https://doi.org/10.31449/inf.v48i11.5959 Informatica 48 (2024) 1 –14 1 
 
The Impact of GA Optimization Model Under the Constraint of 
Maximum Inventory on the Logistics Cost Control of Automotive 
Parts Production in the Factory 
Yuan Yang 
School of Accounting, Xijing University, Xi'an 710123, China 
E-mail: yangyuan20180125@163.com 
Keywords: inbound logistics, genetic algorithm, circular distribution, path planning, cost, maximum inventory 
Received: March 29, 2024 
The logistics of parts entering the factory is an important component of the cost source for 
manufacturing plants. How to efficiently transport is the key for its enterprises to achieve low-cost 
control. To address this issue, this study proposed a path planning model based on an improved genetic 
algorithm. Firstly, a circular distribution model suitable for component transportation logistics is 
selected, and then constraints such as maximum inventory at the line edge are introduced for design. 
The basic design of the genetic algorithm is also carried out. Subsequently, three neighborhood 
structures are introduced for optimization to address the convergence speed and other issues of the 
algorithm. In response to the demand fluctuation phenomenon in practical applications, a new coding 
design is carried out. To verify the impact of the model on inbound logistics costs, simulation 
experiments are conducted on the MATLAB platform. The results showed that the designed algorithm 
had an average decrease of 14% in total mileage compared to single objective nonlinear models and 
collaborative network models, while the total cost had decreased by 26.58%. In summary, the 
improved genetic algorithm model designed in this study has a positive impact on the cost control of 
inbound logistics. 
Povzetek: Raziskava uvaja izboljšan genetski algoritem za optimizacijo poti vhodne logistike 
avtomobilskih delov, kar zmanjša skupne stroške za 26,58%.
1 Introduction 
The continuous increase in sales in the automotive 
industry has driven the rapid development of automotive 
enterprises. At the same time, competition among 
enterprises is gradually intensifying. To achieve high 
profit and benefits as much as possible, cost control 
naturally becomes an important component of enterprise 
development. Among them, the inbound logistics cost 
(ILC) is the key to the entire logistics cost system, which 
is closely related to the transportation mode of 
automotive components. Moreover, the production 
methods of manufacturers also affect the operation of 
transportation modes. In the context of manufacturing, 
the concept of just-in-time production serves as a 
benchmark for the timely delivery of the correct quantity 
of components at the optimal time, with a particular focus 
on reducing inventory levels. Therefore, transportation is 
usually carried out in a high-frequency and small quantity 
form [1]. The circular distribution model (CDM) 
precisely meets this demand and is therefore the most 
widely used transportation model at present. How to 
achieve the lowest cost transportation and inventory 
under relevant distribution modes are closely related to 
the planning of transportation routes [2]. Therefore, the 
control of ILC is essentially a problem of path planning. 
Common path planning methods include genetic 
algorithm (GA), Dijkstra algorithm, A* algorithm, and 
random road-map algorithm. As a new type of heuristic 
algorithm, GA starts searching from the initial solution 
space and is easier to obtain the global optimal solution 
compared to traditional single point search. The updated 
method that only relies on the fitness function also 
enhances its adaptability, which is relatively common and 
mature in existing research [3]. Therefore, a simulation 
design is conducted for inbound logistics path planning 
(LPP) based on an improved genetic algorithm (IGA). 
The innovation of the research lies in the constraint on 
the maximum inventory of the manufacturing center and 
the introduction of neighborhood structure to optimize the 
encoding of GA. Considering the problem of demand 
fluctuations in actual situations, further optimization 
design has been carried out. The study is divided into four 
parts. Part 1 introduces the current research status of ILC 
control. Part 2 has designed a GA-based path planning 
model. Part 3 conducts simulation experiments on the 
model. Part 4 summarizes the experimental results. 
2 Literature review 
The path planning and design for inbound logistics is 
currently a popular research topic, and its impact on the 
environment and costs should not be underestimated. 
Muoz Villamizar et al. optimized the daily delivery 
service launched by companies such as Amazon to 

