## 1 Introduction  
Generally, vehicle routing problems (VRPs) involve a homogeneous fleet of vehicles with a fixed capacity to serve a set of customers from a single depot. All vehicles must depart from and return to the depot. Restrictions such as route lengths or time limits will constrain the distance traveled by the vehicles. The goal is to assign a sequence of deliveries to each vehicle so that service can be provided to all customers while minimizing the total distance traveled or the total time consumed by the fleet. The standard VRP is often referred to as a capacitated vehicle routing problem (CVRP). VRP variations exist, including the multi-depot vehicle routing problem (MVRP), in which vehicles depart from multiple depots, and the open vehicle routing problem (OVRP), in which vehicles do not return to the depot. More detailed lists and descriptions can be found in [1, 2]. Relatively little attention or effort has been paid to the creation of benchmark instances for VRPs with asymmetric costs, or asymmetric cost VRPs (ACVRPs). For an ACVRP, a number of old small-sized benchmark instances exist, but they are not able to adequately reflect real-world problems. There are also many new larger-sized instances that lack rationale for the methods used in their creation. This lack can, in part, be explained by the difficulty in obtaining the exact road distance or time from all nodes to other nodes. However, recent advances in technology have made it possible to clear this hurdle. Now with the advance of map service providers and their efficient application programming interfaces (APIs), the distance or time of paths can be estimated very accurately. As illustrated in Figure 1, map APIs can provide precise costs between nodes. The figure explains why the real road distances from map APIs should be used instead of air distances or the straight-line distances between coordinates. In Figure 1a, A\({}^{\prime}\) exemplifies the closest node from Node A in the road networks of a map service provider. The air distance from A to B may be larger than the air distance from A to C, but the road distance from A to B (blue solid line) is much larger than the road distance from A to C (red dotted line). Figure 1b shows that outbound and return distances can differ by a significant margin. With air distance, the difference of cost from A to B (blue solid line) and from B to A (red dotted line) cannot be properly considered. Travel costs are asymmetric in real-world settings. That is, the cost of traveling from one node to another node, and the cost of the return trip, can vary. This simple but important fact has naively been ignored in VRP research and operations. The cost differences may be too small to be concerned with in cases where obstacles and road directions are less important. This would include long-haul or truck-line transportation. However, on a scale of goods distribution or last-mile deliveries where customer nodes are densely populated, the cost differences of outbound and return trips are too large to be ignored. Taking the asymmetry into account has become not only possible, but also significant. Solving a VRP with air distances and then applying asymmetric road distances has been reported to be suboptimal by almost five percent [3]. The asymmetry has a large effect over the solution methods and quality in VRPs, and this dynamic should be considered when proposing and improving routing algorithms [4]. The research community needs properly designed and realistic ACVRP benchmark instances when developing these algorithms. This paper supplements the pool of ACVRP benchmarks with more realistic instances. An increasing number of governmental authorities are now operating public data portals, which is also true in Korea. Various types and abundant sizes of data have become readily accessible to the public.