Design of a Logistics Allocation Scheme Based on the Approximate:
Relaxed Approach to Batching Algorithm
Xingzou Liu
*
, Jie Yao, Xinyu Zhao, Zhuo Li and Kun Jiang
Information Engineering University, Zhengzhou, Henan, China
Keywords: Relaxationt, Optimization, Logistics.
Abstract: The Ministry of Commerce, the Central Internet Information Office and the Development and Reform
Commission jointly released the "14th Five-Year Plan" for the development of e-commerce, whih provides a
top-level design for the development of e-commerce in China during the 14th Five-Year Plan period. With
the deepening impact of e-commerce on the social economy, the role of e-commerce on the industrial chain
and supply chain is becoming stronger and stronger, and the innovative functions proposed in the industrial
chain and supply chain will enable e-commerce to better support the industrial chain and supply chain. As
online shopping gradually becomes an important consumption mode in today's market. Efficient logistics and
transportation gradually become a concern. The warehouse, as the starting point for the discharge of goods,
has a significant impact on the efficiency of logistics and transportation. In this paper, for a simplified sorting
system, the batching algorithm is designed using the approximate system-relaxation algorithm, the goods
placement problem is optimised using the simulated annealing algorithm, and the assignment of sorting tasks
is finally completed by cross-referencing specific scenarios. (No effect of the paper was seen, i.e. whether
there was any improvement in the data, or whether anything new was proposed).
1 INTRODUCTION
This template, modified in MS Word 2007 and saved
as a “Word 97-2003 Document” for the PC (Yao,
2022), provides authors with most of the formatting
specifications needed for preparing electronic
versions of their papers (Huang, 2017). In recent
years, online shopping has developed very rapidly in
China. The convenience and affordability of e-
commerce has made it rapidly popular in China (Yao,
2022). As the logistics support for the e-commerce
industry, the express delivery industry is also growing
rapidly with the development of the e-commerce
market scale (Huang, 2017; Zhao, 2021; Li, 2022). At
the same time, China's governments at all levels also
attach great importance to the development of e-
commerce and express industry, in the "express into
the village" and many other people-friendly policies,
the development of China's express industry has
expanded rapidly, the number of major courier
companies handle more and more express every day.
2016 is already expected to exceed 40 billion express
business volume in China (Reports, 2017). And
according to the "2021 China Express Development
Index Report" released by the State Post Bureau, the
national express business volume in 2021 completed
108.3 billion pieces, with an average daily express
mail handling volume of nearly 300 million pieces.
Among them, Jinhua City's annual express business
volume exceeded 10 billion pieces, becoming the first
city in the country to move into the 10 billion scale
(Xu, 2021). In the face of so many express, how the
courier companies in the accurate and safe premise,
as soon as possible to the hands of customers express
is a widely concerned about the issue. And speeding
up the sorting speed is undoubtedly the most
important part of speeding up the logistics speed, and
is also an important means for major courier
companies to improve their market competitiveness.
Sorting is the process of stacking couriers by order,
type and order of entry and exit. In the beginning, the
most primitive manual sorting was used. At that time,
the flow of goods was small and manual sorting was
sufficient to meet demand, but as the economy
became more global and the number of goods in
circulation grew, manual sorting became difficult to
meet. In the 1920s the Dutch company Erma
developed the world's first letter sorting machine,
which marked the birth of automatic sorting
equipment. After the Second World War a number of
developed countries began to work on automatic
Liu, X., Yao, J., Zhao, X., Li, Z. and Jiang, K.
Design of a Logistics Allocation Scheme Based on the Approximate: Relaxed Approach to Batching Algorithm.
DOI: 10.5220/0012142300003562
In Proceedings of the 1st International Conference on Data Processing, Control and Simulation (ICDPCS 2023), pages 17-22
ISBN: 978-989-758-675-0
Copyright
c
2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
17
sorting techniques and equipment and applied them in
practice (Li, 2013). With the popularisation and
development of computers and the subsequent
application of technologies such as big data and the
internet in automatic sorting, logistics sorting systems
in foreign countries became increasingly
sophisticated (Le, 2022). Although China's logistics
industry has made good progress since the reform and
opening up, especially in the 21st century, not only in
land logistics, but also in air logistics and water
logistics (Li, 2022; Huang, 2021), automated sorting
in China started very late, so there is still a certain
distance between the overall level and the world's
advanced level, especially in the area of sorting speed.
