*4.4. Sensitivity Analysis on Coefficients*

After the above analysis, it can be seen that the model in this paper has a good effect on mitigating the path risk cost based on the assurance of service completion. Trade-off effects of service benefits and risk costs will be discussed in this part. In the model, the parameter *Mbenefit* determines the priority for the service, thus affecting service completion. When *Mrisk* has a fixed value, a larger *Mbenefit* makes the drone more inclined to satisfy more customers, and the drone will bear more risk costs and path lengths due to the overlap of customer locations and risk areas. On the contrary, a smaller *Mbenefit* means that the drone will ignore some customers but reach the destination directly with a shorter path and lower risk cost. As shown in Figure 12, service completion and average risk will increase with the increase of *Mbenefit*.

**Figure 12.** Sensitivity analysis of the parameter *Mbenefit* (*Mrisk* = 5).

Since *Mbenefit* is the coefficient of customer service benefit, its change had the most significant impact on service completion among the three indicators, which was 0.51 when *Mbenefit* = 0 and increased to 1 when *Mbenefit* = 2 with a growth ratio of 49%; while the average path length increased from 1.07 to 1.165 with a growth ratio of 8.87%; the average path risk increased from 1.385 to 1.832 with a growth ratio of 32.27%.

Average path length and average path risk increased much less than service completion. Due to the increase in *Mbenefit*, drones tend to complete more services, resulting in the drones needing to detour farther to reach the customer service area. The path risk also increased due to the overlap of customers and risk areas. However, since the minimisation objective in this paper's model includes path length and risk cost, this constraint ensures that the path length and risk cost remain stable when customer service completion increases rapidly. It can be found that our model achieves a flexible balance of service benefit with risk and path cost by adjusting *Mbenefit*.

Similar to parameter *Mbenefit*, *Mrisk* controls the drone's tolerance for risk. When *Mrisk* increases, drones are more inclined to avoid the risk zone to reduce path risk, which leads to a rapid decrease in the average risk. The average path risk decreases by 79.09%, with a 52.90% decrease from *Mrisk* = 0 to *Mrisk* = 10 and a 26.19% decrease from *Mrisk* = 11 to *Mrisk* <sup>=</sup> 20. Customer service completion remained at 100% when *Mrisk* <sup>≤</sup> 10. Due to the overlap between customer location and risk area, when *Mrisk* <sup>≥</sup> 11, the coefficient of risk cost was much higher than customer service benefit, drones tended to avoid risk instead of serving customers in the risk area, leading to a decrease in customer service completion rate, which decreased by 25% when *Mrisk* = 20.

With the increase of *Mrisk*, drones tend to move away from the risk area, leading to an increase in path length. Due to customer demand, the drone still needs to enter the customer area while avoiding the risk area, so the path length grows faster with an increase of 16.37% when *Mrisk* <sup>≤</sup> 10. In the stage of *Mrisk* <sup>=</sup> 11 to *Mrisk* <sup>=</sup> 20, the influence of the customer is significantly weaker than the risk area, which can be proved by the 25% drop in demand completion analysed above. A sufficiently large *Mrisk* value made the drone less likely to extend the detour distance, which can be demonstrated by the average risk value decreasing by 26.19% from *Mrisk* = 11 to *Mrisk* = 20, which is about 50% less than *Mrisk* = 0 to *Mrisk* = 10. The reasons mentioned above eventually led to a significant slowdown in the growth of drone path length, which increased by only 0.5% from *Mrisk* = 11 to *Mrisk* = 20. The results for the parameter *Mrisk* are shown in Figure 13.

**Figure 13.** Sensitivity analysis of the parameter *Mrisk* (*Mbenefit* = 0.5).

According to the analysis of the above results, it is evident that the adjustment of the coefficients *Mrisk* and *Mbenefit* changes the preference for risk and benefit in path planning, which leads to significant differences in the parameters of the planning results (average path length, service completion ratio, average risk cost). It also further demonstrates the importance of our proposed path planning approach that considers balancing risk cost and service benefit, which can reflect the process of completing customer service while avoiding risks in the actual operation of logistics drones.

Another critical parameter affecting drone paths in complex urban environments is the acceptable service range for customers. Due to the fact that customer locations often overlap with high risk cost areas such as buildings, pedestrians, and vehicles, part of the customer demand may be discarded if the acceptable service range decreases and the drone path needs to traverse more high-risk cost areas to complete the service. Therefore, we further analyse the impact of acceptable service range *R* on path planning results.

According to the results shown in Table 6, it can be seen that as the acceptable service range decreases, the overall service completion decreases significantly due to balancing the risk cost and service benefit, and the path risk cost will decrease due to ignoring some customers. The acceptable service range decreases from 200 m to 100 m, and the service completion decreases by 57.00%, while the average path risk cost only increases by 12.26%. This is because the reduction of the acceptable service range causes the drone needs to traverse more high-risk cost areas to complete the service, which is detrimental to the goal of balancing risk cost and service benefit, so the drone discards part of the customer requirement. When *R* = 150m, only the service to Customer 2 was dropped due to balancing risk cost and service benefit, so service completion decreased. However, providing service to Customers 4, 5, and 6 leads to a 5.97% increase in risk cost due to the reduction in the acceptable service range.

**Table 6.** Sensitivity analysis of the parameter *R*.


The variation of completion degree in customer demand shows that the reduction of the acceptable service range does not affect the completion degree for Customers 1 and 3, which do not overlap with the high-risk cost area. Meanwhile, Customers 2, 4, 5, and 6, which overlap with high-risk cost areas, were not served. The comparative experimental results of adjusting the risk cost preference parameter *Mrisk* also demonstrate that the purpose of discarding some customer demands is to balance the service benefits and risk costs. For the case that the acceptable service range was 100 m, the drone path accepted a higher risk cost when *Mrisk* = 5; thus, Customers 4, 5, and 6 that were not served at *Mrisk* = 20 could be served, and the service completion was improved to 90%. While path risk costs increased by 83.06% due to serving customers whose acceptable service ranges overlap with high risk cost areas.

In summary, it is important to improve the acceptable service range of customers for logistics drone risk management. Logistics drone companies also need to adjust the risk cost and service benefit preferences according to the acceptable service range and customers' location in order to ensure service quality.
