In the traditional logistics distribution network, the distribution mode of goods has been preset prior to entering the logistics network. The source and destination of any transport have experienced advanced planning, and the goods are passed layer by layer from the delivery point (DP), warehouse (WH), distribution center (DC), and terminal node to the consumers. However, the aid of PI data-driven, connectivity, depth of collaborative and efficient features can form a highly efficient logistics distribution model as shown in Figure 1. Each peer distribution between nodes is closely interconnected, and establishes a widely shared each other’s logistics network environment, and thus has many path selections, the real-time dynamic adjustment of the new key characteristics, and increases the distribution of various possibilities. It helps to explore more flexible distribution solutions to further reduce the waiting time and inventory cost of goods at each node. To explore the best logistics distribution method based on PI, the following three core factors namely PI infrastructure, distribution route, and transshipment standard are analyzed to effectively depict the urban logistics distribution model of PI.

(1) Infrastructure: The classical logistics network layout gave rise to the layout mode known as PI infrastructure layout. The introduction of PI does not change the geographical location of the original node facilities. The PI is a revolutionary logistics system that seeks to level the playing field for the logistics network’s traditional centralized hierarchical structure through hierarchy-based development. The biggest differences of PI with traditional layout are that all nodes are in the network facilities, transportation facilities, and service personnel. The global infrastructure of PI is based on the principles of maximum efficiency within reasonable use. To overcome the initial industrial hurdles, increase distribution efficiency, and reduce distribution costs, PI is incorporated into city logistics.

(2) Distribution route: When Montreuil [16] initially proposed the concept of PI, it was obvious that the complete path in the PI network could be transformed from private network to open network. Due to delivery lead times and transportation cost restrictions, the shortest route is typically considered to be the best distribution route in a traditional logistics network of distribution. However, if distance is the only criterion used to choose the order of goods in the logistics network, which is predetermined at the starting location, then there is a significant loss of flexibility in the logistics system. However, the transportation and distribution in the PI environment are more dynamic, and the flexible communication between warehouses and distribution centers at all levels gives a higher degree of freedom in route selection. PI considers the distribution distance and the use of network facilities with equal weightage, which helps to realize the uniform distribution of network traffic and improves the general satisfaction of customers.

(3) Transshipment standard: All goods in the PI network are uniformly packaged in standard intelligent green modular containers. Considering the negative impact of long-distance transportation on society and the environment, the ordered goods often need to go through multi-stage combined transportation in PI. In the process of transit at each transport node for the comparative test and research results of Pan et al. [19] and Yang [16] et al., it can be seen that the best effect is achieved by direct transfer with the source substitution method, which is based on an intuitive and simple standard. Instead of dividing delivery orders or recombining existing containers, PI selects vehicles that meet the transport capacity and are close enough to the transfer node for transferring the goods.

The urban logistics distribution scheme based on PI should be directly related to the construction layout and logistics level of the city in which it is located. The gap between the layout and logistics capacity of different cities affects the focus of urban logistics distribution decision-making. But regardless of where they are in the PI network. The city logistics distribution follows a set of standards, making it possible to view the city logistics distribution model as a whole at each shipping port, industrial center, and distribution center based on its PI essence. For the reasonable of all varieties of cargo and container transport distribution problems, the need to use the symbol definition comes down as follows:

Notations
$O$:	collection of dispatching points $o$,
$I$:	collection of logistics warehouse $i$,
$K$:	collection of distribution centers $k$,
$T$:	time of logistics distribution system represented by $n$ days,
$D{1}_{oi}$:	distance between the delivery point $o$and each logistics warehouse $i$,
$D{2}_{ik}$:	distance from each logistics warehouse $i$ to each distribution center $k$,
$({\mu }_0,u_0)$:	The shipment quantity at point$o$follows normal distribution$({\mu }_0,u)$,
$f_i, f_k$:	fixed cost of opening logistics warehouse $i$and distribution center $k$,
$h_i,h_k$:	daily unit inventory cost of logistics warehouse$i$and distribution center$k$,
$c_{oi}$:	unit transportation cost per kilometer upstream from point $o$to warehouse$i$,
$c_{ik}$:	unit transportation cost per kilometer downstream from warehouse$i$to distribution center $k$,
$L_{in}, L_{ik}$:	daily inventory of logistics warehouse $i$ and distribution center $k$,
$S_i^{max}$:	logistics warehouse $i$ storage capacity ceiling,
$U{P}_i$:	if the warehouse can be used normally, it is 1. If it cannot be used due to warehouse explosion or emergency, it is 0,
${\lambda }_i$:	if container $\pi$ does not arrive on time, its unit penalty cost is ${\lambda }_i$.
These are the following decision variables:
$z_{oin}$:	select warehouse $i$ to receive container $\pi$ sent by point $o$ on day $n$,
$z_{ikn}$:	select distribution centers $k$ to receive container $\pi$ sent by warehouse $i$on day $n$,
$q_{oin}$:	number of containers A transported from point $o$to warehouse$i$on day $n$,
$q_{ikn}$:	number of containers $\pi$transported from warehouse$i$to distribution center $k$on day $n$,