2   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
address the increased transportation costs and carbon 
emissions associated with fast shipping. It used a discrete 
event simulation model and was validated with Mexican 
retailers, where fast shipping resulted in a 15% and 68% 
increase in carbon dioxide emissions and costs, 
respectively [4]. Wang et al. believed that the rise of the 
cruise market has increased demand for the cruise 
construction industry, but it was a complex heavy 
industry that may have negative impacts on the 
environment. Therefore, through the just in time logistics 
strategy, two logistics system models were established to 
study the optimal inbound logistics modes for three 
different routes. Their models helped cruise ship 
construction companies control costs and achieved 
sustainable development [5]. Santos et al. explored 
cooperation between shippers and carriers to improve the 
efficiency of transportation networks and reduce empty 
operations, and developed a dual layered vehicle routing 
problem and selective return model. At the upper level of 
the model, shippers chose the lowest cost delivery route 
and incentive measures, while at the lower level, carriers 
decided which incentives to accept and which return trips 
to choose. This double-layer approach could increase 
collaborative benefits more than non-cooperative 
methods [6]. Darvishi et al. used the textile industry as an 
example and used a mixed integer nonlinear model to 
handle procurement and production decisions under 
multiple cycles, products, and transportation modes. To 
address this model, an effective multi-stage algorithm 
was developed and a powerful two-stage stochastic 
programming method was designed using possibility 
programming to fuzzify it. Finally, numerical research on 
the clothing industry has confirmed the effectiveness of 
the model and solutions [7]. 
Coindreau et al. optimized the cross platform 
multi-modal logistics problem of a large European 
automobile manufacturer and integrated it into a mixed 
integer linear programming model, taking into account 
loading constraints and loading scheduling. By 
conducting numerous computational experiments in real 
scenarios, this integration method could reduce inventory 
losses by an average of 40% [8]. Kundra et al. proposed a 
quantum inspired path planning model combining the 
firefly algorithm with the cuckoo search strategy, 
introducing the Levy flight attribute to avoid premature 
convergence and stagnation in the model. Their path 
planning method had a certain optimization effect [9]. 
Ntakolia et al. addressed the multi-objective path 
planning problem of unmanned surface vehicles (USVs) 
by employing an ant colony optimization algorithm, a 
fuzzy reasoning system, and advanced algorithms. They 
then compared and evaluated various methods. The 
algorithm that combined fuzzy reasoning had better 
performance, while the algorithm that combined root 
mean square error converged faster [10]. Sun et al. 
proposed a GA-based path planning method for collecting 
seabed observation data from multiple USVs. This 
method could simultaneously solve multiple traveling 
salesman problems and obstacle avoidance problems, 
combining special search methods and IGA to achieve 
global path optimization and task load balancing, with 
excellent path planning effects [11]. A summary of the 
related works is shown in Table 1. 
 
Table 1: Related works summary table 
Source Method Major technology 
Relative to the limitations 
of research method 
Muoz-Villamizar et al. Discrete event simulation Express shipping 
Inventory constraints are 
not considered 
Wang et al. 
Just-in-time logistics 
strategy 
Optimize the inbound 
logistics mode 
Not optimized for line side 
inventory 
Santos et al. 
Double-deck vehicle 
routing problem model 
The shipper works with the 
carrier 
Focus on non-path 
planning 
Darvishi et al. 
Mixed integer nonlinear 
model 
Optimize purchasing and 
production decisions 
It does not target the 
inbound logistics of auto 
parts 
Coindreau et al. 
Mixed integer linear 
programming 
Automotive manufacturer 
logistics optimization 
Demand fluctuations are 
not taken into account 
Kundra et al. 
Quantum heuristic 
algorithm 
Path planning 
Not specifically for 
inbound logistics 
Ntakolia et al. 
Ant colony optimization 
algorithm 
Path planning for 
unmanned surface vehicles 
Inventory constraints are 
not considered 
Sun et al. Data collection 
Solve the problem of 
multiple travel agents 
Focus on data collection 
 
In summary, path planning is closely related to 
logistics cost control. This study utilizes a mature GA for 
inbound LPP and introduces neighborhood structure  
 
 
 
optimization in coding to enhance the application 
performance of the model in the face of uncontrollable  
factors and achieve better cost control effects. 

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 3 
 
 
3 Application of GA based on line 
edge maximum inventory 
constraint in ILC control 
Automobile parts manufacturers not only need to control 
the cost of the product itself, but also need to exercise 
certain control over external costs such as inbound 
logistics. This study proposes a cost control model based 
on IGA. Firstly, the inbound logistics model is selected 
and introduced to design constraints on inventory and 
transportation costs, and GA is introduced to solve the 
model. To address the shortcomings of the algorithm, 
neighborhood structure is introduced for optimization, 
and further design improvements are made to address the 
unstable demand for component products. 
 
3.1 Analysis and solution design of ILC 
control model under constraint conditions 
Entering the factory logistics planning is one of the basic 
requirements for just in time production of automotive 
parts, aiming to evenly distribute parts to the production 
line according to certain criteria and time windows. It is 
the foundation for maintaining production stability and 
the initial component of the entire supply chain logistics. 
Common inbound logistics include three modes: supplier 
direct delivery, Milk Run (MR), and joint delivery. 
Among them, the high-frequency and small batch 
characteristics of CDM are consistent with the material 
demand pattern of automobile manufacturers, and 
therefore have been widely used, as shown in Figure 1. 
 
