Transport has long been considered a concern for rural residents around the world, under the topic of rural transport [1], rural mobility [2], rural accessibility [3], etc. Researchers have found that transport, especially public transport, strongly influences the economy and livability of a region. In the U.S., the American Public Transportation Association reported that transport services are seriously lacking in many rural areas, which is a key concern for rural residents’ well-being [4]. In New Zealand, the Public Transport 2045 study was commissioned, finding that public transport services are important in any scenario, including rural transport, and will need to become more flexible, more frequent, and more responsive to travelers’ needs [5]. In Cambodia, Lao’s Republic, and the Philippines, transport needs of rural people are associated with basic needs such as water, food, and firewood, social welfare aspects of rural life such as health and education, and with economic aspects of rural life such as agriculture, livestock, and home industries ^[6][6]. This paper focuses on rural express logistics, which is one of the topics under rural transport, aiming at expanding express service coverage while considering plan feasibility.

Rural e-commerce turns out to be a new economic growth point in China. Rural online retail sales reached CNY 2.05 million in 2021, with an increase of 11.3% over the previous year, and is more than twice as much as that of 2016. The rapid growth of rural e-commerce is supported by an express network, which is promoted by the government as a kind of “new infrastructure”. According to the government plan, the rural express service network should reach all administrative villages by 2025, and it is suggested that logistic centers are built in every town.

Although rural e-commerce has made great progress in China, the last-mile delivery has become an obstacle and bottleneck of rural ecommerce and economic development. One of the key problems in enhancing last-mile express delivery service in rural areas is how to properly place logistics centers, which carry out logistics activities (e.g., transportation, forwarding, distribution of goods, etc.). Compared with urban areas, the rural areas have a relatively low population scattered in a wide area, which significantly increases last-mile logistics costs. Most rural areas, especially in West China such as Tibet, suffer from great challenges in operating rural logistic centers. Some rural logistic centers used to charge extra high fees for delivery but stopped doing so under the pressure of superior local departments. As a result, most end-to-end logistic enterprises stop at counties or towns, providing no service for villagers. These problems lead to a low service level of last-mile delivery, as well as reduction in rural e-commerce users’ enthusiasm.

2. Rural Logistics

Existing research on rural logistics mostly stays at the qualitative level, putting forward general suggestions and introducing new logistic modes. Brovarone and Cotella proposed a multitiered policy system, recommending demand responsive services [7]. Fu and Li proposed to guide rural residents to change their transaction patterns and consumption habits [8]. Jin called for the integration of joint distribution resources [9]. Wang and Chen emphasized the influence of resident factors on urban–rural distribution [10]. Li suggested that run-resistant vehicles should be used to improve service [11]. As for rural e-commerce logistics, Song suggested adopting the joint distribution mode, setting up rural e-commerce logistic centers [12]. Jin proposed to adopt the “X + 1” rural e-commerce business model [9]. Wang and Chen suggested the establishment of a rural logistics distribution alliance to build branches [10]. Xie and Zhou introduced an agreement between Chongqing government and Cainiao to build rural logistics network and to achieve coverage goals [13]. Joint distribution and crowdsourcing are recommended to improve service levels. In recent years, researchers began to use the cost optimization model to study rural logistics and explore issues such as route design and distribution mode. Ren and Shi applied the milkrun model in urban–rural distribution route design [14]. Jiang established an optimization model to pursue the lowest total system cost (including customer time penalty cost) for joint distribution center locating and vehicle routing [15]. Liu designed three codistribution modes for distribution enterprises, recommending alliance operation mode, and gave a route calculation method for cargo mixed vehicles considering customer satisfaction [16]. Xiahou constructed a multiobjective and multicenter vehicle routing optimization model [17]. Wang and Zhou proposed an optimization strategy of multicenter joint distribution alliance based on vehicle sharing [18].

3. Facility Location Problems

Proper placement of rural logistic facilities plays an important role in improving distribution efficiency and lowering cost, which in general falls into the facility location problem. The facility location problem is a widely discussed topic in transportation and logistics ^[19][20][19,20] and involves the selection of specific locations of ^[21][22][23][21,22,23]: warehouses, distribution centers, transportation hubs, passenger and cargo terminals, etc. The location problem is one of the classical problems in operational research and has been extensively studied in the literature [24]. Study of the location problem began in 1909, when Alfred Weber described a 1-median problem (the famous Weber problem) in Euclidean space in order to decide how to locate a single warehouse [25]. So far, three basic types of location problems have been put forward, including the P-median problem (PMP), P-center problem (PCP), and covering problem (CP).

(1)

PMP is a “MinSum” problem, which aims to select P facilities from a given set to serve all demand points while minimizing the total weighted distance from demand points to their nearest facilities [26]. PMP is proven to be a NP-hard problem [27]. Both heuristic and optimal algorithms are provided [28]. PMP is still a research hotspot, with various extensions studied by modern researchers, including capacitated PMP [29], simplified PMP [30], and uncertain PMP [31].

(2)

PCP is a “MinMax” problem, which aims to select P facilities from a given set to serve all demand points while minimizing the maximal distance from any demand point to its nearest facility [26]. PCP is proven a NP-hard problem as well, with heuristic and optimal algorithms provided [32].

(3)

CP, including set covering problem (SCP) and maximal covering problem (MCP), introduces the constraint of service radius, which means a facility cannot serve a demand point beyond a given distance. First raised by Toregas, SCP is a “Min” problem, aiming to serve all demand points with as few facilities as possible [33]. MCP is a “Max” problem, aiming to serve as many demand points as possible with a given number of facilities, and was first proposed by Church and ReVelle [34]. The problem is further discussed by Daskin, Hogan, Berman, Krass, and many other researchers ^[35][36][37][35,36,37].

In recent years, the maximal covering problem (MCP) and maximal covering model (MCM) have been widely applied in describing and solving location problems. Yu proposed the capacitated reliable fixed-charge location problem and provided solving algorithms [24]. Tian used the flow capture location model to solve the charging pile point layout problem, which is essentially a flow-based maximal covering problem [38]. Li, Sylvia, and Xue also took advantage of MCM ^[11][39][40][11,39,40].

(4)

In addition to the above methods, a number of other locating methods have emerged in recent studies, considering facility capacity, road capacity, dynamic decision process, competitive situation, and many other factors. Kulakova described a locating model based on geographic coordinates [41]. Muravev used the Dematel–Marica method and applied the multicriteria decision model to locate China Railway Express International Logistics Centers [42]. Stienen developed a single deterministic optimization model for locating disaster relief warehouses [43]. Rabe combined the system dynamics simulation model with the multicycle capacity-limited facility locating problem to locate automated parcel lockers [44].