Mathematics Events

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Abstract: Drug shortages have been one of the most challenging problems facing the U.S. pharmaceutical industry and government in recent years. Although this problem has drawn tremendous attention from the government and media, limited academic research has been devoted to this problem, and few solutions have been proposed based on rigorous research. This study addresses the drug shortage problem from a supply chain perspective, a key aspect missing in the literature, and proposes to mitigate shortages through drug purchase contracts. By modeling the drug supply chain pertaining to shortages, we capture the objectives of the many parties involved in the shortage problem, derive structural properties of key decisions, and characterize Pareto-improving contracts that mitigate drug shortages, improve drug manufacturer's and group purchasing organization (GPO)'s profits, and cut government spending and healthcare providers' costs. We further conduct numerical analysis with realistic industry data. Our results show that increasing drug prices only (IP approach), a solution advocated by much literature, is not effective in shortage mitigation. Price increases must be paired with strengthened failure-to-supply clauses (IPS approach) to achieve consistent and significant shortage reduction as well as Pareto improvement: across all parameter sets tested, a 30% price increase under IPS can lead to a minimum, average, and maximum shortage reduction of 25%, 53% and 70%, respectively. Our analysis also shows the impacts of IPS on different parties in the supply chain and the impacts of various model parameters on shortage mitigation. IPS rewards reliability of drug supply and in turn lowers shortage risks, which is in line with FDA's strategic plan to reward quality, but is much easier to achieve in this regulation-based industry. Interactions with FDA and some top GPO staff indicate that IPS also challenges the current mindset of the pharmaceutical industry in their drug purchase contracting.

Authors: Justin Jia and Hui Zhao

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Anh Ninh