171.50	44.6816
15	1	2	0.6	0.1	3		248	234	256	247	246.25	47.8139
16	1	3	0.4	0.3	3		282	264	289	281	279.00	48.8974
17	1	3	0.5	0.1	4		285	296	303	302	296.50	49.4327
18	1	3	0.6	0.2	2		284	266	296	289	283.75	49.0380

Note: ** represents Taguchi orthogonal design operator.

. Each experimental run was carried out according to the corresponding parameter setting model, and the statistical throughput in seven hours of AGV operation was registered as the response. This quality characteristic is non-negative, and larger values indicate a better performance. Thus, based on the condition of an infinite ideal value, the definition of the larger-the-better characteristic is as follows:

Supposing the characteristic value of the throughput for EMAF $y$ is a random variable, the $S/N$ equation of the larger-the-better case can be expressed as Equation (5).

$$S/N_{p-LTB}=-10\cdot {\log }_{10}\left[\frac{1}{n}{\displaystyle \sum _{i=1}^N{\left(\frac{1}{y_i}\right)}^2}\right]$$

(5)

In the actual calculation, the mean square deviation for the larger-the-better case can be expressed as Equation (6).

$$\begin{array}{ll}\hfill MS{D}_{p-LTB}& \approx \frac{1}{{\overline{y}}^2}\left[1+\frac{3s^2}{{\overline{y}}^2}+\frac{4{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^3}}{n{\overline{y}}^3}+\frac{5{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^4}}{n{\overline{y}}^4}\right]\hfill \\ & \approx \frac{1}{{\overline{y}}^2}\left(1+\frac{3s^2}{{\overline{y}}^2}\right)\end{array}$$

(6)

$$S/N_{p-LTB}=-10\cdot {\log }_{10}\left(\frac{1}{n}{\displaystyle \sum _{i=1}^N\frac{1}{y_i^2}}\right)\approx -10\cdot {\log }_{10}\left[\frac{1}{{\overline{y}}^2}\left(1+\frac{3s^2}{{\overline{y}}^2}\right)\right]$$

(7)

where

$y$: the experimental response throughput of the EMAF in atypical condition;

$n$: the number of experiments;

${\overline{y}}^2$: the square of average value for throughput of the EMAF in period time;

$s^2$: the variance of throughput for the EMAF in period time.

The mean and the $S/N$ ratios were calculated for each experimental run, and the results are given in Table 6. The aim is to maximise the $S/N$ ratio.

3.2. Experiment Results and ANOVA Analysis

The Taguchi response tables representing the factors with different levels of the $S/N$ ratio under different noise conditions are presented in Table 6. In addition, Figure 7 shows the $S/N$ response chart, illustrating the relationship between the $S/N$ ratio and the parameter levels under various control factors. A larger $S/N$ ratio indicates a larger throughput performance and a smaller variance. Figure 7 shows that the optimal condition for the AGVs of the EMAF is P1 at level 0, P2 at level 3, P3 at level 0.6, P4 at level 0.2, and P5 at level 4.

The ANOVA results for the $S/N$ ratio are presented in

Table 7. Effect of control factors on the signal-to-noise ratio ($S/N_{p-LTB}$) for each level of the response parameters.

No.	Control Factor Parameters	Magnitude of the Signal-to-Noise Ratio $\left(\mathit{S}/{\mathit{N}}_{\mathit{p}-\mathit{L}\mathit{T}\mathit{B}}\right)$			Sensitivity	Rank
		1	2	3
1	P1	47.38	45.90	/	1.48	5
2	P2	42.80	47.95	49.16	6.36	1
3	P3	46.31	46.02	47.58	1.56	4
4	P4	45.55	47.23	47.14	1.68	3
5	P5	44.76	47.02	48.13	3.37	2

and

Table 8. ANOVA for the ($S/N_{p-LTB}$) ratio.

Analysis of Variance (ANOVA)
Factor	DF	Seq SS	Adj SS	Adj MS	F	p
(P1)	1	9.850	9.850	9.850	5.12	0.053
P2	2	136.838	136.838	68.419	35.59	0.000
(P3)	2	8.304	8.304	4.152	2.16	0.178
(P4)	2	10.693	10.693	5.346	2.78	0.121
P5	2	35.354	35.354	17.677	9.20	0.008
Residual Error	8	15.379	15.379	1.922
(P1)	17	216.418

Note: () represents an insignificant contribution.