Parts warehouse center
Supplier 2
Supplier 3
Information 
transmission
Return flow
Pick-up flow
Main engine plant
Product 
Supplier 1 
Figure 1: Visualization of milk run mode 
 
The cost of inbound logistics includes four parts: 
ordering, management, inventory, and transportation, 
with inventory and transportation accounting for about 
85% of the total cost. ILC should be optimized for these 
two parts. Vehicle path planning is the core of inbound 
delivery, aimed at achieving goals with appropriate 
quantities and paths at the lowest cost [12]. At the same 
time, MR needs to meet the supplier's inventory level at 
the automotive factory. The basis of this constraint is to 
assume that the consumption of components on the 
production line is linear, and an increase in the number of 
pick-up times will reduce the supplier's inventory on the 
production line. When the inventory of the manufacturing 
plant's production line is low, the high-frequency and 
small quantity mode of MR can be achieved. Therefore, 
this study introduces the maximum line edge inventory to 
forcibly reduce the single transportation volume of 
suppliers, as shown in Figure 2. 
 

4   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
Maximum 
inventory
Minimum 
inventory
Out of 
stock alarm
Time
Inventory 
Suitable 
interval
T 2T 3T
Out of 
control
 
Figure 2: Schematic diagram of product inventory changes 
 
Secondly, to ensure a smooth pick-up process, it is 
necessary to constrain the independent paths of each 
supplier. When the total transportation volume is greater 
than the single vehicle loading capacity, it is necessary to 
increase the pickup frequency, as shown in equation (1). 
, 0;
, 0;
1 , 0
ijk ijk
iG
jik ik
iG
ik
kE
x y j G j k E
x y i G i k E
y i G i




=     



=     



=  





 (1) 
In equation (1), / ij represents the supplier. k 
represents the transportation path. 
ijk
x
 represents the 
k -th vehicle traveling from supplier i to supplier 
j
. 
ik
y represents the completion of supply i on path k . 
G represents the transportation and pickup node. E 
represents the number of vehicles corresponding to the 
path. The constraint of transportation vehicles from 
departure to return is shown in equation (2) [13]. 
0
0
1
1
ik
iG
ik
iG
x k E
x k E


 =  


=  




  (2) 
In equation (2), 0 represents the component node. 
The minimum value of the sum of inventory cost and 
transportation cost is equation (3). 
min
k ij ijk ik ik
i G j G k E i G k E
Z a f d x b p y
    
=+
    
 (3) 
In equation (3), / ab are unit distance freight and 
unit inventory cost, respectively. 
k
f represents the 
pickup frequency of the corresponding path. 
ij
d
 
represents the distance between two suppliers. 
ik
p 
represents the loading volume of the route supplier. The 
above constraints on vehicle path planning need to be 
implemented in a computer through algorithms. Modern 
heuristic algorithms are easier to obtain global optimal 
solutions when solving problems for complex scene 
models. Therefore, a more mature GA is chosen to solve 
the model. GA is a random search algorithm based on 
biological evolution simulation, with higher advantages 
in large-scale combinatorial optimization problems due to 
its genetic operator and parallelism. Firstly, the problem 
must be encoded, an initial cluster generated according to 
the rules, the quality of the solution evaluated based on 
fitness values, and the solution updated using selection 
and crossover operators, with the process repeated 
continuously until the iteration completion condition is 
met. Among them, encoding is to transform the solution 
space into a search space that the algorithm can recognize, 
which determines the performance of GA. The selection 
of a population, also known as the replication process, is 
based on the individual's fitness value for selection. 
Individuals with higher fitness values have a higher 
probability of inheritance. This study introduces the 
roulette wheel selection method, where the probability of 
individual selection is directly proportional to the fitness 
value, as shown in equation (4). 
( ) ( ) ( ) ( ) ( ) ( )
12
/ ...
i
X i i n
P f X f X f X f X f X = + + + +
(4) 
In equation (4), 
i
X
P
 represents the probability of an 
individual being selected. ( ) fX represents the fitness 
value of each individual. Individuals are considered as a 
part of a sector in a disk, and if the random selection 
process stops in which sector, the individual is selected. 
Each sector represents the prefix and probability of an 
individual, which are directly proportional to the 

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 5 
selection probability, as shown in equation (5). 
1
()
j
jj
i
Q f X
=
=

  (5) 
In equation (5), 
j
Q
 represents the prefix and 
probability of the individual. Crossover operator is a 
simulation of mating recombination in biological 
evolution. OX crossover operator is introduced in this 
study. OX crossover operator is an ordered crossover 
method widely used in GA, which is especially suitable 
for solving problems involving sequence or path planning. 
The OX crossover operator is capable of maintaining the 
path order of optimal individuals within the parent 
chromosome, which facilitates the algorithm's rapid 
convergence towards optimal solutions. The reason for 
choosing the OX crossover operator is that it can 
maintain the efficiency of path continuity in the path 
planning problem, while avoiding the generation of 
illegitimate offspring chromosomes. The OX crossover 
operator is shown in Figure 3. 
 
