## 7 Conclusions  
In this paper, an approach has been presented to compare direct deliveries (DD) with APL systems for last-mile deliveries in larger cities. For the evaluation of DD, three different levels of detail have been compared. The results show that further studies should not only rely on simple formulas to estimate the distances traveled for distribution. At least correction factors should be verified or estimated anew for each given problem instance. Such a verification should be performed on the basis of rather detailed models, with respect to both the underlying data for customer locations and the planning methods applied to generate tours. The results presented show that using data from the open street map (OSM) leads to significantly different, here shorter, tour lengths than using random data within the given areas. Furthermore, further studies should model the methods used for planning tours for vehicles according to the actual situation for the given problem instance. As in practical cases, often Vehicle Routing Problems are solved using heuristics; these approaches, such as the savings algorithm and further improvements methods, which have also been applied in this paper, should be implemented. With respect to the comparison of APL systems and DD on the basis of CO\({}_{2}\) emissions, the results show that it is necessary to also model the customer behaviour to reach APL locations for a fair and profound comparison. It is, of course, favorable for logistic providers to use APL systems in terms of operational costs as less distance has to be traveled compared to dropping off each parcel at the customer location. The savings range from 30% to 90% for different scenarios, which are in line with the findings of previous works presented in Section 2.2. Figure 19: Sensitivity analysis for parameter ratio of stop on an individual vehicle tour of the customer. However, also taking distances traveled by customers by car to reach the APLs into account leads to a completely different picture. As a conclusion, APL systems are only competitive with direct deliveries if a sufficient number of APLs are introduced and more customers pick up their parcels with zero emission (by foot or bike). In the results presented, a system with 250 APLs leads to lower emissions than DD for most demand scenarios, if the capacity of the vehicle serving the APLs is set to 500. These findings are nearly in line with the results presented by [47], who conclude that APL systems are competitive in urban areas if the distance a customer must travel by car to reach the APL is within 0.94 km. As shown in Figure 11, for APL configurations A5 and A6, which lead to better results than direct deliveries in most demand scenarios, nearly 100% of all customers are within this radius. In comparison, for A4 (150 APLs), only about 95% of all customers are within that distance range, and direct deliveries lead to better results in all demand scenarios. Setting the parameters correctly is one of the most challenging tasks for using the proposed model as the ratios for the different means of transport for customers in dependence of the distance to be traveled are only roughly estimated. Here, conducting a sensitivity analysis is a possible way to check the robustness of the results. Our results for the sensitivity analysis show that typically the different factors need to be increased by a high--and rather unrealistic--degree to obtain different results than in the standard parameter settings proposed. This leads to the conclusion that the results obtained can be rated as robust, even though only one parameter has been analyzed at a time. Future research could focus on a broader design of experiments, with two or more parameters analyzed at the same time. Besides the problem of valid parameter settings of the model, there are further limitations set in the modeling approach. The possible positions of APLs have been determined randomly, and the actual road network has not been modeled in detail.