Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 9, No. 2, 2023 

 

262 

Research	on	Vehicle	Routing	Problem	in	Auto	Parts	
Inbound	Logistics	Based	on	Milk	Run	Mode	
Ruyu Yang 

School of Shanghai University, Shanghai 200000, China 

 

Abstract: The application of milk run in domestic automobile parts supply was studied. A mathematical model for routing a 
milk run system was formulated by minimizing the transportation and inventory cost under the restriction of tiered storage pricing 
scheme and multiple vehicle types. In solving the model, a modified genetic algorithm was developed, which is suitable for 
realistic sized problems. The utility of the approach was demonstrated through a computational experiment. 

Keywords: Inbound logistics, Milk run, Genetic algorithm, Inventory routing problem, Supply hub. 
 

1. Introduction 
As the first phase of automotive logistics, the inbound 

logistics of parts has attracted the attention of researchers due 
to its complexity, management challenges, and high costs. 
Considering the Milk Run inbound logistics model in the 
consolidation center, which involves multiple pickups, can 
not only reduce transportation costs by increasing vehicle 
load capacity and reducing empty return trips, but also meet 
the just-in-time (JIT) delivery requirements of the assembly 
plant through frequent and small-batch supplies, thereby 
reducing inventory costs. This approach has gradually gained 
favor among automotive manufacturing companies. 

Transportation and warehousing are the two main cost 
sources in inbound logistics. Designing optimal delivery 
routes and transport frequencies is of significant practical 
importance in reducing loading time, decreasing vehicle 
empty rates, saving vehicle resources, and lowering 
transportation costs. Vehicle routing optimization has been a 
focal point in research on cost control in inbound logistics, 
but real-world considerations often neglect tiered 
warehousing price ranges and the use of multiple vehicle 
types for transportation. In 2008, Ohlmann et al. [1] proposed 
a two-stage algorithm to solve the cyclic pickup problem with 
time windows and demand partitioning characteristics. In 
2009, Wang Jinlian and Jiang Zuhua introduced the concept 
of maximum line-side inventory into Milk Run, transforming 
the problem into a common frequency routing problem. In 
2013, Zhu Ling and Wu Di presented a cyclic pickup model 
with time window constraints and demand partitioning. In 
2014, Chen et al. [2] proposed a new method for computing 
transportation costs and improved the ant colony algorithm 
for solution. In 2017, Guner et al. [3] considered vehicle 
locations and real-time congestion, utilizing dynamic 
stochastic programming to derive dynamic paths. In 2021, Li 
Tong et al. studied the cooperative optimization of paths and 
3D loading in cyclic pickup transportation problems under 
demand uncertainty. In 2022, Zheng Renrong et al. made 
decisions based on multi-stage inventory levels of parts and 
pickup sequencing of transport vehicles, considering the 
dynamic demand of production lines and the characteristics 
of bulk transportation for parts. 

Based on the aforementioned research background, it can 
be observed that current studies on inbound logistics of 
automotive parts primarily focus on pickup modes and 

vehicle routing optimization, often emphasizing rigid 
inventory control and single-vehicle type solutions. Research 
on multi-vehicle cyclic pickup path optimization considering 
inventory costs is relatively scarce. This study takes a well-
known domestic automotive company as the background and 
conducts route optimization design. A mathematical model is 
established based on the cyclic pickup operation mode, with 
the objective of minimizing transportation and inventory 
costs. A genetic algorithm is employed for solving the model. 
Finally, numerical experiments are conducted to validate the 
effectiveness and optimization capabilities of the proposed 
method. 

2. Consideration of Inventory Costs in 
The Optimization Model for Multi-
vehicle Cyclic Pickup Routing 

2.1. Problem Description 
This study defines the problem of multi-vehicle cyclic 

pickup with consideration of inventory costs as follows: In an 
inbound logistics process with a supply-demand balance, with 
the assembly plant as the demand point, multiple vehicles of 
different types, without quantity restrictions, depart from the 
consolidation center. Following the material requirements of 
the assembly plant within a designated operational cycle 
(typically one day), pickups are made from corresponding 
suppliers according to predetermined routes and pickup 
frequencies, and ultimately return to the consolidation center. 
The consolidation center then delivers the goods at a uniform 
speed based on the production requirements of the assembly 
plant. 

