  Drug shortages have been a persistent problem in American healthcare for
decades, and the resulting lack of access to necessary drugs has been
disastrous to patient health. A majority of these shortages were caused by
quality issues related to problems in the manufacturing process. More frequent
inspections can reduce quality concerns, but deciding when to inspect is a
complex problem; strict regulation enforcement can force low-profit facilities
to close due to excessive maintenance costs, while lax enforcement allows for
regulation violations to persist, both of which can cause drug shortages. We
propose a novel model to assist the FDA in determining when to inspect
manufacturing facilities. We formulate this problem as a finite-horizon
partially observable Markov decision process (POMDP) based on the
classifications the FDA assigns to each facility after inspection, as well two
disruptive events: a manufacturing failure occurring or the facility closing
for non-mandatory maintenance. We theoretically show that this problem can be
reduced to only needing to consider whether or not to inspect immediately,
which is independent of the time horizon. We additionally determine the
sensitivity of the optimal inspection time on the penalty incurred for an
unexpected disruptive event occurring. Our computational study demonstrates a
quadratic relationship between the relative difference in average value
accumulated between inspecting based on the optimal inspection time produced by
our model and inspecting based on the expected time to an unexpected disruptive
event, highlighting the importance of allocating more inspection resources to
high-risk facilities that produce drugs that highly impact public health. We
additionally find that optimal inspection time is more sensitive to changes in
the penalty incurred from a disruptive event occurring the longer it has been
since the last inspection.
