The relief distribution problem with trucks and drones under incomplete demand information

Abstract

Disaster relief operations often take place under uncertainty regarding the extent of damage across locations. In this paper, we study the delivery of relief aid in the aftermath of disasters when delivery vehicles are assisted by surveillance drones and the demand for relief supplies is initially unknown. We introduce a stylized problem that arises in many emergency supply delivery settings -- the relief distribution problem (RDP). In RDP, emergency vehicles, referred to as trucks, must distribute relief supplies on a network, starting from the depot to potential delivery locations, whose demand is initially unknown. The trucks are assisted by surveillance drones, which cannot deliver relief supplies, but scout delivery locations to see whether relief supplies are needed or not. The objective is to visit all location by any vehicle, deliver supplies to all damaged ones, and minimizing the completion time of the relief operation. We study two natural policies for the online problem RDP which we evaluate in two ways: the competitive ratio quantifies the performance in comparison to an optimal solution obtained under full information on damages, the drone-impact is the ratio of the algorithm's performance to the best outcome achievable without drones. Through theoretical analysis and computational experiments, we characterize the operational trade-offs between these policies and derive insights for the effective deployment of drones in disaster response.

Figures (8)

• Figure 1: Drone surveillance during earthquake in Nepal, 2015
• Figure 2: Example of an RDP$^*$ instance (full-information counterpart) Note.Left figure: An instance with $\alpha=2$, i.e., the drone is two times faster than the truck; damaged nodes $D=\{v_1,v_2,v_3\}$, 1 truck, and 1 drone. Right figure: An optimal solution for this instance with makespan 17: the truck travels $(v_0, v_1, v_3, v_2, v_1, v_0)$, the drone travels $(v_0, v_1, v_3, v_5, v_4, v_1, v_0)$.
• Figure 3: $\textsc{Optimistic}$ and $\textsc{Regretless}$ for the example in Figure \ref{['fig:1']}
• Figure 4: Examples of star graphs
• Figure 5: Observed competitive ratios $\hat{\sigma}$ for $\textsc{Optimistic}$ and $\textsc{Regretless}$ on LARGE Note. The red line indicates analytical competitive ratios $\sigma$ from Section \ref{['sec:analysis']}.

Theorems & Definitions (85)

• Definition 1: $\textsc{TSP}_{m,n}(W)$, $S^*_{m,n}(W)$
• Lemma 1
• proof
• Lemma 2
• proof
• Definition 2: $\tilde{\mathcal{G}}(n, d)$
• Definition 3: $\tilde{\mathcal{G}}(n_1, n_2, d_1, d_2)$
• Lemma 3
• proof
• Lemma 4