2.2. Model Assumptions 
Based on the analysis above, the following assumptions 

and definitions can be made for the cyclic pickup routing 
optimization problem studied in this paper:  

(1) Consolidation Center: There is a unique consolidation 
center with a known geographical location.  

(2) Vehicles: There are multiple vehicle types, each with 
different capacity, fixed costs, and variable costs. The number 
of vehicles is not limited.  

(3) Suppliers: The geographical locations of all suppliers 
are known. The daily volume for each supplier is known. 
Each supplier provides only one type of component.  

(4) Components: Each component is consumed evenly over 



 

263 

time, and the synchronization of pickup frequencies with the 
production schedule is not considered.  

(5) Paths: Each path can only be used by one vehicle type. 
Each supplier has only one pickup path passing through it. 
The pickup frequencies for all supplier points on a single path 
can be different, but they are the same for all suppliers on that 
particular path. The consolidation center serves as the origin 
and destination of the paths.  

(6) Inventory Tiers: The storage prices at the consolidation 
center increase in gradient with the growth of inventory tiers. 
The price for each inventory tier is known. 

2.3. Page Numbers.  
2.3.1. Related parameters 

V: { | 0,1, 2, , }V i i n  �   is the set of n supplier 
points and distribution centers, where i=0 represents the 
distribution cent 

U: { | 0,1, 2, , }U u u a  �   represents a type of 
vehicle, and the volume of u type of vehicle is qu 

R: { | 0,1, , }R r r e  �  represents e inventory level 
K: { | 1, 2, , }K k k m  �  is a collection of m path 
cij: The distance from supplier i to j, specifically cii=0 
v: The average driving speed of the vehicle 
di: Daily cargo volume of supplier i 
ti: Average loading time for supplier i 

tij: Upplier i to j transportation time，
ij

ij

c
t

v
  

T: The maximum allowable time for a single cycle per path 
J: Maximum number of suppliers accessed per path 
G: Maximum frequency per path 
Smax,r: The maximum frequency corresponding to the r 

inventory interval 
Smin,r: The minimum frequency corresponding to the r 

inventory interval 
 : Unit distance transportation cost 
r : The storage price per cubic meter corresponding to the 

inventory level of category r 

u : Fixed single departure cost for u vehicles 
m: Total number of scheduled paths 
Fk: Pickup frequency of path k 
Pi: Single pickup quantity at supplier i 

2.3.2. Model building 
Based on the above parameter symbols and decision 

variables, a mathematical model is constructed as follows: 
Objective function: 
 
min iku k ik r r u ku k

i V j V k K u U i V k K u U r
i

R k K
j i k

u U
j uZ y Z P ff c x b 

         

           (1) 
 
Formula (1) represents the objective function, Z represents 

the total logistics cost incurred during a cycle of picking up 

operations, Where
j

k ij ijk
i V V k K u U

uf c x
   
   represents 

transportation cost, iku kr i r
i V k K u U r R

y Z P
   
   represents 

inventory cost, and u ku k
k K u U

b f
 
  represents total fixed 

departure cost; 
Constraint condition: 

- =0,ijku ijku
j V j V

x x
 
    , ,i V k K u U       (2) 

 

0 1,iku
i V

x


   ,k K u U           (3)   
 

0 1,i ku
i V

x


     ,k K u U           (4)  
 

,ijku iku
j V u U u U

x y
  

      , 0,i V i k K      (5)  
           

,ijku jku
i V u U u U

x y
  

      , 0,j V j k K     (6)   
           

1,iku
k K u U

y
 

   , 0i V i              (7)  
           

1,ijku
u U i M j M

x W
  

     , 0 , 2W V W W     (8)  
           

= ,iku ik
i V u U u

y d
f G

q 

 
 

 
    k K        (9) 

 

,ikui i
k K u U k

y
P d

f 

 
  
 
   , 0i V i         (10)    

           

1,kr
r R

Z


    k K           (11)  
           

min, ,k kr r
r R

f Z S


     k K           (12)  
           

max, ,k kr r
r R

f Z S


       k K       (13)   
           

1,ku
u U

b


       k K        (14)   
           

,i iku u ku
i V u U u U

Py q b
  

        k K       (15)   
           

, 0

,i iku ij ijku
u U i V i i V j V u U

t y t x T
     

      k K  (16)   
           

,iku ku
i V u U

y b J
 

     k K        (17)   
       

Formula (2) indicates that the number of vehicles entering 
and leaving each supplier is equal, ensuring that the vehicles 
leave after the pickup is completed; 

Formulas (3) and (4) indicate that the starting and ending 
points of the pickup path are the distribution centers, ensuring 
that a complete loop can be formed; 

Formulas (5), (6), and (7) indicate that each supplier is only 
assigned to one path; 

Formula (8) is famous for eliminating constraints in sub 
circuits. 



