A bilevel formulation of the pediatric vaccine pricing problem

We consider the characterization of optimal pricing strategies for a pediatric vaccine manufacturing firm operating in an oligopolistic market. The pediatric vaccine pricing problem (PVPP) is formulated as a bilevel mathematical program wherein the upper level models a firm that selects profit‐maximizing vaccine prices while the lower level models a representative customer’s vaccine purchasing decision to satisfy a given, recommended childhood immunization schedule (RCIS) at overall minimum cost. Complicating features of the bilevel program include the bilinear nature of the upper‐level objective function and the binary nature of the lower‐level decision variables. We develop and test variants of three heuristics to identify the pricing scheme that will maximize a manufacturer’s profit: a Latin Hypercube Sampling (LHS) of the upper‐level feasible region, an LHS enhanced by a Nelder–Meade search from each price point, and an LHS enhanced by a custom implementation of the Cyclic Coordinate Method from each price point. The practicality of the PVPP is demonstrated via application to the analysis of the 2014 United States pediatric vaccine private sector market. Testing results indicate that a robust sampling method combined with local search is the superlative solution method among those examined and, in the current market, that a manufacturer acting unilaterally has the potential to increase profit per child completing the RCIS by 35 percent (from 231.84 to 312.55 dollars) for GlaxoSmithKline, 47 percent (from 63.96 to 93.70 dollars) for Merck, and 866 percent (from 25.99 to 251.04 dollars) for Sanofi Pasteur over that obtained via current pricing mechanisms.