However, China has a great demand for the
development of the express delivery industry, and the
modern logistics industry plays an important
fundamental and pioneering role in the national
economy and social development (Xu, 2022). The
scale of China's express business continues to rank
first in the world, accounting for more than 40% of
the global share, and contributing 60% to the growth
of the world's express business, which has become a
new engine for the development of the global express
market (Yang, 2017). The 14th Five-Year Plan and
the 20th Five-Year Plan are the most important and
most important of all. The Outline of the 14th Five-
Year Plan and Vision 2035 proposes to "optimise
international logistics channels and accelerate the
formation of a safe and efficient logistics network
with internal and external connections" (Li, 2021;
Wang, 2022). Sorting efficiency is a major focus on
the competitiveness of the express industry. In order
to enable the rapid development of China's express
industry, to achieve efficient automated sorting as
early as possible, to promote the mechanisation and
modernisation of the entire industry and to improve
the competitiveness of enterprises internationally, it
is essential to study and analyse sorting algorithms. In
response to this call, and also out of practical
considerations, major logistics companies are striving
to find faster and more efficient sorting methods.
2 PREVIOUS WORK
2.1 Problem Analysis
In order to improve the sorting efficiency of e-
commerce systems and provide algorithmic support
and theoretical basis for the next step of e-commerce
automation, we select three steps: goods aggregation,
goods on shelves, and assigned sorting according to
the existing courier delivery workflow, refine the
objective functions for these three steps, and carry out
modelling and optimisation respectively. The optimal
solution for the three steps in the target scenario is
finally derived, forming an optimal courier picking
solution for existing e-commerce conditions.
2.2 Introduction to the Approximate,
Relaxation Algorithm
Constraint and relaxation algorithms are common
algorithms for making abstract problems concrete,
and initially researchers put this idea into practice in
order to find better transfer equations and to ensure
that the resulting solution is optimised in an attempt
to transfer the equation. The 'constraint' approach is
generally described as adding conditions and
restrictions that are appropriate and more realistic to
ensure that the solution is still obtained after the
addition of these conditions and restrictions. The
'relaxation' approach, on the other hand, relaxes the
harsh and unreasonable conditions and restrictions of
the abstract problem and ensures that the solution is
still found after relaxing these conditions and
restrictions. The current constraint and relaxation
algorithm is very effective in optimising known
solutions to reasonable problem constraints. Figure 1
is the flow chart of the restriction relaxation
algorithm.
2.3 Constraint, Relaxation Algorithm
Implementation Steps
Step 1: add appropriate constraints, compare the
initial solution with the new solution and update the
values of the more optimal solution.
Step 2: Remove some of the stringent conditions,
compare the initial solution with the new solution, the
increment of the objective function and update the
values of the more optimal solution.
Step 3: If the solution is still obtained by
modifying the constraints, repeat steps 1 and 2 until
the more optimal solution no longer changes.
2.4 Introduction to the Simulated
Annealing Algorithm
The simulated annealing algorithm is a commonly
used optimization algorithm based on Monte-Carlo
iterative solving. Initially, researchers combined the
general combinatorial optimization problem in
optimal combinatorial problems with the solid
annealing process in thermodynamics, trying to break
through the local optimum and find the global
optimum with a certain probability. Today, this
ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation
18
algorithm has become the classical algorithm for
finding globally optimal patterns.
2.5 Simulated Annealing Algorithm
Model Construction Steps
Step 1: Generate the initial solution randomly, update
the optimal solution as the initial solution and
calculate the corresponding objective function taking
values.
Step 2: generate new solutions randomly in the
domain of the optimal solution, calculate the
increment of the objective function between the
optimal solution and the new solution, and update the
optimal solution when the increment of the objective
function is greater than zero.
Step 3: Repeat step 2 until the optimal solution no
longer changes.
Start
End and print y
Generate random
vector ď vĐ
The probability of
producing ď 1Đ gose
down
Is ď vĐ selected
Reduce the
requir em ents for s helf
utilization
Whether ď vĐ make the
shelf utilization to meet the
the requirements
Have all orders been
completed
The sele cted order
completes inď vĐ
Outputď vĐ
N
Y
Y
N Y
N
3 METHODOLOGY
3.1 Design of Batching Algorithms
Using the Approximate - Relaxed
Approach
First create a matrix representing the orders of the day.
