## 6 Conclusions  
Recognizing the lack of benchmark instances in VRPs with asymmetric costs, or ACVRPs, this paper supplemented the instances with new and more realistic ones. The instances were generated with the help of a wide range of publicly shared data and advanced map API services in Korea. They were created using publicly shared spatial data for depot and customer locations. The locations included UDCs, regional hubs for postal services, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Benchmark** & **Number** & **Dimensions** & **Depot and Customer Nodes** & **Road Distance** & **Rood Distance** & **Reported BKS*** \\ \hline [PERSON] & 32 * & 34–74 & Real data of pharmaceutical product delivery & O & X & O \\ \hline De Smet & 10 ** & 50–2750 & Administrative districts & O & O & X \\ \hline [PERSON] & 2700 & 50–500 & Random, grid, and radial & O & X & X \\ \hline Proposed instances & 648 & 50–500 & Real data of UDCs, postal hubs, large malls, residential complexes, restaurants, and convenience stores & O & O & O \\ \hline \hline \end{tabular}  
* The original number was eight, but the instances grew in terms of population by modifying vehicle capacity. ** The number of instances is 50, but after netting only the ACVRP instances, 10 instances are available. *** The availability of best-known solutions.  
\end{table} 
Table 4: Comparison of ACVRP benchmark instances. Figure 12: The number and ratio for node pairs regarding air distance. shopping malls, restaurant businesses, residential facilities, and convenience stores. For road distance and road time matrices, T map, a map API renowned for its accuracy in Korea, was used. A total of 648 ACVRP benchmark instances are now available online. The proposed benchmark instances contribute to the research community since they carefully and realistically reflect urban transportation environments. Real road distance and road time matrices are asymmetric, and this asymmetry has a large effect over the solution methods and quality in a VRP [4]. The benchmark instances will be useful in the development of routing algorithms. In addition, the proposed instances are based on cities in Korea, which makes them the first benchmarks based on any region outside of Europe. Additionally, this paper is the first to present instances that satisfy all of the following criteria: be large in number, include instances of large dimension, include both road time and road distance matrices, reflect the realities of urban transportation, and provide records on best-known solutions. Using the benchmark instances' abundant road distance and road time matrices, this paper analyzed and answered three important questions in urban transportation planning that have rarely been considered: (i) the frequency and magnitude in which air distance differs from reality when measuring closeness, (ii) the differences in distance and time for outgoing and return trips, and (iii) rough conversion ratios from air distance to road distance and road time. The analyses were carried out for each boundary of 1 km within 10 km of air distance. Overall, using air distance results in inaccurate decisions when measuring closeness. For distance measurements, it is wrong 34.9% of the time by a magnitude of 27.9%. For time measurements, it is wrong 40.6% of the time by 29%. On average, the outbound and return trips differ by 20.6% in distance and 32.9% in time. The value 1.57 may be multiplied to air distance when estimating road distance, and 0.14 may be used when converting air distance in meters into road time in seconds. The analyses contribute to the research community by highlighting characteristics of urban transportation environments. Furthermore, this paper can be referenced when emphasizing the necessity of using map APIs instead of air distances in transportation planning. This paper provides some managerial implications. Accurate planning can only be conducted with accurate distance and time measurements.