The research scope of the urban logistics distribution model based on PI is as follows: after arrival of the goods in a city, the whole level of process is covered from the point of delivery to the logistics warehouse and then to the basic distribution center. The fundamental goal is to minimize the total cost of logistics distribution as much as possible under the premise that accurate goods arrive on time. The proposed model needs to use the traditional logistics distribution model of facilities distribution and operation rules as the template to form its interconnectivity and offer a unique logistics distribution model. Since the composition of urban logistics distribution cost is complex and easily changeable with the characteristics of the city, fixed construction cost , inventory holding cost, transportation and distribution cost and lastly penalty cost can be given priority according to the importance of degree. The fixed construction cost$C_1$, inventory holding cost$C_2$, transportation, distribution cost $C_3$ and last penalty cost $C_4$ that can be given priority according to the importance of degree. The fixed construction cost $C_1$ given in (1) represents the construction cost of site selection, decoration, acquisition of fixed assets for all warehouses and distribution centers in PI city logistics distribution.

The inventory holding cost $C_2$ given in (2) is used to represent the cost of daily storage and guarantees the containers to be transferred for from each transport node to other transport node in PI.

Due to the influence of batch economy law, the unit inventory cost of the warehouse and distribution center should be different. The unit inventory cost of the warehouse is slightly lower than that of the distribution center. The transportation and distribution cost $C_3$ given in (3) is composed of the upstream transportation cost from the delivery point to the warehouse and the downstream transportation cost from the warehouse to the distribution center.

According to the actual logistics and distribution situation, the upstream and downstream transportation cost should also differ. By adding ${\mathrm{C}}_1,{\mathrm{C}}_2$ and ${\mathrm{C}}_3$, we get notation $\mathrm{C}$, which is called as penalty cost. The penalty cost $\mathrm{C}$ also includes the compensation loss cost $C_4$given in (4) caused by consumer complaints if ordered goods do not arrive on time that leads to the loss of invisible potential customers and damage to the company image.

Based on these settings, we present the following proposed PI based city logistics model:

The goal of objective function (5) is to reduce the logistics distribution costs in PI city, taking into account the fixed construction cost of the logistics warehouse and distribution center, the inventory holding cost of the logistics warehouse and distribution center, the full transportation and distribution cost, and the possible penalty cost associated with failing to satisfy customer demand. The constraints (6)-(8) are transport requirements of warehouses and distribution centers, or any transferred orders that cannot be split before arriving at the final destination. The use of the normal operation node as the transport destination helps to ensure that the logistics distribution model accurately reflects the current situation while also making it simple to avoid the logistics warehouse $\mathrm{U}{\mathrm{P}}_{\mathrm{i}}=0$ after incuring a lost function $\mathrm{i}$ in the system failure model. The constraint (9) indicates that the upper limit of the storage capacity of the logistics warehouse at a single time should not exceed${ S}_i^{max}$ is as follows:

The above difference condition (11) is between the accumulated inflow and outflow of $\pi$ containers in any warehouse to prevent the warehouse from exploding or the nearby path from blocking and interrupting due to overload of material flow during operation. The constraint (10) indicates that the number of $\pi$ containers to be distributed in the PI system must be an integer to meet the PI operation standard. The urban logistics distribution problem based on PI is a nonlinear optimization problem. It is difficult to determine an optimal solution directly. Therefore, this paper considers the branch and bound algorithm to obtain satisfactory solutions for decision variables and objective functions.

We compare the city logistics distribution model based on PI with the traditional logistics model. To make the comparision more effective, this paper takes Xi ‘an city as an example and sets the cover points, warehouse. distribution center logistics distribution network, compared with the traditional logistics model, the introduction of the PI based of maintaining the internal node location, for the network into the open feature of the Internet. The GIS module in the simulation software is used to determine the names and geographical locations of the above nodes as shown in Table 1. To accurately explore the performance discrepancies between PI and the traditional logistics model in the comparative test process using the traditional logistics model as the reference group, the number of goods delivered daily by PI and the traditional logistics model are consistent with the target locations of all goods. Each cargo has been defined as the target distribution center when the delivery point is generated, and $\pi$container is responsible for integrating the goods with the same destination and waiting for the corresponding truck to transport them. In a traditional logistics network, the circulation of goods or container needs to follow the route of man-made rules as shown in Figure 3. However, in the PI logistics model all fixed routes will be broken and $\pi$ smart labels on the container for the freedom of choice. The ability to dynamically adjust the goods will be shipped in a single container for adjacent nodes without interrupting all path to choose and form the best distribution route by free combination.