𝐴=
𝑎
𝑎
⋯𝑎
𝑎
𝑎
⋯𝑎
⋮
𝑎
⋮
𝑎
⋱⋮
⋯𝑎
where the rows represent the order number and the
columns represent the type of goods, so that
𝑚=
932, 𝑛= 1941 , and
𝑎
=
0 𝑁𝑜 item j in the 𝑖
order
1 The 𝑗
item in the 𝑖
order
Next, construct the selection matrix:
𝑋=
𝑥
𝑥
⋯𝑥
𝑥
𝑥
⋯𝑥
⋮
𝑥
⋮
𝑥
⋱⋮
⋯𝑥
where the rows represent order batches and the
columns represent order numbers, i.e. 𝑚= 932 , and
𝑥
=
0 𝐵𝑎𝑡𝑐ℎ 𝑖 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑗
order
1 B𝑎𝑡𝑐ℎ 𝑖 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑗
order
where the rows represent order batches and the
columns represent order numbers, i.e. 𝑚= 932 , and
𝑥
=
0 𝐵𝑎𝑡𝑐ℎ 𝑖 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑗
order
1 B𝑎𝑡𝑐ℎ 𝑖 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑗
order
Let the matrix 𝑌= 𝑋× 𝐴 , then it is easy to see that
𝑦
=
0 There are no j goods in 𝑖
the batch
else There are j goods in 𝑖
the batch
To facilitate the calculation, the numbers in 𝑌 all
numbers greater than 1 are set to 1, i.e.
𝑦
=
0 There are no j goods in 𝑖
the batch
1 There are j goods in 𝑖
the batch
In this way, the objective translates into
minimizing the value of𝑔 the minimum value of the
constraint as follows:
𝑠
∙
𝑡
∙
=
⎩
⎪
⎨
⎪
⎧
𝑌
𝑖𝑗
𝑛
𝑗=1
≤200 (1)
𝑋
𝑖𝑗
𝑔
𝑖=1
= 1 (2)
Thus, it is sufficient to find such a matrix𝑋 The
problem can be solved by finding such a matrix that
satisfies the above conditions and has the minimum
number of rows, but such a matrix is not easy to find
because, firstly, the number of rows is unknown and
the matrix cannot be set up in the first place. Secondly,
the number of columns in the matrix is too large to
traverse to find the optimal matrix.
Therefore, abandoning the search for the optimal
solution and moving to an approximate solution, one
can split𝑋 splitting each row of the0 −1 matrix of
rows and solving for them separately.
𝑣
=
0 The 𝑖
order is not selected in this selection
1 The 𝑖
order is selected in this selection
such that 𝑣 its multiplication with the matrix
𝐴 multiply it with the matrix and make the result
satisfy the constraint (1) so that this row matrix is said
to 𝑣 is a correct choice, otherwise it is an incorrect
choice.
Each correct selection is saved in a row of the
matrix 𝑋 in one row of the matrix, and subsequent
selections are made without reselecting 𝑋 the orders
already selected in the matrix. When the matrix 𝑋
satisfies the constraint (2) the selection is complete,
Design of a Logistics Allocation Scheme Based on the Approximate: Relaxed Approach to Batching Algorithm
19
at which point the 𝑋 can be used as a solution to this
problem.
The solution sought for this question 𝑋 The
number of rows should be as small as possible, and for
this reason, as many orders as possible should be
selected for each choice.
Adjusting0 −1 The probability of the random
number being generated is initially set to 1 with a
probability of 1 and when a loop of 100 When the
correct choice is not found after several attempts,
reduce this probability by 0.005. In this way, the final
choice generated has as many orders selected each
time as possible. The solution found is also better than
before.
To further optimise the solution, a further
condition can be added, requiring the highest possible
utilisation of the shelves, in a similar way to before,
setting the minimum number of shelves to be utilised
initially as 200, and discard if the found choice cannot
be satisfied. If the number of consecutive 10 is not
satisfied, then the minimum utilisation number is set
to −1 . After using this method of calculation, the
approximate solution to the problem is eventually
found, using 92 The order is processed in batches.
3.2 Optimising the Placement of Goods
Using Simulated Annealing
Algorithms
The equations are an exception to the prescribed
specifications of this template. You will need to
determine whether or not your equation should be
typed using either the Times New Roman or the
Symbol font (please no other font). To create
multileveled equations, it may be necessary to treat the
equation as a graphic and insert it into the text after
your paper is styled.
