Similar evacuation problems arise during floods, hurricanes, and wildfires, though
here evacuees are not necessarily limited to certain vulnerable populations but are
instead those closest to areas of threat. Moreover, evacuation distances for these
extreme events are frequently longer than in the heat event scenario. Now, uncertainty
in resulting location problems still arises from duration, onset time, and severity, but also
involves uncertain spatial distribution of disasters.
In addition to location theory, various other topics from operations research are
relevant to the evacuation problem. One involves supplying and staffing evacuation
sites. The job assignment problem is a classic problem in operations research that
arises in heat events through the need to assign an appropriate mix of doctors, nurses,
and support staff to relief centers. New twists on this problem arise from uncertainty. We
don’t know how long the heat event will take place. We don’t know whether the staff will
show up for work or instead choose to care for their own families. We don’t know how
many people will show up at the relief center and what underlying health conditions they
will have, requiring different skills among the medical staff. Thus, we face assignment
problems under considerable uncertainty, a major problem in stochastic optimization
calling for new tools and methods. Similar issues arise from having to decide what kinds
of supplies to stockpile in or order for a relief center, whether it’s due to a heat event or a
flood, hurricane, or wildfire. This is related to the classic operations research problem of
inventory planning, but with complex stochastic twists of the kind described above.
The transportation problem is a classic operations research problem that arises
in evacuation planning. In this problem, we want to move goods from sources to
destinations. Here, we want to move evacuees from homes to relief centers. But whom
do we send where? The answer depends upon transportation times (which are
undoubtedly stochastic), the physical condition of evacuees which may allow the less
vulnerable people to be transported further away, and the medical expertise available at
a given relief center that might or might not match the needs of an evacuee. Thus, we
have a stochastic optimization problem with new twists, including uncertainties,
combined with a “matching problem” of operations research that involves assigning
people to relief centers that match their needs and that minimize their travel times. This
is a multicriteria optimization problem of considerable complexity.
Under emergency conditions, particular strategies for evacuation are more
successful than others at maintaining order and maximizing the safety of those being
displaced. Many natural disasters lead to the progressive loss of motor vehicle access,
e.g., by making transversal of specific routes dangerous or impossible through flooding,
making routing strategies that were designed assuming a known and constant set of
accessible roadways inappropriate. Further, exactly these same conditions are those in
which medical transport can be most critical, especially if the affected roadways are
limiting access to local hospitals. As situations change during extreme weather events
(e.g. water level rises), different areas can experience both greater need of immediate
access to medical care and fewer accessible means of transportation into and out of the
area to receive that care. These conditions can lead to very specific and otherwise
unlikely complications, requiring particular attention. This calls for new algorithms for
determining optimal routing for emergency transportation on the road systems in real-
time under dynamically changing network structure, as information about current (and
likely future) access levels change to maximize the efficiency of use of available routes.
Among the relevant areas of the mathematical sciences are spatial analysis, analysis of