 

264 

Formula (9) indicates that the pickup frequency of route k 
does not exceed the maximum pickup frequency limit for 
each path; 

Formula (10) represents the single pickup quantity of 
supplier i; 

Formula (11) indicates that each path can only select one 
inventory interval; 

Formulas (12) and (13) indicate that the picking frequency 
of this path should be within the picking frequency range of 
the inventory interval in which it is located; 

Formula (14) indicates that only one vehicle type can be 
used for each path; 

Formula (15) indicates that the total single pickup volume 
of all suppliers on a pickup path cannot exceed the maximum 
loading capacity of the corresponding vehicle model on that 
path; 

The formula (16) indicates that the total loading time of 
each supplier on a path and the transportation time between 
suppliers should not exceed the maximum time of the circular 
pickup order; 

The formula (17) indicates that the total number of 
suppliers on each path cannot exceed the maximum number 
of suppliers accessed per path. 

3. Improved Genetic Algorithm Design 
To effectively and quickly solve problems, this article 

adopts genetic algorithm, which has good convergence and 
search efficiency.  

3.1. Chromosome coding 
This article adopts integer encoding and designs a three-

layer encoding format to describe the complete transportation 
scheme. The first layer uses integer encoding to describe the 
arrangement order of suppliers in chromosomes, the second 
layer uses integer encoding to describe the position of 
separation points on chromosomes to determine the supplier 
number on each path, and the third layer uses integer 
encoding to describe the selected vehicle type on each path. 

3.2. Initial population 
The initial population size is usually set based on 

experience, and the number of individuals is generally 
between 20 and 200. 

3.3. Fitness function 
Take the reciprocal of the objective function as the fitness 

function of the genetic algorithm, namely: 
 

1

iku kr i r u ku k
i V j V k K u U i

i
V k K u U r R

u
k

k j ij
K u

k
U

F
f Z Pc yx b f 

         


    (18) 

 

3.4. Selection Operator 
This article combines the championship operator and elite 

selection operator to design the selection operator, and the 
specific process is as follows: 

(1) Calculate the fitness function values of each 
chromosome in the current population; 

(2) Set the number of championship groups to p and 
randomly divide the chromosomes in the current population 

into p groups; 
(3) Select the chromosome with the best fitness function 

value in each group and directly replicate it to the next 
generation. 

3.5. Mutation operator 
This article presents a total of seven different mutation 

operators:  
(1) Inversion Mutation: This operator targets the first-tier 

supplier encoding. It randomly selects two gene positions, i 
and j, in the chromosome encoding. It reverses the gene 
segment between the two positions and inserts it back in its 
original location.  

(2) Swap Mutation: This operator targets the first-tier 
supplier encoding. It randomly selects two gene positions, i 
and j, in the chromosome encoding. It swaps the values at the 
two positions while keeping the rest of the gene positions 
unchanged.  

(3) Insertion Mutation: This operator targets the first-tier 
supplier encoding. It randomly selects two gene positions, i 
and j, in the chromosome encoding. It shifts the values 
between positions i+1 and j forward by one position in their 
original order and inserts the value at position i into the 
original position of gene position j.  

(4) Breakpoint Mutation: This operator applies to the 
second-tier breakpoint encoding and the third-tier vehicle 
type encoding. It generates new second-tier breakpoint 
encoding and third-tier vehicle type encoding according to the 
encoding rules, replacing the original encoding for the second 
and third tiers.  

(5) Reverse-Mix Breakpoint Mutation: This operator 
simultaneously targets the first-tier supplier encoding, the 
second-tier breakpoint encoding, and the third-tier vehicle 
type encoding. It combines the inversion mutation and 
breakpoint mutation simultaneously.  

(6) Swap-Mix Breakpoint Mutation: This operator 
simultaneously targets the first-tier supplier encoding, the 
second-tier breakpoint encoding, and the third-tier vehicle 
type encoding. It combines the swap mutation and breakpoint 
mutation simultaneously. 

