Exploring The Discrete Mathematical Models of Express Logistics Networks

ZHANG Mingjun; ZHANG Yujing; YANG Jianqing; YAO Bing

doi:10.11999/JEIT240767

Volume 47 Issue 3

Mar. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(3): 769-779

ZHANG Mingjun, ZHANG Yujing, YANG Jianqing, YAO Bing. Exploring The Discrete Mathematical Models of Express Logistics Networks[J]. Journal of Electronics & Information Technology, 2025, 47(3): 769-779. doi: 10.11999/JEIT240767

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ZHANG Mingjun, ZHANG Yujing, YANG Jianqing, YAO Bing. Exploring The Discrete Mathematical Models of Express Logistics Networks[J]. Journal of Electronics & Information Technology, 2025, 47(3): 769-779. doi: 10.11999/JEIT240767

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Exploring The Discrete Mathematical Models of Express Logistics Networks

doi: 10.11999/JEIT240767

1.
School of Information Engineering and Artificial Intelligence, Lanzhou University of Finance and Economics, Lanzhou 730020, China
2.
Gansu Provincial Key Laboratory of Smart Commerce, Lanzhou 730020, China
3.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (61363060, 61662066), Lanzhou University of Finance and Economics Research Funding Programme (Lzufe2022B-002), The Natural Science Foundation of Gansu Province (23JRRA1785, 25JRRA232)

Received Date: 2024-09-09
Rev Recd Date: 2025-02-19

Available Online: 2025-03-05

Publish Date: 2025-03-10

Abstract

Abstract

Objective With the rapid growth of e-commerce, express delivery volumes have surged, placing increased demands on existing logistics infrastructure and operational models. An efficient express logistics network can help reduce costs, improve transportation efficiency, and enhance logistics management. Therefore, analyzing the structure and operation of express logistics networks, as well as identifying ways to optimize these networks, has become a critical focus for logistics companies. The goal is to improve operational efficiency and support balanced regional economic development. Current research on express logistics networks involves constructing various models, such as mathematical optimization models, decision models, and network evaluation models, and applying algorithms like heuristic, genetic, and greedy algorithms, as well as those based on complex network theory, to optimize network structure, performance, and planning decisions. However, a limitation of existing studies is the lack of models closely aligned with the practical realities of express logistics, and the absence of effective new algorithms to address the complex, evolving challenges faced by express logistics networks. This study proposes a novel discrete mathematical model, also known as a topology model, for express logistics networks from the perspective of graph theory. The model comprises a road network (physical network), a topology network (mathematical model), and an information network (soft control system), providing a closer alignment with real-world express logistics scenarios. Through both qualitative and quantitative analyses of the model, along with the design of corresponding optimization algorithms, this research offers a reference for the in-depth study and scientific optimization of express logistics networks. Methods This study employs various methods: (1) Mathematical Model Construction: A new discrete mathematical model for express logistics networks is developed, accounting for the nonlinear, stochastic, and discrete characteristics of the network. The model integrates physical, topological, and informational networks. (2) Qualitative Analysis: The topology model of the express logistics network is qualitatively analyzed using graph theory concepts and algorithms, where the network topology model is represented as a weighted structure in graph theory. (3) Quantitative Analysis: The mathematical model is analyzed quantitatively using statistical parameters, optimization algorithms, and other mathematical techniques. The edges in the topological model are assigned route length weights, and new optimization algorithms—such as the distribution algorithm, control set algorithm, and pre-designated subgraph algorithm—are proposed to optimize the express logistics network topology. (4) Case Study and Optimization: The topology model is applied to the express logistics network in the central district of Lanzhou City (Chengguan District), where corresponding optimization algorithms are implemented. Solutions to challenges, such as the computational complexity of the model, are proposed. Results and Discussions The mathematical model in this study is a topological graph based on graph theory, where various matrices are used to input the express logistics network’s topology into the computer for subsequent calculations. Innovation 1: A topological model of the express logistics network is created. Innovation 2: The topological model of the express logistics network is optimized and quantitatively analyzed, and a minimum weight path m-control set algorithm (m ≥ 2) and a pre-designated subgraph control algorithm are developed(Algorithm 3, Algorithm 4). These models and algorithms are then applied to the study of the express logistics network in the Chengguan District of Lanzhou City. Innovation 3: In response to the large-scale data and the limitations in computer computing power, as well as the absence of a super-large computer at the author’s institution, the large-scale matrix calculation is divided into smaller regional matrices for optimized computation. Innovation 4: Different optimization algorithms are selected for different areas of the road network map of Lanzhou City’s Chengguan District (Fig. 4, Fig. 5). Multiple calculation results are integrated to obtain the minimum weight path of the pre-designated subgraph for the Chengguan District, validating the effectiveness of the model and algorithms. Conclusions This study addresses existing issues in express logistics network research through the aforementioned work and innovations. A new model and new algorithms, better suited to practical logistics scenarios, are developed. Based on the case study, new problems and methods are proposed, offering further possibilities for optimizing express logistics networks. With the rapid development of emerging technologies such as the Internet of Things, big data, and artificial intelligence, future research could focus on deeply integrating these technologies to enable real-time and accurate collection and analysis of logistics data. Access to high-quality and diverse data can further improve the accuracy of the model’s calculations and enhance intelligent decision-making capabilities. This study has only considered assigning route length weights to the edges in the topological model; future work may explore multi-objective, multi-weight optimization models for express logistics networks to meet the practical decision-making needs of different logistics service providers.
- Express logistics networks,
- Topological model,
- Optimization algorithm,
- Computation complexity,
- Weighted graph

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