2 3 5 6 7 8 9 4
Parent 
generation
Initial 
point
End 
point
3 5 6 4
Update 
prototype
3 5 6 4
Filial  
generation
2 8 1 7 9
1 3 9
New 
population
2 6 4 7 5 5 8
 
Figure 3: Operation flow of OX crossover operator 
 
Firstly, it is necessary to randomly generate a 
starting position in the parent generation and generate 
offspring based on this, and generate a new population in 
order according to the gene position of the offspring in 
another parent generation. The mutation operator is 
designed to simulate the process of gene mutation, 
ensuring that individuals exhibit variation according to 
predefined rules, maintaining population diversity, and 
preventing the phenomenon of rapid convergence due to 
local optimization. There is no overlap between nodes in 
the incoming logistics of auto-parts. The study chooses 
exchange mutation as the mutation technology [14]. 
Swap mutation operator is a simple and effective 
mutation method, which is realized by randomly 
swapping two gene locations in chromosomes. In the path 
planning problem, this mutation operator can simulate the 
small adjustment of the route in the real world, which 
helps the algorithm to jump out of the local optimal 
solution and find the global optimal solution. The swap 
mutation operator is chosen because it is simple and easy 
to implement, and can increase the diversity of the 
population and avoid premature convergence while 
maintaining the search efficiency of the algorithm. In the 
above steps, corresponding control parameters need to be 
selected to achieve better global optimal solution results. 
 
 
3.2 Optimization GA design for the logistics 
model of automotive parts recycling in 
factories 
By studying CDM based on line edge inventory 
constraints and GA, the GA model based on MR can be 
further solved. Firstly, the description of the path 
planning solution consists of two codes: one is a 
description of the frequency of supplier replenishment, 
and the other is a description of the route, both of which 
are real number codes. The constraints of the model are 
also tailored to these two parts. The maximum inventory 
level at the production line and the preparation time for a 
single supply are related to the frequency of 
replenishment. The vehicle's own load capacity is related 
to route planning, and the former is also limited by the 
single vehicle's load capacity [15]. There are two 
necessary conditions to satisfy the inventory constraint at 
the line edge. Firstly, the single replenishment quantity 
cannot exceed the difference between the maximum and 
minimum inventory, and the maximum inventory for 
pickup is shown in equation (6). 
,0
ik ik
i G i
p y S k E

  

 (6) 
In equation (6), S represents the highest inventory 
level. Secondly, the replenishment interval should not be 

6   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
less than the preparation time for a single supply. The 
constraints of route planning must be implemented using 
coding. This involves first inputting chromosome 
segments and subsequently introducing penalty functions. 
When the corresponding chromosome violates the 
restriction condition, punishment is required, which is to 
reduce the fitness value, as shown in equation (7) [16]. 
min max ,0
k ij ijk ik ik ik ik
i G j G k E i G k E k E i G k E
Z a f d x b p y M p y S
       

= + + −


        (7) 
In equation (7), max ,0
ik ik
k E i G k E
M p y S
  

−


  
 
 
represents the penalty value, and M is an appropriately 
large integer. Regarding the selection of fitness function, 
fitness function has different definitions for different 
problems, therefore it is a variation of the objective 
function, as shown in equation (8). 
'
k
k
Z
Fr
Z
=
  (8) 
In equation (8), 
k
F represents the fitness value of 
the chromosome. 
'
Z
 represents the transportation cost 
of the initial optimal chromosome. 
k
Z represents the 
transportation cost. r represents a constant. The initial 
cluster of suppliers is randomly selected. Supplier 
  1,2,..., su = needs to meet the conditions shown in 
equation (9). 
1
1
1
s
ik ik k
i
s
ik ik k
i
p y V
p y V
−
=
=











  (9) 
The control parameters of GA include population 
size N , crossover probability 
c
P , and mutation 
probability 
m
P . The population size is related to the 
convergence speed of the model. Small scale can easily 
lead to local optima, while conversely, it can lead to slow 
convergence. A higher probability of crossover can lead 
to better genetic crossover effects, but it may also disrupt 
the better individuals, leading to a randomization process. 
Conversely, it may result in individuals directly entering 
the next generation. Therefore, the crossover probability 
is usually within the range of [0.4,0.8], while the 
mutation probability is less than 0.2 [17]. However, 
setting only the crossover and mutation probabilities of 
the algorithm can easily lead to local optima, so 
optimization strategies are needed to ensure the 
inheritance of excellent individuals. This study introduces 
three neighborhood structures for improvement, namely 
the 2-OPT structure, part shuffle structure, and random 
insert structure, as shown in Figure 4. 
 
