# Instances of "Humanitarian relief distribution with trucks and drones under travel time uncertainty"

## Description

This data set concerns the experimental instances of the paper "Humanitarian relief distribution with trucks and drones under travel time uncertainty". We adapt the R101, C101, and RC101 instances of Solomon (1987), which are used to benchmark vehicle routing problems with time windows, with locations randomly scattered over the area (R), clustered in groups of locations (C), and locations both clustered in groups as well as randomly distributed over the area (RC). Besides the Solomon inspired cases, we evaluate two historical disaster cases, namely the 2015 earthquake in Nepal and 2018 tsunami in Indonesia. The level of uncertainty within an area can differ, e.g., parts close to the path of a hurricane or near the epicenters of earthquake aftershocks are likely to exhibit larger variance in travel time. We created risk matrices for all node pairs. The real-world cases we consider the disaster areas after the 2015 earthquake in Nepal and the 2018 tsunami in Indonesia. In 2015, a 7.8M earthquake caused major disruption in Nepal. Eleven districts near the capital city Kathmandu were affected the most, where the mountainous surroundings posed challenges to the road transport. We focus on two districts that were significantly disrupted: Nuwakot and Dhading. Based on data collected from a field trip in August 2021 (carried out as part of our research) along multiple municipalities in the affected districts, we composed a set of 84 demand nodes and a depot located in Dhading Besi, the district headquarter of the Dhading district. We marked risk levels for all node pairs, with high risks close to the epicenter, and medium risk nodes up in the mountains. In 2018, an 7.5M undersea earthquake and a tsunami that followed resulted in a massive disruption of the city Palu and surrounding areas around the Palu Bay on the Indonesian island Sulawesi. Data from a displacement tracking matrix (International Organization for Migration 2019) with locally collected data from 2018 allows us to extract a set of 343 demand nodes and a depot at the Palu Airport. We marked the risk levels along the coast line and medium risk levels in areas that experienced soil liquefaction. For our experiments, we consider two fleet configurations. One fleet with only trucks, and one fleet where 50% of the trucks are replaced by drones. For the instances with 26 nodes, we deploy two vehicles, with the 101 node instances eight vehicles, with the Nepal case six vehicles, and with the Indonesia case 16 vehicles considering the large number of nodes. We assume that a truck has a capacity of 10 units. Considering demands between one and five, a truck can visit at least two and at most 10 nodes. The specifications of the drone are inspired by the MiniFreighter from Wings For Aid. For the experiments, we assume that drones carry one unit of demand, and travel with a constant speed of 120 km/h following Euclidean distances, as their flights are not disrupted by damaged infrastructure.

## Files

## Steps to reproduce

For all cases, we consider a maximum time period for the operation of 8 hours, i.e., t-max = 480. We generate random time windows between 60-180 minutes for each demand node and sample the demand at each node between 1 and 5 from a discrete uniform distribution. Regarding the Solomon instances, we create six cases: three cases with 25 demand nodes, and three cases with 100 demand nodes. We use the coordinates for the depot and demand nodes given in R101, C101, and RC101. To obtain a realistic estimation of travel times for trucks, we create a network between nodes by generating a minimum spanning tree and extending this by connecting those nodes whose ratio between the Euclidean distance and the shortest path in the network is below the predetermined threshold, similar to Chen et al. (2019). The links in the instances are transformed to a complete origin-destination matrix by calculating the shortest paths between all node pairs. Preliminary experiments showed that thresholds of 0.1, 0.2, and 0.3 for R101, RC101, and C101, respectively, provided reasonably connected networks. The distances between some locations are Euclidean, but most trips take longer, up to 10 times longer than the Euclidean distance. Based on this network, we calculate the expected truck travel times (we assume a truck driving speed of 30 km/h). For drones, we calculate travel times based on Euclidean distances between all nodes and a flight speed of 120 km/h. For the smaller instances, we have selected a fixed set of 25 random demand nodes out of the 100 demand nodes and use the same distance matrix as obtained for the 100 demand node instances. For the real-world instances, demands and time windows are again determined similarly to the Solomon instances, as detailed data was not available. To obtain realistic estimates of the actual travel times of trucks in the Nepal and Indonesia cases, we used ESRI ArcMap 10.7 to determine the expected times between each pair of nodes. The average travel speeds of trucks in both areas are approximately 30 km/h (hence we assumed that trucks drive 30 km/h in the Solomon instances).