. A greater sensitivity, represented by a larger F-value and a smaller p-value ($\alpha \le 0.05$), indicates that variation of the setting parameter (control factor) will significantly affect the production performance.

Based on this analysis, for the AGVs of this EMAF, factors P2 and P5 are important and have a significant effect on the $S/N$ ratio. Factors P1, P3, and P4 are insignificant in this case. The residual errors of Seq SS and Adj MS are both equal to 15.379 because this is an OA design. Therefore, the optimal parameters for the AGV-LS were set to P1 at level 0, P2 at level 3, P3 at level 0.6, P4 at level 0.2, and P5 at level 4. The other three excellent parameter combinations, P1(0), P2(2), P3(0.6), P4(0.2), and P5(4); P1(0), P2(2), P3(0.4), P4(0.2), and P5(4); and P1(0), P2(2), P3(0.4), P4(0.1), and P5(4), also had high $S/N$ ratios.

4. Taguchi Orthogonal Experiments

To verify the performance of the excellent parameter combinations, additional experiments were carried out with the DES model during the observed period (7 h). The experimental data were collected and are summarised in

Table 9. Crossed array with throughput (7 h) of excellent parameter combinations.

Control Factors (Column L18(2**1 3**4))							Noise Factors (Column L4(2**2))
						Q1	95%	95%	99%	99%
						Q2	300	600	300	600
No.	P1	P2	P3	P4	P5		Response				Mean	SNR
1	0	3	0.6	0.1	4		286	295	304	303	297	49.4448
2	0	2	0.6	0.2	4		285	295	303	302	296	49.4154
3	0	2	0.4	0.2	4		284	293	302	301	295	49.3860
4	0	2	0.4	0.1	4		284	293	302	301	295	49.3860

Note: ** represents Taguchi orthogonal design operator.

. It can be seen that the average throughput of the flowshop under different noise conditions is 297 units in the seven-hour observation period. When the number of AGVs is reduced to the second optimal level, i.e., there are two AGVs in the flowshop, while the other control factors remain at the optimum theoretical levels, the average throughput of the flowshop is only reduced by one. Therefore, the second group of parameter combinations is better than the first group in terms of economy.

It can be seen from Table 9 that the speed and acceleration of the AGV have little influence on the overall throughput of the flowshop. Therefore, two further optimisations are made in this study under the conditions of the second set of parameters by reducing the levels of these two impact factors. Through the verification experiment, it was found that the average throughput of the flowshop under the two parameter combinations was 295 pieces.

Based on the above comprehensive analysis and verification, it can be concluded that without significantly affecting the throughput of the flowshop, the best parameter combination of the DES model in this study is a running speed of the AGVs of 0.4 m/s, an acceleration of 0.1 m/s², a buffer capacity of 4, and a safe boundary capacity for the buffers of 0.

According to

Table 10. Comparison of current and new optimal production means and larger-the-better $S/N_{p-LTB}$.

Setting	Factors	Mean	$\mathit{S}/{\mathit{N}}_{\mathit{p}-\mathit{L}\mathit{T}\mathit{B}}$ Ratio
Current	[P1(0), P2(1), P3(0.6), P4(0.3), P5(2)]	134	48.5627
Optimal	[P1(0), P2(2), P3(0.4), P4(0.1), P5(4)]	295	49.3860
Improvement		120.15%	1.69%

, the experimental data show that with the optimal AGV configuration, the throughput increased from 134 units to 295 units. That is, the final overall optimal theoretical throughput of the EMAF within the observed period (7 h) was increased by approximately 120.15% compared to the previous design. In addition, as shown in Figure 6A–F, the proportion of the buffer storage in the zero state significantly improved. Meanwhile, the work efficiency of the handling robot and each workstation was also improved to a certain extent after optimisation, according to

Table 11. Comparison of current and new optimal robot utilisation (working).

Setting	Robot1	Robot2	Robot3	Robot4	Robot5
Current	4.02%	6.89%	18.63%	23.77%	18.08%
Optimal	7.49%	14.37%	34.56%	52.05%	35.50%
Improvement	86.32%	108.56%	85.51%	118.97%	96.35%

and

Table 12. Comparison of current and new optimal tasks of station utilisation.