Based on the results obtained in the previous
section, it is possible to obtain the number of orders
completed in each batch and to calculate the types of
goods contained therein according to the previous
method. The objective is to find a sequence of goods
that minimises the total picking distance of a batch of
orders. That is, to find a sequence of equal length to
the number of goods in a batch, so that when the goods
are arranged according to this sequence, the total
picking distance is minimised.
In this way, the problem is transformed into
finding a sequence that minimises the objective
function, which can be equated to TSP problem. Let
the first 𝑚 order contains the set of item numbers
as 𝑔
and the total picking distance for all orders
is𝑆
(
𝑚
)
, then use the following formula.
𝑆
(
𝑚
)
= 𝑑
(
𝑂
)
∈
(
3
)
In this way𝑆
(
𝑚
)
is the total picking distance to
be found, which should next be minimized.
For each batch of orders obtained from the
previous results, the number of occupied shelves is
relatively large and it is not computationally feasible
to traverse the entire arrangement, so a simulated
annealing algorithm is used to find an approximate
solution.
with 𝑆
(
𝑚
)
as the main function, the 𝑚 The order
of the goods contained in the batch of orders is the
input, and the inverse order and the pair of orders are
used to find the proximity solution, and the initial
temperature is set to 1000 and the end temperature is
set to 8 and the cooling rate is set to 0.94 The results
obtained by the two methods are compared and the
better one is used as the best order for this batch of
orders.
From the results, it can be seen that the solution
sequences obtained by both the pairwise and inverse
order methods of finding proximity solutions are each
good or bad in different orders but do not differ much,
so the solution sequence with the smallest total
picking distance is taken directly as the final solution
sequence.
3.3 Assignment of Sorting Tasks
The equations are an exception to the prescribed
specifications of this template. You will need to
determine whether or not your equation should be
typed using either the Times New Roman or the
Symbol font (please no other font). To create
multileveled equations, it may be necessary to treat
the equation as a graphic and insert it into the text
after your paper is styled.
In this question there are 5 sorters, initially
located on 1 shelf number, and based on the results in
(2) the results in this question, calculate the number
of orders to be picked from the current position after
picking the first 𝑖 after picking the first order, from
the current position P
The picking of the next order
starts at the current position. At this point there are
four scenarios. The following is the first case:
𝑃
<min
∈
(
𝑖
)
(
4
)
At this point the sorter simply moves from the
current position to the highest numbered shelf position
where the goods in the order are located, moving a
distance of max
∈
𝑆
(
𝑖
)
−𝑃
.
This is the second case:
ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation
20
𝑃
>max
∈
𝑆
(
𝑖
)
(
5
)
At this point the sorter simply moves from the
current position to the lowest numbered shelf position
where the goods in the order are located, moving a
distance of 𝑃
−minS
∈
(
𝑖
)
.
This is the third case:
minS
∈
(
𝑖
)
< 𝑃
<
∈
(
)
∈
(
)
(
6
)
The shortest distance the sorter can move is from
the current position to the mini∈O k S(i) position and
then to the maxi∈O k S(i)
position, the total distance moved is 𝑃
−
minS
∈
(
𝑖
)
+ maxS
∈
(
𝑖
)
−min
∈
𝑆
(
𝑖
)
This is the forth case:
∈
(
)
∈
(
)
< 𝑃
<max
∈
𝑆
(
𝑖
)
(
7
)
The shortest distance the sorter can move at this
point is from the current position to positionmaxS
∈
(
𝑖
)
and then to minS
∈
(
𝑖
)
The total distance travelled is
𝑃
−minS
∈
(
𝑖
)
+ maxS
∈
(
𝑖
)
−min
∈
𝑆
(
𝑖
)
Initially, any
sorter is first asked to complete the first batch of orders
and the distance travelled is calculated, and
subsequent orders are picked by the sorter who has
travelled the least distance, so that the picking task is
as even as possible.
4 RESULT AND DISCUSSION
The following two results are scatter plots of the
distance of the express sorting system and the sorting
results between different groups after using the
annealing algorithm and the restriction relaxation
algorithm.
4.1 Analysis of Results
This paper provides a model for the order batching
method, the order in which different goods are placed
and the task allocation of pickers in the courier
distribution process, and tests this model in one case.
