Supply chain resource scheduling optimization of e-commerce enterprises in international trade based on mobile edge computing

Supply chain network optimisation

The reasonable arrangement of CBESCN can enhance its reliability. In the node scale design of a supply chain network, Toro, Franco & Echeverri (2017) constructed a partition integer programming model considering inventory cost, drop shipment cost and equipment location cost, and determined the optimal quantity and location of warehouses and the optimal inventory strategy of warehouses and retailers. Moghaddam Kamran (2015) proposed a mixed integer linear programming model for designing on and reverse-flow supply chain networks. They verified the model’s feasibility through the European supply chain case.

In putting forward the optimisation goal, fuzzy optimisation, robust optimisation, topological network theory and system engineering are used to study some optimisation problems of CBESCN. Liu & Li (2020) took cross-border electronic commerce as the background. The research method discusses how to develop a set of corresponding technologies and methods under the blockchain background to achieve the traceability of products and transactions in supply chain management. Regarding material storage and distribution, especially for inventory control, which still needs to be optimised to minimise costs while maintaining high customer satisfaction, Yu, Hou & Li (2019) applies the basic ideas of the ant colony algorithm and fuzzy model to the supply chain inventory optimisation model. Yan, Zhou & Li (2021) pointed out that due to problems, such as explosive growth trends and high transportation costs in cross-border electronic commerce, it is urgent to study the supply chain from the perspectives of decision-making and coordination.

In the existing research on the joint optimisation of resource allocation and computing and unloading, the main consideration is the scenario of complete unloading. There are few types of research on partial unloading and resource joint optimisation; significantly, when the number of users increases, the number of computing increases, and the computing capacity of edge servers is limited. How to optimise the amount of computing data for unloading is the leading research content of this work.

MEC

Much attention has been paid to improving the overall performance of the MEC system by offloading computation and jointly optimising various resources (Dai, Liu & Guo, 2019; Mukherjee et al., 2019; Jošilo & Dán, 2019; Eshraghi & Liang, 2019; Zhu, Chen & Chen, 2019). Dai, Liu & Guo (2019) built a layered edge cloud computing architecture for a scenario with a large amount of computing. Taking energy consumption of terminal equipment and task execution delay as optimisation objectives, a centralised computing unloading method based on the Lagrange multiplier method and an optimal resource allocation mechanism was proposed for mobile edge nodes. The computing and communication resources among multiple edge servers and between edge servers and cloud servers are jointly optimised. Quadratic programming with quadratic constraints obtains an approximate solution to ensure task delay (Mukherjee et al., 2019). Jošilo & Dán (2019) based on the Stackelberg game model, analysed how mobile devices used operators’ communication and computing resources independently and proposed a decentralised approximate computing unloading decision algorithm to minimise the task completion time of mobile terminal devices. Because the computing requirements are not fully known before the task is executed, Eshraghi & Liang (2019) proposed a method to jointly optimise the unloading decision to minimise the weighted sum of the average cost and cost changes. Zhu, Chen & Chen (2019) proposed a joint unloading decision and resource allocation algorithm based on deep learning, which comprehensively considered the optimisation of unloading decision, local CPU, bandwidth and external CPU occupancy to reduce task delay and equipment energy consumption. Gao, Zhang & Yu (2022) proposed a system overhead minimisation model for ultra-dense network scenarios, combining the unloading strategy, channel allocation and power allocation. Partial unloading can upload some tasks to the edge server for calculation under limited bandwidth and effectively use the computing resources of mobile devices and servers in parallel (Bozorgchenani, Tarchi & Corazza, 2018). Bi & Zhang (2018) studied the maximisation of the weighted sum computing rate in multi-user wireless edge computing networks with a binary computing offload strategy.

The scenario of complete offloading is mainly considered in the existing research on joint optimisation of resource allocation and computing offloading. In contrast, the research on joint optimisation of partial offloading and resources is less, especially on optimising the offloaded computing data when the number of users increases and the computing capacity of the edge server is limited.