(7) Insert-Mix Breakpoint Mutation: This operator 
simultaneously targets the first-tier supplier encoding, the 
second-tier breakpoint encoding, and the third-tier vehicle 
type encoding. It combines the insertion mutation and 
breakpoint mutation simultaneously. 

3.6. Mutation operator 
Because the Rate of convergence of different population 

sizes is different, the algorithm uses the maximum number of 
fitness function calculations as the termination condition. 

4. Numerical Experiment 

4.1. Data preparation 
This article randomly generated 18 suppliers to be included 

in the circular pickup operation system, numbered 1-18, 
where 0 represents the centralized distribution center. 

(1) Transportation distance 
See Table 1 of the Distance matrix for the distance between 

each supplier and the gathering and distribution center, in 
kilometers (km): 

 
 



 

265 

Table 1. Distance matrix(a) 
 0 1 2 3 4 5 6 7 8 9 

0 0.0 66.1 65.3 78.4 66.0 125.8 91.7 100.8 72.8 40.1 
1 66.1 0.0 38.8 49.1 36.9 59.7 38.5 51.1 29.5 41.6 
2 65.3 38.8 0.0 14.1 2.4 81.8 31.9 37.3 67.6 64.7 
3 78.4 49.1 14.1 0.0 14.6 82.2 28.9 29.2 78.6 78.6 
4 66.0 36.9 2.4 14.6 0.0 79.5 29.9 35.9 65.8 63.9 
5 125.8 59.7 81.8 82.2 79.5 0.0 53.5 59.0 65.3 96.2 
6 91.7 38.5 31.9 28.9 29.9 53.5 0.0 12.7 65.5 78.3 
7 100.8 51.1 37.3 29.2 35.9 59.0 12.7 0.0 78.3 90.3 
8 72.8 29.5 67.6 78.6 65.8 65.3 65.5 78.3 0.0 34.8 
9 40.1 41.6 64.7 78.6 63.9 96.2 78.3 90.3 34.8 0.0 
10 13.6 52.5 54.3 67.9 54.7 112.2 79.0 88.7 60.8 30.7 
11 127.2 64.1 71.1 66.8 69.1 29.0 39.3 38.6 80.7 105.3 
12 41.5 61.2 36.1 45.0 38.0 115.1 67.9 72.9 82.9 63.2 
13 44.4 30.9 23.3 37.4 23.3 87.3 47.4 56.6 53.7 42.5 
14 23.7 69.0 54.2 65.1 55.7 127.1 84.8 91.5 84.2 56.8 
15 31.8 34.7 46.1 60.2 45.8 94.3 65.2 76.1 43.6 20.6 
16 63.8 44.1 6.1 14.6 8.4 87.8 37.1 41.3 72.4 67.0 
17 81.3 22.1 31.9 36.1 29.5 50.5 16.7 29.4 49.0 63.0 
18 123.3 82.6 58.4 44.9 58.1 84.2 45.0 32.4 110.5 119.6 

 
Table 2. Distance matrix(b) 

 10 11 12 13 14 15 16 17 18 
0 13.6 127.2 41.5 44.4 23.7 31.8 63.8 81.3 123.3 
1 52.5 64.1 61.2 30.9 69.0 34.7 44.1 22.1 82.6 
2 54.3 71.1 36.1 23.3 54.2 46.1 6.1 31.9 58.4 
3 67.9 66.8 45.0 37.4 65.1 60.2 14.6 36.1 44.9 
4 54.7 69.1 38.0 23.3 55.7 45.8 8.4 29.5 58.1 
5 112.2 29.0 115.1 87.3 127.1 94.3 87.8 50.5 84.2 
6 79.0 39.3 67.9 47.4 84.8 65.2 37.1 16.7 45.0 
7 88.7 38.6 72.9 56.6 91.5 76.1 41.3 29.4 32.4 
8 60.8 80.7 82.9 53.7 84.2 43.6 72.4 49.0 110.5 
9 30.7 105.3 63.2 42.5 56.8 20.6 67.0 63.0 119.6 
10 0.0 113.8 37.3 32.1 26.2 18.4 53.7 68.0 112.7 
11 113.8 0.0 107.1 84.1 123.1 97.6 76.4 45.9 57.2 
12 37.3 107.1 0.0 30.4 21.5 43.2 31.6 64.7 88.0 
13 32.1 84.1 30.4 0.0 39.9 23.0 24.6 38.6 81.3 
14 26.2 123.1 21.5 39.9 0.0 40.6 50.8 78.3 109.0 
15 18.4 97.6 43.2 23.0 40.6 0.0 47.6 52.3 103.2 
16 53.7 76.4 31.6 24.6 50.8 47.6 0.0 38.0 59.5 
17 68.0 45.9 64.7 38.6 78.3 52.3 38.0 0.0 61.5 
18 112.7 57.2 88.0 81.3 109.0 103.2 59.5 61.5 0.0 