Setting	Working (Current)	Working (Optimal)	Working (Improve)	Waiting (Current)	Waiting (Optimal)	Blocked (Current)	Blocked (Optimal)	Failed (Current)	Failed (Optimal)
T1	15.98%	32.78%	105.13%	0.00%	0.00%	84.02%	67.22%	0.00%	0.00%
T2	22.63%	46.67%	106.23%	0.11%	0.11%	74.42%	50.38%	2.84%	2.84%
T3	17.42%	36.05%	106.94%	73.41%	6.72%	1.99%	50.05%	7.18%	7.18%
T4	21.20%	44.03%	107.69%	66.73%	8.69%	12.07%	47.28%	0.00%	0.00%
T5	37.59%	78.45%	108.69%	62.08%	20.86%	0.33%	0.69%	0.00%	0.00%
T6	15.78%	33.22%	110.52%	67.68%	60.60%	16.54%	6.18%	0.00%	0.00%
T7	11.77%	24.92%	111.72%	82.25%	51.11%	0.45%	18.44%	5.53%	5.53%
T8	11.43%	23.57%	106.21%	58.17%	68.41%	30.40%	8.02%	0.00%	0.00%
T9	9.44%	19.77%	109.43%	46.43%	19.70%	39.98%	56.38%	4.15%	4.15%
T10	11.11%	23.17%	108.55%	40.00%	7.87%	48.89%	68.96%	0.00%	0.00%
T11	14.35%	29.93%	108.57%	13.68%	48.26%	65.65%	15.49%	6.32%	6.32%
T12	13.69%	28.87%	110.88%	76.94%	27.20%	9.37%	43.93%	0.00%	0.00%
T13	9.31%	19.56%	110.09%	85.96%	74.33%	1.12%	2.50%	3.61%	3.61%
T14	5.47%	11.51%	110.42%	91.80%	45.49%	2.73%	43.00%	0.00%	0.00%
T15	5.48%	11.51%	110.04%	89.30%	31.55%	1.08%	52.80%	4.14%	4.14%
T16	12.03%	25.32%	110.47%	73.91%	25.27%	12.51%	47.86%	1.55%	1.55%
T17	32.62%	69.05%	111.68%	66.06%	28.15%	1.32%	2.80%	0.00%	0.00%
T18	5.44%	11.51%	111.58%	94.56%	88.49%	0.00%	0.00%	0.00%	0.00%
T19	5.42%	11.51%	112.36%	91.34%	81.98%	3.24%	6.51%	0.00%	0.00%

. That is, idle time was reduced, and cost was considerably saved.

5. Conclusion and Discussion

In the face of dynamic and changeable individual demand, manufacturing enterprises need to develop a comprehensive, sustainable, and robust strategy for the entire production process. The purpose of this investigation is to provide an efficient and accurate optimisation and decision guidance to ensure the optimal solution for the electric motor assembly process with regard to time, economy, and sustainability.

In this study, to alleviate the impact of the AGV logistics system on the throughput of an intelligent motor assembly flowshop, a method integrating DES and Taguchi orthogonal experimental design was proposed to investigate the influence of the main logistics configuration factors on the overall production performance. The following conclusions can be drawn:

By simulating the real-word assembly flowshop in Tecnomatix Plant Simulation, state representation and action representation in the DES model were adopted to simplify the complex production process. The number of assembly stations was decreased from 13 to 9, and the balance ratio increased from 65.08% to 84.65% in the first layout optimisation stage. From the practical point of view, this study shows that complex production processes and the logistics of the manufacturing flowshop can be developed efficiently through DES software and the proposed modeling method. It not only simplifies the complexity of the related production planning research, but also brings considerable economic benefits to the enterprise.

Through the Taguchi orthogonal experimental design and comprehensive verification, the best parameter combinations can be achieved in fewer experiments to allow the AGVs to operate more efficiently under various states. The increase in the throughput of the EMAF was from 134 to 295 units within the seven-hour observation period. In addition, the idle time and energy consumption were reduced, the utilisation efficiency of the robot and the stations was increased, and the costs were also considerably reduced. These findings indicate that the comprehensive production plan and flowshop configuration settings can be derived in fewer experiments, which is critical to the possibility of ensuring sustainable development through rational management of the production resources, better adjustment of production to meet the needs of the modern consumer, and care for environmental aspects.

The results of this study validate the effectiveness and adaptation of the proposed approach. Future work will focus on two aspects. The first is the improvement of the AGVs in more complex operation situations. The second is the multi-objective optimisation of the AGVs considering more objectives, such as energy consumption, equipment utilisation, and maintenance costs. Our subject of interest is the upgrading of the traditional automation manufacturing enterprises in the Zhejiang Province of China, and we will focus on combining our simulation model with optimisation methods to provide feasible and optimal guidance for an actual production flowshop and the corresponding logistics systems.