Model construction

Consider a typical CBESCN spanning two different countries or regions, in which the network boundary is the supply chain transportation route, and the nodes are suppliers, warehouses, cross-border checkpoints, manufacturing plants and end customers in the logistics transportation route, as shown in Fig. 1.

Since the cross-border inspection point is located downstream of CBESCN, the warehouse delivery process should be emphasised. If unique warehouse picking and distribution operations are arranged to adapt to any particular situation, the chance of delay can be significantly reduced. Secondly, at the cross-border inspection point, the delivery of goods requires cross-border inspection procedures, including product inspection and verification of delivery documents. Diversifying the cross-border inspection process will lead to longer and longer transportation time and higher transportation costs. Given this, reducing the barrier effect of the cross-border supply chain that the delivered products meet the inspection is a fundamental rule.

This article constructs a resource scheduling model of the supply chain of e-commerce enterprises in international trade.

The objective function K1 represents the total cost in CBESCN. It consists of four parts: the total cost of all services in the supply chain, including conventional and other logistics services that are different from other logistics models. The second part is the time delay cost caused by the delay of the previous process due to the enterprise service process. The third part, the last process, is compressed by the enterprise service process, which leads to the time compression cost of the next process. The fourth part is the cost of sorting and packaging in overseas warehouses C₀. In objective function K1, the delay of the previous process due to the enterprise service process leads to the time delay cost of the next process, which is realised in different cross-border enterprises. It can be expressed as

Total cost = Normal service cost + Delayed service cost + Compressing service cost + C₀ (1)${\displaystyle \begin{array}{cc}{K}_1=\hfill & \sum _{\mathrm{m}=1}\sum _{\mathrm{n}=1}\left(C_{\mathrm{mn}}{T}_{\mathrm{mn}}+C_{\mathrm{mn}}^{{}^{\prime }}\left|T_{\mathrm{mn}}^{{}^{\prime }}\right|\right)+\sum _{\mathrm{m}=1}\left(T_{\mathrm{mn}}+T_{\mathrm{mn}}^{{}^{\prime }}-{\mathrm{t}}_{\mathrm{m}}\right)X_{\mathrm{m}}^{{}^{\prime }}\hfill \\ \hfill & +\sum _{\mathrm{m}=1}\left({\mathrm{t}}_{\mathrm{m}}-T_{\mathrm{mn}}-T_{\mathrm{mn}}^{{}^{\prime }}\right)Y_{\mathrm{m}}^{{}^{\prime }}+C_0.\hfill \end{array}}$

The objective function K2, which consists of three parts, indicates that all logistics service orders in CBESCN should be completed as soon as possible. This article considers minimising the difference between expected and normal service time, extra service time and total time. That is, the expression is:

Time = expected service time - normal service time - extra service time + T₀ (2)${\displaystyle K_2=\sum \left({\mathrm{t}}_{\mathrm{m}}-T_{\mathrm{mn}}-T_{\mathrm{mn}}^{{}^{\prime }}\right)+{\mathrm{T}}_0.}$

The objective function K3 indicates that the weighted satisfaction of all service provider enterprises can be maximised in the CBESCN. It consists of two parts: the first refers to the ratio of regular service cost to all average total costs generated by all service provider enterprises, representing satisfaction with the price. The other part is satisfied with service time. The second one is related to time, which refers to the ratio of the average operation time of service provider enterprises to the sum of standard time and extra time. (3)${\displaystyle K_3=\sum _{m=1}\sum _{n=1}\frac{T_{\mathrm{mn}}{C}_{\mathrm{mn}}}{T_{\mathrm{mn}}{C}_{\mathrm{mn}}+C_{mn}^{{}^{\prime }}\left|T_{\mathrm{mn}}^{{}^{\prime }}\right|}\left(\frac{T_{\mathrm{mn}}}{T_{\mathrm{mn}}+T_{\mathrm{mn}}^{{}^{\prime }}}\right){\mathrm{a}}_{\mathrm{mn}}.}$

