## 4 Case Study
### Sensitivity Analysis  
The study model is different from the traditional vehicle routing problem. The total delay penalty and the early penalty amounts are introduced to the study by taking customer dissatisfaction and the total missed time window into account. To understand the impact of the total route distance, time window penalty amount, and total company profit, the study conducted a sensitivity analysis on different weighted parameters. The study found that the premise of the weighted penalty of missing the expected time window is confirmed; the profit will decrease when the minimum route weight increases. At the same time, the total missed time window will decrease. However, the decreasing level of profit is obviously much greater than the missed time window. When the logistics service providers require the shortest route, they will only receive new requests that are near the logistic center, which further limits the request selection amount and results in a decrease in profit. Furthermore, the unmanned vehicle will not often miss the customer's expected time window due to the decreasing requests; therefore, missed time windows will also decrease (shown in Figure 6). Figure 7 shows the impact of changing the weight of missing time windows on the profit and total route distance under the premise of a fixed shortest route weight. Noticeably, we can see the revenue decrease along with the increase in the weight of missed time windows. The reason for this is that under the premise of the company requiring fewer missed time windows, the number of requests that can be accepted is reduced, thus the profit decrease. There is no fixed changing trend for the shortest route distance; it continuously decreases with the fluctuations, along with the increasing weight of missed time windows. The reason for this is that the time window of the request around the logistics center does not have a fixed changing trend; the shorter the traveling distance, however, the less likely it will miss the time window; thus, the shortest route distance will constantly fluctuate. Figure 8 shows the impact of changing the weight of missed time windows on the profit and total route distance under the premise of fixed profit. Noticeably, we can see that the profit and total route distance increase along with the increased missed time window weight. The reason for this is that we can only try to reduce the total route distance and maximize the profit, while the weight of missed time windows constantly increases. In the end, once the profit and total route distance are stable, the approximate optimal solution has been found (maximum revenue with the fewest missed time windows). Figure 6: The result of correlations between the shortest route weight, the profit, and missed time windows. Traditionally, the process of receiving a request and scheduling are considered two separate functions on the decision-making platform of the logistics provider. The logistics service provider proposed the route planning after confirming the request of the customer. Technological improvement is a factor of transformations in urban delivery. Specifically, UAV implementation by logistics service providers will reduce the limitations of urban delivery. The logistics service provider can receive the new request in order to obtain revenue, rather than considering limitations in real-time. However, if a new request is added to the routing, it may not be a good solution, because the customer will be dissatisfied if the expected time window fails to meet their expectations. Thus, this study has proposed an equivalent mathematical model that focuses on the new route planning problem. We liberalize the time condition and add a penalty coefficient to the time window in order to deliver on time as often as possible to each node and  
Figure 8: The result of the relationship between the weight of missed time windows and the profit and total route distance under the logistics service provider’s profit.