Informing pediatric vaccine procurement policy via the pediatric formulary design, pricing, and production problem

ABSTRACT

This research improves upon the monopsonist vaccine formulary design problem in the literature by incorporating several modeling enhancements and applying different methodologies to efficiently obtain solutions and derive insights. Our multi-objective formulation seeks to minimize the overall price to immunize a cohort of children, maximize the net profit shared among pediatric vaccine manufacturers, and minimize the average number of injections per child among the prescribed formularies. Accounting for Centers for Disease Control and Prevention (CDC) guidelines, we restrict vaccines utilized against a given disease within a given formulary to those produced by a single manufacturer. We also account for a circumstance in which one manufacturer's vaccine has a greater relative efficacy. For the resulting nonconvex mixed-integer nonlinear program, we bound the second and third objectives using optimal formulary designs for current public sector prices and utilize the ϵ -constraint method to solve an instance representative of contemporary immunization schedule requirements. Augmenting our formulation with symmetry reduction constraints to reduce the required computational effort, we identify a set of non-inferior solutions. Of practical interest to the CDC, our model enables the design of a pricing and purchasing policy, creating a sustainable and stable capital investment environment for the provision of pediatric vaccines.

KEYWORDS:

• Multi-objective optimization
• mixed-integer nonlinear programming
• vaccine economics

Acknowledgments

The authors gratefully thank the Associate Editor and three reviewers for their constructive comments that have helped improve the presentation of this article.

Additional information

Notes on contributors

Brian Lunday

Brian J. Lunday is an Associate Professor in the Department of Operational Sciences at the Air Force Institute of Technology. He earned a Ph.D. in Industrial and Systems Engineering from Virginia Tech, an M.S. in Industrial Engineering from the University of Arizona, and a B.S. in Mechanical Engineering from the United States Military Academy. His research interests include theoretical developments in math programming, game theoretic models, and algorithmic design for global optimization, as well as applications in the areas of network design, network optimization, network interdiction, network restoration, facility/resource location, and resource location/allocation & assignment.

Matthew J. Robbins

Matthew J. Robbins is an Associate Professor in the Department of Operational Sciences at the Air Force Institute of Technology. He holds a Ph.D. in Industrial Engineering from the University of Illinois at Urbana–Champaign, an M.S. in Operations Research from the Air Force Institute of Technology, and a B.S. in Computer Systems Engineering from the University of Arkansas. His research interests include approximate dynamic programming, game theory, simulation, and applications of operations research in the military and public healthcare domains. He has been recognized with a number of awards, most notably winning the 2011 Pritsker Doctoral Dissertation Award (First Place) from the Institute of Industrial Engineers.