Regarding constraints, the m-th service process can sustain the upper limit of time compression. This is a strong constraint because it is necessary to ensure a continuous running time link of the supply chain in the process of providing imported logistics services. (4)${\displaystyle {\mathrm{t}}_{\mathrm{m}}-T_{\mathrm{mn}}-T_{\mathrm{mn}}^{{}^{\prime }}\le T_{\mathrm{m}+1}^{{}^{\prime }}.}$

The second constraint is that CBE service integrators put forward the completion time requirements for service orders of corresponding service provider enterprises. (5)${\displaystyle T_{\mathrm{mn}}+T_{\mathrm{mn}}^{{}^{\prime }}\le {\mathrm{t}}_{\mathrm{m}}+{\mathrm{b}}_{\mathrm{m}}Q{\mathrm{t}}_{\mathrm{m}}.}$

The third constraint is to ensure the satisfaction of each service provider enterprise, which must be higher than their acceptable lower limit. (6)${\displaystyle \frac{T_{\mathrm{mn}}{C}_{\mathrm{mn}}}{T_{\mathrm{mn}}{C}_{\mathrm{mn}}+C_{mn}^{{}^{\prime }}\mid T_{\mathrm{mn}}^{{}^{\prime }}}\left(\frac{T_{\mathrm{mn}}}{T_{\mathrm{mn}}+T_{\mathrm{mn}}^{{}^{\prime }}}\right)\ge S_{\mathrm{mn}}^{{}^{\prime }}.}$

In terms of time, cross-border e-commerce logistics service integrators tend to follow customised time requirements and set corresponding requirements related to order completion time for service providers. The satisfaction of each service provider will directly determine the quality of the order and the likelihood of completion.

Model solving

This article selects the linear weighting method to solve the CBE time scheduling optimisation model, and the above model is transformed into a single objective programming problem. The linear weighting method can make the interaction of each evaluation index get linear compensation and ensure the fairness of the comprehensive evaluation index. Firstly, the data is imported, then the multiple linear regression is carried out on the data, and the regression is carried out on all variables. The stepwise regression can also be used for factor screening, and the model after the preferred factor can be obtained and the objective function is finally solved.

In this article, the cost adjustment factor d is introduced into the model, which represents the relationship of cost increase in this case. d > 1 to express the limit of cost increase. Because I set a new constraint, the original time scheduling optimisation model becomes a goal-planning problem about time and satisfaction. (7)${\displaystyle K_1<K_1^{min}\ast \mathrm{d}.}$

The model constructed in this article has three objective functions and four constraints. We combine the specific problems and make a choice analysis, which will help solve the problems and improve efficiency. We introduce V₂ and V₃, and make them add up to 1. Objective function K₂ And objective function K₃ respectively means that the service order is completed on time as much as possible, and the satisfaction of the service provider is maximised. This article needs to standardise them. Therefore, K₂ and K₃ Divide by the maximum possible value and subtract from the corresponding results. t the comprehensive objective function K can be obtained as follows: (8)${\displaystyle K=V_3\frac{K_3}{m{K}_3}-{\mathrm{V}}_2\frac{K_2}{m{K}_2}.}$

Problem description

MEC is used to optimise the solution process proposed in ‘Resource scheduling model of CBESCN in international trade’ to improve the efficiency of node calculation. It is assumed that the MEC system knows relevant information such as channel gain, calculated data volume, calculated energy consumption, etc., to determine the amount of data unloaded by each user and the allocated channels and computing resources, thereby reducing the calculation delay and energy consumption of users.

Each supply chain node k contains a computation-intensive task with limited delay to complete, and the maximum delay of the task is $T_k^{max}$, the maximum energy consumption is $E_k^{max}$, the data size of the task is S_k. The CPU cycle required to compute each bit on the client side is C_k . When users k When the computing power of cannot meet the requirements of task delay or energy consumption, all or part of the task can be unloaded to the edge server of the base station, and the unloading ratio is λ_k ∈ [0, 1] . Therefore, the time that the task runs locally is $t_k^{\text{local}}$, expressed as (9)${\displaystyle t_k^{\text{local}}=\left(1-{\lambda }_k\right)S_k{C}_k/f_k^0}$ where $f_k^0$ represents the computing power of user k.