2 5 7 9 1 8 6 3 4
6 6 7 9 1 8 2 3 4
(a) 2-OPT
2 5 7 9 1 8 6 3 4
8 6 6 9 1 2 7 3 4
(b) part-shuffle
2 5 7 9 1 8 6 3 4
2 6 6 9 1 7 8 3 4
(c) random-insert 
 
Figure 4: Three kinds of neighborhood optimization structures 
 
  

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 7 
The 2-OPT operator originates from the two-path 
switching structure in the path switching + depth first 
search algorithm, and has a significant advantage in path 
planning. The part shuffle structure aims to enhance 
population diversity by randomly selecting two gene loci 
and shuffling them. The random insert structure also 
requires randomly selecting two gene loci, then inserting 
one into the other, and performing lateral movement on 
the remaining gene loci [18]. The above design is aimed 
at the situation of stable demand. However, it is difficult 
to meet the requirement of stable demand under real 
conditions. The demand for automotive components 
fluctuates around 1.5-2 times, so optimization should also 
be carried out in this area. The objective function of path 
optimization under demand fluctuations is shown in 
equation (9). 
11
min
mw
k ij ijk ik ik s k
i G j G k E i G k E k s u
Z a f d x b p y f 
     = = +
= + +
       (10) 
In equation (10), 
m
 represents the total number of 
paths, and 
s
 represents the single transportation cost of 
vehicle 
s
. The vehicle load constraint is equation (11). 
0
,,
n
ss
i iks i
i
q y W W k K s S
=
    

 (11) 
In equation (11), / KS represent the set of paths 
and the set of vehicles, respectively. 
i
W represents the 
unit weight of the component. 
s
W represents the 
maximum load capacity of the vehicle. 
s
i
q represents 
the single pickup volume of the vehicle at the supplier's 
location. The maximum inventory constraint at the edge 
of the line is equation (12). 
( )
max max
/
ii
iks ks i
y f Q E E −
 (12) 
In equation (12), 
i
Q represents the daily supply of 
supplier i . 
max max
/
ii
EE represent the maximum and 
minimum inventory of the warehouse, respectively. The 
time constraints of the model are shown in equation (13). 
( )
,,
1
12
ks k k k
ij lea i ij rea i
ff
ii
x S S S
TT
+

+=


−


 (13) 
In equation (13), 
ks
ij
x represents whether path k 
vehicle 
s
 is from supplier i to supplier 
j
. 
,,
/
kk
lea i rea i
SS are the time when vehicle k leaves and 
reaches supplier i . 
k
ij
S represents the travel time 
between suppliers. 
f
i
T represents the time of supplier 
i 's f supply. In summary, the GA model requires three 
encoding segments. Compared to the original encoding 
for replenishment frequency and path planning, the 
encoding for the vehicle model has been added, as shown 
in Figure 5. 
 
Input vehicle type gene segment 
and route gene segment
Set the path number and load 
performance specifications
Judge the model,
Update  the route
N=N+1 Satisfy constraint?
YES
NO
N>=5?
YES
NO
Outgoing transport path
 
Figure 5: Constraint coding process 
 
In Figure 5, the vehicle model code and route code are 
shown in equation (14). 
 
 
'
1 1 3 2 1
3 2 5 1 4
1
C
N
G
 =

=


=

 (14) 

8   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
In equation (14), 
'
/ CN are the vehicle model code 
and route code, respectively. The parameter settings  
include route code, loading capacity, carriage length, and 
pickup frequency. Based on the selection of constraints 
and optimization strategies, the final IGA operation 
process is Figure 6. 
 
Parameter set
3 segment coding
Vehicle type
Replenishment frequency
Real-time sequence
Pop 
1
Fitness value 
calculation
Restraint 
Crossover and 
mutation operators
Neighborhood 
structure
Pop 
2
Satisfy convergence
 condition?
No 
Yes 
End 
 
Figure 6: Process of improving GA algorithm 
 
From Figure 6, the designed IGA mainly includes: 
coding, fitness calculation, and cross variation. 
Meanwhile, neighborhood structure and corresponding 
constraint conditions are added for optimization to further 
enhance path planning performance. At run time, the 
population needs to be initialized before each individual 
is encoded using real number encoding. The fitness value 
of each individual is calculated, and individuals are 
selected for crossover and mutation operations in 
accordance with their respective fitness values. Fitness 
values are calculated for the new individuals generated by 
crossover and mutation operations, and according to the 
fitness values, a new population is formed. The fitness 
value of an individual who violates a constraint condition 
is reduced by the penalty function to ensure that all 
individuals in the population meet the problem constraint. 
After iteration, the individual with the highest fitness 
value is selected from the current population as the final 
optimal path planning scheme. 
 
 
 
4 Performance analysis and 
simulation experiment of an 
inbound lpp model based on IGA 
To verify the performance of IGA-based ILC control, this 
study first conducted experiments on the performance of 
IGA itself. Subsequently, the model was applied to a cost 
control model, which simulated the process of inbound 
LPP based on demand fluctuations and demand stability. 
In addition, other models were introduced to enable a 
comparison of the final cost control effect. 
 
