Modeling Pharmaceutical Supply Chains to Mitigate Drug Shortages

Abstract

The use of medically-necessary drugs has extended the lives of countless patients. While healthcare providers rely on the pharmaceutical industry for treatments, in recent years, the drug supply in the United States has become volatile and drug shortages are common. Shortages are considered a public health crisis and are often caused by disruptions to vulnerable pharmaceutical supply chains. The tightly optimized supply chains have little redundancy and low levels of inventory. This combination can cause minor supply interruptions to become widespread shortages. I study the dynamics of shortages by developing new models of supply chains under disruption, and I identify regulations and incentives to induce companies to reduce the occurrence and impact of shortages. There has been minimal analysis on the quantitative impact of proposed policies.

I present four mathematical models. The first two are static supply chain design problems (SCDD and SCDD-I). The company decides at the beginning of the horizon how to configure its supply chain. In the second model (SCDD-I), the company may also choose to hold inventory. The models are two of the first to include disruptions and recovery over time. They are solved using Sample Average Approximation. The analyses suggest that it is either not economically feasible or attractive for companies to maintain resilient supply chains for some drugs that are vulnerable to shortage. I use the models to compare policies that have been proposed to reduce shortages. It is less expensive to raise prices in combination with resilience requirements than to raise prices alone. Requiring a second supplier may have the largest incremental benefit than requiring a back-up at other levels of the supply chain.

The third model (D-SCDD) is a dynamic supply chain design model. It is a multi-stage stochastic program. At the beginning of the time horizon, the company selects the supply chain configuration and may add components or stop production if disruptions occur. The formulation applies the geometrically-distributed times to recover and disruption via an inverse sampling approach to maintain stage-wise independence. It is solved using the Stochastic Dual Dynamic Integer Programming (SDDiP) algorithm. I find that substantial reductions in the lead times to add components or reducing the mean time to recover disrupted components may reduce shortages. Minor lead time reductions have little impact.

The fourth model (SCR) is comprised of closed-form expressions that describe the reliability characteristics of a given supply chain configuration. The analyses provide evidence that increasing component quality would be effective at reducing shortages. The model can also be used to calculate break-even prices.

This project provides insight to policymakers and companies to support the profitable production of a reliable drug supply. The implications and use of these models is widely relevant to other regulated industries and supply chains under distribution.