According to the findings about xi ‘an region logistics, the PI distribution system infrastructure construction fixed cost is 27381.13 USD, $\pi$container logistics warehouse inventory cost is 2.33 USD per day. In the distribution center level, inventory transportation lost focus size of dividends, so the $\mathsf{\pi }$ container inventory costs rise accordingly to the upstream of the 1.5 times about 3.56 USD per day. At the same time, the upstream (transportation between the delivery point and the warehouse) cost is 1.53 USD per km with a full load, and the downstream (transportation between the warehouse and the distribution center) cost is 2.19 USD per km with a full load. In addition, assume that the maximum total simulated time is T=100 days, the daily containerized quantity to be delivered at the delivery points A and B are respectively 100 pieces, the upper limit of the single transport quantity of the distribution vehicles is 20 pieces, and the random probability interval of daily abnormal use of each warehouse is [0.08,0.10]. As shown in Figure 4 and Figure 5, model operation and simulation are carried out on the hardware environment with Intel(R) Core(TM) I5-10210U CPU, 16G memory, and anylogic software. By taking the mean value of 10 simulation results and eliminating the interference of random factors, the total cost changes of the traditional logistics model and PI distribution model under different distribution rules are obtained.

(1) Comparative Analysis of Distribution models: With given computation, we receive the traditional logistics model and PI logistics model under the condition of the same infrastructure. The total cost of logistics distribution changes over time. From Figure 6 and Table 2, it is obvious that the PI logistics model continues to provide the cost advantages over the traditional logistics model in the simulation process, despite the fact that the PI logistics model’s simulation period is less than 20 days. The traditional logistics model and the PI logistics model have similar distribution costs; but, as time goes on, the cumulative logistics cost saved by the PI logistics model keeps growing, and the PI logistics model’s cost advantage progressively becomes apparent. The PI logistics model’s greatest saving value, which is 3147.60 USD on day 100, has an average daily saving rate of 3.96%. This demonstrates that when compared to traditional logistics networks, the PI logistics distribution network is open and interconnection performance can efficiently provide more distribution paths. Additionally, when the scale of local logistics service consumers reaches medium or above and is stable, the cost of the PI logistics distribution network is significantly lower than the cost of traditional logistics. In particular, the trend line of the logistics distribution model based on the PI is not steep, and the growth rate is comparatively stable. It is also difficult for an increase in freight volume to cause a rise in distribution costs. For every 200 containers deployed inside the system, the overall logistics cost rises by 493.82 USD on average. Additionally, because the internal infrastructure of PI serves all demanders in the form of public rental, common third-party logistics companies, and e-commerce activities are exempted from the cost of building basic logistics facilities, further lowering logistics distribution costs and raising customer satisfaction.

(2) The Core Factors Analysis: A surge in demand for logistics service providers and consumers has resulted from the gradual replacement of offline retail with online shopping. However, serious challenges have been brought about by “Shopping Day” blowing up and new crown outbreaks, which could cause transportation disruption on the elasticity of the logistics network. Experiments are carried out by gradually increasing the number of distribution centers from 8 to 12 with a step size of 1, while keeping the same parameters in Table 1 and Figure 3, in order to further investigate the impact of the scale of logistics infrastructure and emergency interruption events on the cost advantage of the logistics distribution model in PI cityFor simulation, the random outage chance for each warehouse was incrementally raised from 0.1 to 0.25 with a 0.125 step size. From Figure 7, it can be seen that the size of the logistics infrastructure for distribution has a positive promoting effect, lowering the total cost of the distribution center to give up the number of PI is higher at the end of the logistics distribution model of flexible selective, so the PI total cost of logistics and distribution center is roughly inversely proportional to the size number, with each increase in a distribution center the cost of distribution costing an average of about 99.12 USD. With the largest decrease in total cost 2029.22 USD, the cost optimization rate was 2.55%, only 48% of the PI logistics model improvement, and the visible PI cost optimization model was significantly higher than that of the traditional logistics model, the expansion of the scale of the distribution center also brought some distribution advantages for the traditional logistics model. It can be seen from Figure 8 (taking the mean value after 10 simulations) that when the random interruption probability of each warehouse increases, the logistics network risk, and uncertainty increase, and the total cost of PI logistics distribution shows an increasing trend. When the interruption probability increases from 0.10 to 0.25, the total cost increases from 76325.72 USD to 77035.30 USD, but the PI logistics model does not affect the optimization ability of the total cost. This is mainly reflected in that the cost difference value and cost difference rate of the PI logistics model and traditional logistics model continues to rise, especially in the interval of interruption probability [0.10,0.15] optimization increases significantly. Compared with the traditional logistics model, the total distribution cost savings of the PI logistics model is increased by 954.23 USD, and the savings rate is increased by 1.23%. Moreover, the saving rate is consistently higher than 5.00% when the outage probability is greater than 0.15, which shows that PI has good robustness to sudden logistics outage events, while the traditional logistics distribution model has to start emergency response when the interruption occurs and recover the distribution supply through manual allocation, which lacks good fault-tolerance. While comparing with the traditional logistics distribution model, comprehensive Figure 7 and Figure 8 show that the distribution of scale expansion and interrupt probability increases when the PI cost savings rate has a high level of the model, the maximum of 6.87% and 5.55% respectively. This further shows that the advantages of PI logistics model in the escalating scale of logistics infrastructure and emergencies that frequently occur are still preserved. The cost and elasticity advantages more magnified under large-scale and highly intrusive external conditions.