A robust optimization problem for drone-based equitable pandemic vaccine distribution with uncertain supply

Abstract

Widespread vaccination is the only way to overcome the COVID-19 global crisis. However, given the vaccine scarcity during the early outbreak of the pandemic, ensuring efficient and equitable distribution of vaccines, particularly in rural areas, has become a significant challenge. To this end, this study develops a two-stage robust vaccine distribution model that addresses the supply uncertainty incurred by vaccine shortages. The model aims to optimize the social and economic benefits by jointly deciding vaccination facility location, transportation capacity, and reservation plan in the first stage, and rescheduling vaccinations in the second stage after the confirmation of uncertainty. To hedge vaccine storage and transportation difficulties in remote areas, we consider using drones to deliver vaccines in appropriate and small quantities to vaccination points. Two tailored column-and-constraint generation algorithms are proposed to exactly solve the robust model, in which the subproblems are solved via the vertex traversal and the dual methods, respectively. The superiority of the dual method is further verified. Finally, we use real-world data to demonstrate the necessity to account for uncertain supply and equitable distribution, and analyze the impacts of several key parameters. Some managerial insights are also produced for decision-makers.

Keywords: Drone delivery; Facility location; Pandemic vaccine distribution; Robust optimization; Uncertain supply.

Fig. 1

Illustration of the vaccine distribution chain.

Algorithm 1

C&CG framework.

Algorithm 2

Procedure to get the vertex set of ${\mathcal{U}}_{\gamma }$.

Fig. 2

Map of Linshui County.

Fig. 3

Comparative results on profits under different uncertainty levels $ϵ\in [0,0.9]$ with $\alpha =5$.

Fig. 4

Impact of the weight coefficient $\alpha$ on the optimal decisions.

Fig. 5

Impact of the weight coefficient $\alpha$ on the profits.

Fig. 6

Impact of the wastage penalty $C^w$ on the optimal decisions.

Fig. 7

Impact of the wastage penalty $C^w$ on the profits.

Fig. 8

Impact of the facility fixed cost $C^f$ on the optimal decisions.

Fig. 9

Impact of the facility fixed cost $C^f$ on the profits.

Fig. 10

Map of Linshui County with the facility location-allocation decisions considering or neglecting equity.