A mixed integer programming model for vaccine pricing within a group purchasing organization - Yu, Zhuoting; Keskinocak, Pinar; Orenstein, Walter A.; Toktay, L. Beril (Vaccine, 2024)
Setting prices for life-saving medical or pharmaceutical products needs to consider multiple factors, e.g., affordability and health outcomes across different populations. When a group of buyers (e.g., countries) combine their purchasing power (e.g., via a group purchasing organization), the average procurement price decreases in the total volume. Decisions about what price to then charge to each member in a group are particularly challenging, considering the disparities in their respective ability and willingness to pay. Tiered pricing can be an effective way to set prices for a group of buyers, but its performance needs to be quantified and evaluated. We modeled the decision of setting prices of a medical product (for example, a vaccine) for a group of buyers using a mixed integer programming model, considering the buyers’ ability and willingness to pay. The objective is to minimize the unit price disparity adjusted by the buyers’ willingness to pay, subject to the constraint that the prices decrease in the buyers’ ability to pay. We also developed an analogous subsidy allocation model that applies if the group receives philanthropic donations to support procurement. The models were illustrated with two case studies based on the Bacillus Calmette-Guerin (BCG) vaccine procurement by Gavi, the Vaccine Alliance and Pan American Health Organization, and the performances of uniform, tiered, and differentiated pricing schemes were examined. The adjusted unit price disparity is non-increasing in the number of price tiers allowed. The biggest decrease in the adjusted price disparity occurs when switching to two-tier pricing from uniform pricing. Tiered pricing performs better in the Gavi group compared to the PAHO group, in part because the ability to pay and willingness to pay have a higher degree of rank correlation within the former group of countries. This work provides a model for price-setting (subsidy allocation) decisions for a group of buyers and provides a quantitative comparison of different pricing schemes. The results of the case studies suggest that the performance of tiered pricing depends on various factors, including the disparities in the ability and willingness to pay across the buyers. This research has been supported in part by the Center for Health and Humanitarian Systems, the William W. George endowment, and the following benefactors at Georgia Tech: Andrea Laliberte, Richard Rick E. and Charlene Zalesky, and Claudia and Paul Raines.