Optimal Timing of Influenza Vaccine Production Under Yield-Improving and Knowledge Acquisition Strategies

Abstract

We consider a manufacturer of a new vaccine, such as the COVID-19 vaccine, characterized by evolving demand and production yield uncertainties. At the beginning of the time horizon, a vaccine may not be manufacturable due to its low production yield and the resulting lack of profitability. Prior to launching large-scale production, the manufacturer stochastically increases the uncertain yield of the vaccine by learning through small-scale experimental production runs about manufacturing conditions that are conducive to raising that yield, thus forsaking, in the process, immediate profits but raising future ones. After starting large-scale production and receiving revenues from the sale of the vaccine, the manufacturer can continue to stochastically improve vaccine yield by acquiring knowledge from real-time production data. The two key decisions faced by the vaccine manufacturer who seeks to maximize his total expected profit over the time horizon concern the optimal timing and capacity of the vaccine’s large-scale production. We formulate and solve a stochastic, multi-period, sequential-decision model to determine the structure of the vaccine’s manufacturer’s optimal decisions, while incorporating the dynamic evolution of vaccine yield uncertainty under those two yield improvement strategies. In particular, we establish the optimality of a threshold stopping policy for the timing of the large-scale vaccine production. This policy is found to depend in a fundamental way on the relative stochastic rates of the two yield improvement strategies. We also characterize the manufacturer’s optimal capacity decision and identify conditions under which, for a new vaccine, optimal capacity and production yield become substitutes. We analyze the implications of our results and underlying yield improvement strategies for rendering a new vaccine large-scale manufacturable, and bringing it to the market sooner in the time horizon.