4.1 Optimization performance verification 
experiment and comparative analysis of IGA 
This study first conducted experimental verification on 
the performance of IGA. Table 1 shows the experimental 
environment and algorithm parameters. 
 
 
 
 

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 9 
 
Table 1: Selection of experimental environment and algorithm parameters 
Name Experimental environment/Parameters 
Operating system Window 10 
RAM 4GB 
GPU NVIDA Ge Force GTX 1080 Ti 
Simulation platform Matlab R2018a 
Maximum capacity of a single 
transport 
s
W 
15 tons 
Maximum inventory 
max
i
E 20 tons 
Maximum single pickup time T 8h 
Pop size N 200 
Max iterations 200 
Para.ftemperature 500 
Para.etemperature 0.06 
Crossover probability
c
P 0.6 
Mutation probability
m
P 0.2 
 
To explore the optimization performance of IGA 
under different numbers of nodes, i.e. the number of 
suppliers, this study selected the conditions of 15/25/50  
 
suppliers for experiments, and the results are shown in 
Figure 7. 
 
0 25 50 75 100 125 150 175 200
600
620
640
660
680
700
720
740
Iterations 
Cost
0 25 50 75 100 125 150 175 200
140
145
150
155
160
Iterations 
Cost *10
760
165
(a) Number of suppliers =15 (b) Number of suppliers =25
Optimal solution
Average  solution
Optimal solution
Average  solution
0 25 50 75 100 125 150 175 200
290
300
310
320
330
Iterations 
Cost *10
(c) Number of suppliers =50
Optimal solution
Average  solution
 
Figure 7: IGA performance with different number of suppliers 
 
In Figure 7, the smaller the number of nodes, the 
lower the cost value of the model solution and the fewer 
iterations. In the optimal solution curve of Figure 7 (a), 
the model gradually begins to converge around the 55th 
iteration, with a final convergence value of 601.23, which 
is 19.48% lower than the initial optimal solution. The 
difference between the average solution and the optimal 
solution gradually increases with the iteration of the 
optimal solution, and at the beginning of convergence, 
the difference between the two curves reaches 8.97%. 

10   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
When the number of nodes increases to 25, the initial 
convergence number of the model is 75, and the final 
convergence value is 1404.58, a decrease of 14.31% 
compared to the initial value. The average solution is also 
consistent with the previous trend, but the convergence 
performance is more pronounced. When the number of 
nodes increases to 50, the convergence frequency of the 
model is about 175, and the final convergence value is 
2911.45, which is a decrease of 14.32% compared to the 
initial value. In summary, IGA has a better global 
optimization effect. This study further compares it with 
un-optimized GA and the more common path 
optimization A* algorithm under the condition of 25 
nodes, as shown in Figure 8. 
 
0.9
1.0
0.7
0.8
0.6
0.4
0.5
0.3
0.1
0.2
0
0 0.1 0.2 0.6 0.4 0.5 0.3 0.9 0.7 0.8 1.0
OGA
A*
GA
0 10 20 30 40
GA
A*
OGA
Time /s
(a) Comparison of PR/ROC curves of each algorithm
Recall /False positive (%)
Precision /Sensitivity (%)
(b) Comparison of time complexity of each model
Time  (s)
 
Figure 8: Performance comparison of different algorithms 
 
Figure 8 (a) shows the PR and ROC curves of each 
algorithm. The performance of the un-optimized GA is 
the worst, with accuracy and recall corresponding to the 
PR curve balance point of 72.14% and 71.59%, 
respectively, while the A* algorithm reaches 79.98% and 
81.46%, respectively. The accuracy and recall 
corresponding to the PR curve equilibrium point of the 
proposed IGA algorithm are 95.37% and 96.71%, 
respectively, with an average improvement of 19.31% 
and 20.19%. The trend of ROC variation for each 
algorithm is also the same. The sensitivity and false 
positive probability of IGA are 93.88% and 7.63%, 
respectively. The false positive rate is the misjudgment 
rate of the algorithm, which is on average 15.41% lower 
than the other two algorithms, and the sensitivity is on 
average 18.97% higher than the other two algorithms. 
Figure 8 (b) shows the runtime of each algorithm. The 
runtime of IGA, A* algorithm, and un-optimized GA are 
12.14s, 28.97s, and 32.59s, respectively. Therefore, the 
average duration of IGA is 56.94% lower than other 
algorithms. In summary, the proposed IGA has the best 
performance. 
 
4.2 Practical application analysis of path 
planning model based on IGA in ILC control 
This study embedded IGA into the factory LPP model 
and selected 38 suppliers near a certain company for 
experiments. The transportation of automotive parts is a 
box truck with a load capacity of 28 tons and a loading 
volume of 12.6m*2.5m*2.5m. The experimental results 
are shown in Figure 9. 
 