And as can be seen from these results, this model
solves the problem of determining the batching
method in order batch processing very well, resulting
in high shelf utilisation and the ability to process a
large number of orders at once.
In solving the problem of how goods are placed
on the shelves, the diagram below shows that
individual goods of the same order are placed in
relatively centralised locations, which greatly
facilitates the picking process for the pickers. When
assigning picking tasks, this paper provides a more
general model that can be used to adjust the weights
between distance travelled and mutual averaging, or
even add new judgement factors, according to specific
business needs, without affecting the normal use of the
model. The results are obtained to meet the specific
situation. The shortcomings of the model in this paper
are as follows:
A. When dealing with order batching problems
for orders containing fewer types of goods have good
results, but for large orders, there is a certain
probability of low shelf utilisation and fewer orders
being processed in a single run.
B. In solving the goods placement problem, the
speed of computing is sacrificed to get better results,
and the practical application still requires more
computer arithmetic.
C. The models shown in this paper are
approximate solutions and should not be used when
the number of orders is small and optimal solutions are
available.
Design of a Logistics Allocation Scheme Based on the Approximate: Relaxed Approach to Batching Algorithm
21
REFERENCES
Yao Hanfang. Analysis of the role of e-commerce
development in promoting logistics economy. Modern
Business, 2022(11):47-49. DOI:10.14097/j.cnki.5392/
2022.11.048.
Huang Qiang. Analysis of the development situation of
express delivery industry and intelligent logistics.
Logistics Technology and Applications, 2017,
22(01):126-128.
Zhao Saijian. Current situation and countermeasures of
China's shipping logistics development in the
information era. Ship Materials and Markets,
2021,29(09):7-8. DOI:10.19727/j.cnki.cbwzysc.2021.
09.004.
Li Chengchen,Gao Peng. Analysis of the current situation
and operation mode of cross-border e-commerce
logistics under logistics development. China Storage
and Transportation, 2022(05):138-139.
DOI:10.16301/j.cnki.cn12-1204/f.2022.05.073.
China's express business volume is expected to reach 42.3
billion pieces this year. Transportation and Port and
Maritime, 2017,4(02):76.
Xu Zhaohui. Jinhua's annual express volume exceeds 10
billion pieces and ranks first in the country. Jinhua
Daily, 2021-11-18(A01). DOI:10.28413/n.cnki.njhrb.
2021.004425.
Li, Binshan. Research on the application of automatic
sorting system in express delivery industry. Journal of
Economic Research, 2013(31):43-44.
Le, J. E-commerce logistics and distribution development
strategy under the vision of big data. Business Watch,
2022(11):37-40.
Li Chunyu. Research on modern water transport logistics
management based on sustainable development.
Zhujiang Water Transport, 2022(07):29-31. DOI:
10.14125/j.cnki.zjsy.2022.07.002.
Huang Wenbo, Chen Zishuo. Current situation and
suggestions for the development of air logistics in
China. China Storage and Transportation, 2021(06):
82-83.DOI:10.16301/j.cnki.cn12-1204/f.2021.06.030.
Xu Jing. Research on the high-quality development of
modern logistics in the context of digital economy.
Business and Economic Research, 2022(08):115-117.
Yang Y. China becomes the engine of global express
development. Railway procurement and logistics,
2017,12(04):69.
Ding Guihua. Building an integrated global express hub to
promote the national strategy of Yangtze River Delta
integration. China Logistics and Purchasing,
2019(24):108-109. doi:10.16079/j.cnki.issn1671-
6663. 2019.24.070.
Yu Jiaxiang, Suo Xin, Wang Xun, Feng Junqing, Xiao
Kangyan, Kuang Zijun. Wuhan practice of multi-party
collaborative urban emergency logistics system
construction. Comprehensive Transport,
2022,44(04):111-115.
Li Ran, Huang Lina, Li Xin. The experience and inspiration
of global express giants in building logistics system--
Analysis of the latecomer advantages of China's
express logistics industry. Price Theory and Practice,
2021(11):75-78+197. DOI:10.19851/j.cnki.cn11-
1010/ f.2021.11.404.
Wang Ming, Lu Chengyun, Liu Wenhua. "New
requirements and patterns of logistics development in
the 14th Five-Year Plan. Journal of Beijing Jiaotong
University (Social Science Edition), 2022,21(01):11-
17. DOI:10.16797/j.cnki.11-5224/c.20220107.014.
ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation
22