 

From the Distance matrix, it can be seen that the maximum 
distance between each supplier and the distribution center 
does not exceed 130km, and the distribution among suppliers 
is uniform, which is conducive to the design of recycling 
routes. 

(2) Daily inventory of components 
After summarizing the past daily supply times and 

quantities of 18 suppliers participating in the circular pickup 
project, the daily pickup volume data of each supplier is 
shown in Table 3. Based on past loading and unloading 
experience, this article takes the average loading and 
unloading time at each supplier as 0.5 hours, which is 
convenient for subsequent calculations. 

 

Table 3. Supplier Daily Quantity Table 

Supplier 
Number 

Daily cargo volume 
(m³) 

Average layday 
(h) 

Supplier 
Number 

Daily cargo volume 
(m³) 

Average layday 
(h) 

1 106.9 0.5h 10 48.6 0.5h 
2 74.2 0.5h 11 187.8 0.5h 
3 100.4 0.5h 12 43.6 0.5h 
4 70.1 0.5h 13 38.2 0.5h 
5 183.3 0.5h 14 43.8 0.5h 
6 140.8 0.5h 15 40.6 0.5h 
7 145.5 0.5h 16 78.8 0.5h 
8 146.4 0.5h 17 142.8 0.5h 
9 102.6 0.5h 18 187.5 0.5h 

 



 

266 

 

(3) Vehicle model information 
Three types of vehicle models are used for circular pickup, 

each with different sizes, volumes, speeds, fixed departure 

costs, transportation costs, and single cycle time. The specific 
information is shown in Table 4. 

 

Table 4. Vehicle Model Information Table 

Vehicle model 
number 

Size(m) 
Volume 

(m³) 
Average speed per 

hour (km/h) 

Fixed 
cost 

(RMB/ti
me) 

Transport cost 
(RMB/km) 

Single maximum 
cycle time (h) 

1 
17.5×3×2

.7 
120 70 700 8 8 

2 
15.5×2.7

×2.4 
100 70 550 7 8 

3 
12.5×2.7

×2.4 
80 70 450 6 8 

 

According to the driver's working hours, set the maximum 
single cycle time for each vehicle to not exceed 8 hours. 
Assuming that each vehicle type is traveling at a constant 
speed, with an average speed of 70km/h. 

(4) Warehouse tiered price 

The picking frequency of each route has a certain impact 
on the management cost of the warehouse. The warehouse has 
set tiered prices based on the frequency of circular picking 
routes, and different frequency intervals correspond to 
different prices. The specific prices are shown in Table 5. 

 
Table 5. Warehouse Ladder Price List 

Type 
Maximum frequency of the line 

(times) 
Minimum frequency of the line 

(times) 
Warehouse price
（RMB/m³） 

1 - 6 7 
2 6 3 6.8 
3 3 2 6.3 
4 2 1 6 

 
(5) Operational restrictions 
In order to reduce the difficulty of supplier management 

during operation and reduce operational risks, the number of 
suppliers visited per route is set to not exceed 6, and the 
maximum number of daily cycles per route is not more than 
8. 

4.2. Algorithm implementation 
Through extensive computational verification, this article 

sets the main parameters of the genetic algorithm as follows: 

the population size is 40, the number of championship groups 
is set to 5, each group has 8 chromosomes, and the maximum 
number of fitness function calculations is 8000 times. The 
algorithm iteration results are basically convergent. 

When using multiple vehicle models for cyclic pickup, the 
solution results in 5 routes, with each route picking frequency 
ranging from 3 to 6 times. The average loading rate calculated 
by vehicle model and frequency is 98%. The solution results 
are shown in Table 6, and the route planning is shown in 
Figure 1. 