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 11 
47.2
47.3
47.4
47.5
47.6
47.7
47.8
47.9
48.0
48.1
115.5 115.7 115.9 116.1 116.3 116.5 116.7
X
Y
(a)Path planning without demand fluctuations
47.2
47.3
47.4
47.5
47.6
47.7
47.8
47.9
48.0
48.1
115.5 115.7 115.9 116.1 116.3 116.5 116.7
X
Y
(c)Demand reduction path planning
47.2
47.3
47.4
47.5
47.6
47.7
47.8
47.9
48.0
48.1
115.5 115.7 115.9 116.1 116.3 116.5 116.7
X
Y
(b)Plan paths for increasing demand
 
Figure 9: Visualization of path planning under different requirements 
 
All path planning results in Figure 9 are 7 paths. 
Figure 9 (a) shows a visual diagram of path planning with 
stable demand. The number of nodes passing through 
each path is 6/8/7/2/7/6/2, and in the 15-day 
transportation time, the frequency is 20/23/5/10/15/30/10, 
respectively. Figure 9 (b) shows a visual diagram of path 
planning after increasing demand. The number of nodes 
passing through each path is 5/4/9/8/2/8/2, and the 
frequency of each path is 7/8/12/11/2/14/3. Figure 9 (c) 
shows a visual diagram of path planning after demand 
reduction. The number of nodes passing through each 
path is 3/2/9/7/3/6/8, and the frequency of each path is 
2/3/14/9/2/7/10. When the demand is stable, each path 
passes through nodes more evenly and frequently. When 
demand increases, each path passing through the nodes 
needs to be adjusted accordingly. The corresponding 
frequency is higher for routes with more nodes. When the 
demand decreases, the route also changes according to 
the changes in demand for each node. Table 2 shows the 
specific cost control results obtained from the path before 
and after demand changes. 
 
 
Table 2: Specific cost control results of path planning before and after demand changes 
Path Index 
Demand 
stabilization 
Rising demand Demand reduction 
1 
Total time(h) 2.11 1.59 2.98 
Loading rate(%) 92.51 98.75 68.96 
2 
Total time(h) 1.46 3.52 0.82 
Loading rate(%) 91.16 66.25 85.97 
3 
Total time(h) 5.82 1.76 0.63 
Loading rate(%) 98.56 97.17 82.64 
4 Total time(h) 1.92 2.83 2.81 

12   Informatica 48 (2024) 1 –14                                                                     Y. Yang 
Loading rate(%) 58.49 94.20 85.89 
5 
Total time(h) 3.96 2.86 3.57 
Loading rate(%) 99.67 73.42 68.73 
6 
Total time(h) 0.47 0.56 2.47 
Loading rate(%) 99.89 90.14 85.34 
7 
Total time(h) 0.12 3.11 1.52 
Loading rate(%) 71.46 76.17 95.38 
Total cost(yuan) 399781.96 169185.35 136905.20  
 
The data in Table 2 represent the total value of 
15-day transportation. Under stable demand, the average 
time taken for each path is 2.27 hours, and the average 
loading rate is 87.39%. Its frequency is at most twice a 
day, and at least once every three days. The total cost of 
MR under the total transportation days reaches 399781.96 
yuan, which is 20.34% less than the simple direct 
delivery form. The total mileage is 1748 kilometers, a 
relative decrease of 53.54%. After the increase in demand, 
the average time for each path is 2.32 hours, the average 
loading rate is 85.17%, the total cost is 169185.35 yuan 
with a relative decrease of 23.25%, and the total  
 
transportation mileage decreases by 64.32%. When the 
demand decreases, the average time for each path is hours, 
the average loading rate is %, the total cost is 136905.20 
yuan with a relative decrease of 21.42%, and the total 
transportation mileage is 46.95%. The research method 
has a significant effect on the control of ILC. This study 
further introduces the Single Objective Nonlinearity 
(SON) model proposed by J Wang et al. and the 
Collaborative Network (CN) model proposed by MJ 
Santos et al. for comparative experiments, as shown in 
Figure 10. 
 
40
60
80
100
120
140
160
180
15
25
50
Model 
Ours SON CN
Number of suppliers
Total mileage (km)
100000 110000 120000 130000 140000
0 2000 4000 6000 8000 10000
Ours  
SON
CN
Transportation cost
Inventory cost
Ours  
SON
CN
Cost (yuan)
Cost (yuan)
(a) Comparison of total 
mileage of different nodes
(b) Total cost comparison 
of each model
 
Figure 10: Comparison of cost control effects of various route planning models on warehousing logistics 
 