The energy consumption per CPU cycle of node k is $e_k^0$. When some tasks are executed locally, the energy consumption is (10)${\displaystyle e_k^{\text{local}}=\left(1-{\lambda }_k\right)S_k{C}_k{e}_k^0.}$

The user unloads a part of the task to the edge server, downloads the calculation results from the edge server, and calculates the remaining tasks at the same time. Because the calculation result is very small, the download time of the calculation result is not considered. Task execution time only considers unloading task upload time $t_k^{\text{off}}$, edge server execution time $t_k^{svv}$ and the local execution time of the remaining tasks $t_k^{\text{local}}$. Because of the parallelism of local computing and edge server computing, the total computing time to complete the task is $t_k^{\text{total}}$, expressed as: (11)${\displaystyle t_k^{\text{total}}=m\left(t_k^{\text{local}},t_k^{\text{off}}+t_k^{svv}\right).}$

Multi-user partial unloading with resource allocation under time delay and energy consumption constraints in MEC is considered as an optimisation problem, which is to minimise the total delay of task completion. The goal of problem optimisation is expressed as: (12)${\displaystyle \underset{\lambda ,\delta ,p}{min}\sum _{\mathrm{k}=1}^{N}m\left(\frac{\left(1-{\lambda }_k\right){\mathrm{S}}_k{C}_k}{f_k^0},m\left(\frac{S_k^{i,off}}{r_k^i}\right)+\frac{{\lambda }_k{S}_k{C}^{svv}}{f_k^{svv}}\right)}$

Partial computation unloading

The optimisation goal of the system is to minimise the total delay in task completion. As can be seen from Formula (12), this optimisation problem mainly involves the unloading ratio and system resource allocation (Li, Li & Zhou, 2021). Therefore, this article decomposes the optimisation problem into two aspects: unloading ratio setting and resource allocation. Firstly, according to each user’s time delay and energy consumption limit, an initial unloading ratio is given, then a low-complexity joint allocation strategy of channel and server computing resources is proposed. Finally, the unloading ratio is updated according to the currently available resources.

Firstly, the computing resources are initially allocated according to the following delay constraints: on the one hand, the unloading delay of some data must not exceed the local computing delay, that is, $t_k^{off}<t_k^{\text{local}}$; On the other hand, the calculation delay of the whole task shall not exceed the total delay limit, that is $t_k^{\text{total}}<T_k^{max}$ . The second allocation of computing resources is the allocation of the remaining available computing units, where the user’s computing rate difference is defined here as the objective function σ, that is, a computing resource is allocated to user k, and the computing rate difference before and after the computing resource is allocated is expressed as (13)${\displaystyle \sigma =\frac{S_k}{t_k^{\text{local}}+t_k^{off}+t_k^{svv+1}}-\frac{S_k}{t_k^{\text{local}}+t_k^{off}+t_k^{svv}}}$

where $t_k^{sv+1}$ is the computing time of the server after the server assigns a new cell to the user. Comparing the calculation rate difference between each user before and after obtaining the calculation unit, and assigning a calculation unit to the user who can gain the greatest benefit by adding the calculation resources for the user so that k^∗ = argmax(σ).

