Making combination vaccines more accessible to low-income countries: The antigen bundle pricing problem

Combination vaccines have become the preferred choice for immunizing children in high- and middle-income countries. However, these new vaccines are prohibitively expensive for low-income countries, causing them to rely on older, less-expensive vaccines. This product divergence decreases economies of scale for the purchase of vaccines and eliminates the financial incentive for manufacturers to maintain production of less-expensive vaccines or even to develop new vaccines for diseases affecting developing countries. This paper treats combination vaccines as bundles of antigens that can be priced as a single item. Such bundles are used to formulate an optimization problem that determines the combination vaccine allocation between vaccine producers and different countries under a price discrimination agreement. The objective of the optimization problem is to satisfy countries' antigen demand at the lowest possible price, while providing a reasonable profit for the vaccine producers. The optimization problem results in a mixed-integer non-linear programming model that maximizes the sum of manufacturing profits and the customer surplus, and hence, it maximizes the total social surplus. Moreover, a constructive heuristic is proposed to determine an approximation to the best allocation of combination vaccines and their range of feasible prices. Computational results show that vaccine prices in all market segments become more affordable as the supply of the most complex combination vaccines becomes more available to low-income countries.