Optimal Scheduling and Policy Design of Two-Dose Vaccination Rollout

Abstract

In many countries, the COVID-19 vaccination program faces great challenges, from the management of limited and irregular supply of vaccines, uncertain vaccine take-up rate from the population, and appropriate appointment booking management to reduce congestion etc. In addition, the feature of a two-dose regimen of most COVID-19 vaccines poses a unique operational challenge, the "blocking phenomenon," where the need to reserve vaccines for the second-dose appointment may "block" the take-up rate for the first-dose appointment. Determining the appropriate volume of vaccines to be kept in reserve in case of disruption to the supply schedule is an important operational problem for vaccine rollout. In this paper, we use the concept of "booking curve" (from the revenue management literature) to develop a practical tool that jointly determines the vaccine appointment booking limits that control the administration of the first and second doses, followed by an invitation schedule that decision-makers can use to regulate the appointment bookings (demand). The optimization framework aims to design the vaccine rollout policy to maximize the vaccination rate, while ensuring that the aggregate appointment waiting time in the system remains minimal, with sufficient cushion to account for supply disruption and uncertain take-up of appointments. We show that the optimization problems can be efficiently solved by linear and conic programs. A vaccine rollout numerical study based on the Singapore vaccination program is presented to demonstrate the novelty and advantage of the optimization framework. The optimization framework has been developed into an open-source tool to assist the policymakers in designing an effective and adaptive COVID-19 vaccine rollout policy facing the evolving challenges in fighting against the pandemic.