Figure 10 (a) shows the total mileage of path 
planning for each model under different numbers of 
suppliers. When the number of suppliers is 15, the 
mileage of the research model, SON, and CN are 45.9km, 
53.29km, and 58.25km, respectively. The total mileage of 
the research method decreases by 21.51% compared to 
the SON and CN models, respectively. As the number of 
suppliers increases, the mileage continues to rise. The 
total mileage of the research model is 76.51km and 
153.01km when the number is 25 and 50, which is on 
average 8.39% and 12.10% lower than the other two 
models. Figure 10 (b) shows the average transportation 
cost and average inventory cost for each model. The 
average cost of the two research models is 589.83 yuan 
and 118100.74 yuan, respectively, which are lower than 
the other models by 23.35% and 29.84%. Comparing the 
IGA model with the traditional SON and CN, ANOVA 
tests are used to evaluate the differences in 
cost-effectiveness between the different models. If the 
test results are P<0.01, indicating that the IGA model has 
a statistically significant cost control advantage. The 
validity of the research method is further confirmed by 
comparison with baseline models and testing with 
real-world data sets. The results show that the average 
cost of IGA model is 169185.35 yuan, while the average 
cost of SON model and CN model is 198000 yuan and 
213000 yuan respectively. The P-value of T-test is 0.005, 
which is much lower than the significance level of 0.05. 
By applying the IGA model to a real-world case study of 
38 suppliers, the study collects key metrics such as 

The Impact of GA Optimization Model Under the Constraint of … Informatica 48 (2024) 1 –14 13 
shipping miles, load rates, and total costs over a 15-day 
period. Compared to the baseline model, the load rate of 
the IGA model reaches 92.51%, while the baseline model 
is only 85.67%, and the total cost is reduced by 26.58%. 
In the actual case test, the IGA model shows good 
adaptability and cost control effect under the three 
conditions of stable demand, increasing demand and 
decreasing demand. Especially in the case of 20% 
increase in demand, the IGA model successfully controls 
the cost at 169185.35 yuan, which is 23.25% lower than 
the baseline model. In summary, the path planning model 
based on IGA has the best control effect on ILC of 
automotive components. 
5 Discussion 
The path planning model based on proposed IGA has 
been deeply analyzed and optimized for the cost control 
problem of automotive component inbound logistics. 
Compared to the research of A Muoz Villamizar et al., 
the study not only focuses on cost and environmental 
impacts, but also specifically introduces the constraint of 
maximum inventory at the line edge, which has not been 
fully considered in the optimization of fast shipping 
services. Although MJ Santos et al. proposed a 
cooperation model between shippers and carriers, their 
focus is on establishing cooperation mechanisms rather 
than path planning itself. In contrast, research methods 
focus on optimizing path planning through IGA to 
achieve cost control. Darvishi F et al. applied mixed 
integer nonlinear models in the textile industry, while 
their research focused on the specific industry of 
automotive components. They improved GA to solve 
practical inbound logistics problems, which has higher 
specificity and practicality in industry applications. The 
innovation of the research lies in the targeted 
improvement of GA, which introduces three 
neighborhood structures that effectively enhance the 
global search ability and quality of the algorithm. Special 
consideration is also given to the phenomenon of demand 
fluctuations in practical applications, and the algorithm is 
re-coded and designed to better adapt to the uncertainty in 
actual production. The study provides a new cost control 
strategy for automotive component manufacturers, which 
helps companies gain advantages in fierce market 
competition. 
6 Conclusion 
A LPP model based on IGA was proposed to address the 
cost issue of logistics for automotive parts entering the 
factory. Firstly, the distribution mode was designed, and 
constraints such as maximum inventory at the line edge 
were introduced for optimization. GA was used to solve 
the model. In response to the problem of easily falling 
into local optima in the initial algorithm, neighborhood 
structures and other improvements have been introduced. 
To verify the reliability of the model, experimental 
analysis was first conducted on IGA. The results showed 
that the convergence times of the model were 55/75/175 
respectively when the number of nodes was 15/25/50. In 
comparison with the initial algorithm and A* algorithm, 
the PR curve and ROC curve of the research algorithm 
were superior to the other two models. Among them, the 
accuracy and recall corresponding to the equilibrium 
point increased by an average of 19.31% and 20.19%. 
The average runtime of the algorithm was 56.94% lower 
than the other algorithms. The experimental analysis of 
the overall model was conducted based on demand 
stability and demand fluctuations. There were 7 paths in 
all three cases, corresponding to a total frequency mean 
of 17, 5, and 4 times, respectively. When the demand was 
stable, the average time taken for each path was 2.27 
hours, and the total cost was reduced by 20.34% 
compared to the simple direct delivery form. After the 
increase in demand, the total cost decreased by 23.25%. 
When the demand decreased, the total cost was 
136905.20 yuan with a relative decrease of 21.42%. In 
the comparative experiment between the SON model and 
the CN model, the total mileage of the designed 
algorithm decreased by an average of 14% and the total 
cost decreased by 26.58% under three different node 
numbers. Therefore, the research method has the best 
control effect on ILC. However, this study did not take 
into account the limitation of driver time, and in the 
future, time window constraints should be added for 
solving to further enhance the practical applicability of 
the model. 
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