After completing the initial allocation of resources for each supply chain node, the system determines the available computing resources of the edge server. It updates the user’s unloading ratio so that more computing tasks of mobile users are unloaded to the edge server for execution, and the computing delay is reduced. When the calculation time of the local task and partial unloading calculation time is balanced, the delay reaches the minimum. The user’s updated unloading ratio can be obtained from Eq. (13). (14)${\displaystyle {\lambda }_k=\left(\frac{S_k}{f_k^0}-m\left(\frac{S_k^{i,\text{off}}}{r_k^i}\right)\right)/S_k\left(\frac{1}{f_k^{sv}}+\frac{1}{f_k^0}\right).}$

Because the computing resources are dynamically changing when Eq. (14) is less than 0, it means that the resource conditions cannot meet the task requirements, and the unloading ratio is 0; When Eq. (14) is greater than 1, it means that the resources are sufficient to completely unload the task execution, and the unloading ratio is 1.

experimental settings

Take the optimisation of the CBESCN location of a CBE enterprise as an example to analyse. To meet the decentralised needs of consumers and reduce the logistics cost of the whole cross-border supply chain, the optimisation of terminal distribution path selection from network nodes such as overseas warehouses to demanders is also a common decision variable in the location scheme. MEC simulation scenario considers a base station and multiple nodes, and the base station deploys edge servers. The radius of the coverage area of the base station is 500 m, and the supply chain nodes are randomly distributed in this area.

Total time solution for service providers

Assuming that the recombinant inbred lines are 200 and the genetic algebra is 300 when the time adjustment coefficient is Q = 1 and the cost adjustment coefficient is d = 1.15, the calculation result of the objective function K is equal to 0.6612. The time parameters of each service provider in each service process are shown in Fig. 2.

From the results of an example, in completing the CBESCN, among the 15 service provider enterprises, six completed time-compressed orders and nine completed time-delayed orders. It shows that when different functional service providers face service orders, CBE service integrators will delay or compress the service time in different service processes, although the compressed time will be more responsive to customer needs.

Figure 3 shows the range of the K value. With the cost adjustment coefficient increase, K also increases, which is stable at 0.6710. It means that when the cost adjustment coefficient of CBE service integrators increases, the comprehensive level of CBESCN is also improved.

The above analysis and comparison show that the time adjustment coefficient of the CBE service integrator can be divided into two stages. When the time is compressed to the time delay, the comprehensive level of CBESCN increases with the increase of the time adjustment coefficient. However, after reaching a specific value, the comprehensive level of CbesCN will be stable, and the effect will be relatively apparent. Both the time delay strategy and the cost adjustment strategy can somewhat improve the comprehensive capability of CBESCN. However, the former works better.

MEC optimisation results

The proposed method is simulated by Python and compared with local computing, complete and binary unloading (Bi & Zhang, 2018). Local computing means that all computing tasks are performed on the mobile terminal. Full uninstall means all computing tasks are uninstalled to the edge server for execution. Binary unloading refers to choosing a local computing or unloading mode by comparing local computing and unloading computing rates.

The influence of the number of nodes on the total delay is shown in Fig. 4.

Because all tasks of local computing run on user terminals, the total delay increases linearly with the number of users. Complete unloading and unloading all tasks to the server for calculation. The delay of the server is lower when the number of stages is small. The computing resources allocated to each node decrease when the number of nodes increases. The total delay increases faster than when the number of nodes is small, but it is still lower than the local calculation. The adopted method is partial unloading. When the number of nodes is large, the competition for supply chain resources increases and the computing pressure of the server increases. Rational use of server resource allocation to optimise the number of task unloading can maximise the use of server computing resources, thus reducing the time delay of task completion.

The influence of server computing power on the average delay of nodes is shown in Fig. 5.

Because local computing has nothing to do with the server, the average delay remains unchanged. The time delay of the complete uninstall method is only affected by network transmission and server computing power. With the increase in server computing power, the average time delay of users decreases significantly. In binary unloading, with the improvement of server computing power, the average delay of the system shows a slow decline trend. With the increasing capacity of the server, due to the limitation of network resources, the time delay gradually approaches the complete unloading mode. In this method, some tasks are transmitted to the server, and the user terminal and the server execute in parallel. Because the allocation of server computing resources is considered, the average delay of this method is low. When the server’s computing power reaches a certain level, the impact on the average delay of users mainly comes from network transmission.