 

 
Figure 1. Hybrid vehicle cycle pickup roadmap 

 

 



 

267 

Table 6. Hybrid vehicle cycle pickup route information 

Line number Pickup sequence Vehicle model Pickup frequency Inventory Price (RMB/m³) Loading rate 
1 0-18-3-0 2 3 6.3 96% 
2 0-10-17-6-7-0 3 6 6.8 99.5% 
3 0-14-12-16-2-4-13-0 1 3 6.3 96.9% 
4 0-15-8-9-0 2 3 6.3 96.5% 
5 0-11-5-1-0 1 4 6.8 99.6% 

 

4.3. Result analysis 
In the supplier direct delivery mode, each route is delivered 

by a single vehicle model. The vehicle model, loading rate, 
and inventory price information for each route are shown in 
Table 7, and the transportation route is shown in Figure 2. 

 

Table 7. Supplier Direct Delivery Line Information 

Line number Pickup sequence Vehicle model Pickup frequency Inventory Price (RMB/m³) Loading rate 
1 0-1-0 3 2 6 66.8% 
2 0-2-0 3 1 6 92.8% 
3 0-3-0 1 1 6 83.7% 
4 0-4-0 3 1 6 87.6% 
5 0-5-0 2 2 6 91.7% 
6 0-6-0 3 2 6 88% 
7 0-7-0 3 2 6 90.9% 
8 0-8-0 3 2 6 91.5% 
9 0-9-0 3 2 6 64.1% 

10 0-10-0 2 1 6 48.6% 
11 0-11-0 2 2 6 93.9% 
12 0-12-0 3 1 6 54.5% 
13 0-13-0 3 1 6 47.8% 
14 0-14-0 3 1 6 54.8% 
15 0-15-0 3 1 6 50.8% 
16 0-16-0 3 1 6 98.5% 
17 0-17-0 3 2 6 89.2% 
18 0-18-0 2 2 6 93.8% 

 

 
Figure 2. Supplier Direct Delivery Route Map 

 

The comparison of key indicators for each project between 
the supplier direct delivery mode and the circular pickup 

mode is shown in Table 8. 

 

Table 8. Comparison of key indicators under two modes 

Supply mode 
Number of transportation 

vehicles (vehicles) 

Average 
loading rate 

(%) 

Transport 
mileage (km) 

Total rental volume of 
warehouse (m³) 

Total cost 
(RMB) 

Direct delivery 26 80.4% 2515 1210.1 42933 
Milk run 19 98.0% 1043.6 507.9 34936 

Optimization 
amplitude (%) 

26.9% 17.6% 58.5% 58.0% 18.6% 

Note: Average loading rate=total cargo volume of all suppliers/total volume of all operating vehicles 



 

268 

 

Total rental volume of the warehouse=total single pickup 
volume of all routes 

From the above table, it can be seen that compared to the 
supplier direct delivery mode, the circular pickup mode 
greatly improves transportation efficiency and reduces 
logistics costs, which is reflected in the following aspects: the 
average loading rate of the fleet has increased from 80.4% to 
98%, an increase of 17.6%; The total transportation mileage 
decreased from 2515km to 1043.6km, a reduction of 58.5%; 
The total cost decreased from 42933 yuan to 34936 yuan, 
saving 18.6%. The total rental volume of the warehouse has 
increased from the original 1210.1 m³ Lowering to 507.9 m³, 
Reduced by 58%. The number of transportation vehicles 
decreased from 26 to 19, a decrease of 26.9%. 

5. Summary 
Many existing studies on the optimization of cyclic picking 

paths only consider rigid inventory costs and single vehicle 
types, often overlooking the impact of tiered warehousing 
prices and multiple vehicle types on transportation schemes. 
This study investigates the vehicle path optimization problem 
for cyclic picking, taking into account inventory costs and 

multiple vehicle types. A genetic algorithm is designed and 
employed to solve the problem, and the effectiveness of the 
method is validated using real-world data. The experimental 
results demonstrate that compared to the direct delivery mode, 
the cyclic picking mode can optimize the automotive parts 
inbound logistics in terms of operational efficiency and cost. 
Additionally, considering tiered warehousing prices and 
multiple vehicle types enhances the feasibility of the cyclic 
picking scheme.  

References 
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production systems [J]. Transportation Science, 2008, 42(3): 
352-370. 

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