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In this recitation, we'll
discuss operating room

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scheduling.

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That is, how hospitals can
be made to run smoothly.

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In particular, we'll discuss how
an operating room manager can

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use integer optimization to
make sure the hospital runs

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smoothly.

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So hospitals have a limited
number of operating rooms,

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or ORs.

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And operating room managers
must determine a weekly schedule

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assigning ORs to different
departments in the hospital.

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If you look on the
right, you'll see

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a picture of an operating room.

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You can see immediately how much
specialized and fancy equipment

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there is.

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And you have to remember that
for any surgery, staffing

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the OR doesn't just involve
the surgeon performing

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the surgery, but also other
doctors, nurses, residents,

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and fellows.

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There's usually an
entire surgery team.

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So due to the specialized
equipment in an OR,

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as well as the
specialized staff members,

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it's been estimated that
staffing an operating room

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costs over $100 a minute.

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Therefore, for a hospital
to run on a budget,

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it's very critical for
the operating room manager

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to create a good schedule.

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However, this isn't
without difficulties.

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Creating an acceptable schedule
is a highly political process

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within the hospital.

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Surgeons are frequently paid on
a fee-for-service basis, which

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means they get paid for
every surgery they perform.

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That means that when you
change their allocated

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number of operating
room hours, it directly

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affects their income.

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Therefore, the operating room
managers' proposed schedule

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must strike a delicate
balance between all

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the surgical departments
in the hospital.

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However, there are
many logistical issues

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for the operating room
manager to consider

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when designing the schedule.

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Operating rooms are staffed
in eight hour blocks.

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Each department sets
their own target number

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of allocation hours,
which may not be integer.

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In addition,
departments may have

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daily and weekly requirements.

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For example, gynecology might
need at least one OR per day.

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Ophthalmology might need
at least two ORs per week.

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And for example,
the oral surgeon

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might only be present on
Tuesdays and Thursdays.

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The operating room manager
needs to take into account

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all of these
logistical issues when

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designing a feasible schedule.

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In this recitation, we'll
consider a case study

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of Mount Sinai
Hospital in Toronto.

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There are 10 operating
rooms at Mount Sinai, which

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are staffed from
Monday through Friday.

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So 10 ORs times 5 days
times 8 hours per day,

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means that they have 400
hours to assign between five

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different surgical departments.

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The departments
they are assigning

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are ophthalmology, gynecology,
oral surgery, otolaryngology,

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and general surgery.

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Each of these
departments has come up

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with a weekly number of
target allocation hours.

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For example, ophthalmology
requests 39.4 hours

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of operating room time,
and otolaryngology requests

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26.3 hours of
operating room time.

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Now, it's very clear that just
by looking at these numbers

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they are not integer, and
they are certainly not

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multiples of eight hours.

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This means that it's impossible
for the operating room manager

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to give any department exactly
their weekly number of target

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allocation hours.

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However, the
operating room manager

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would like to try to give as
many hours to each department

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as possible up to their
target allocation number.

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We'll see how to solve this
with integer optimization.

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Let's consider the rest
of the problem data.

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For example, we need to consider
the number of surgery teams

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from each department that
is available each day.

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We also need to consider the
maximum number of operating

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rooms required by each
department each day.

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Frequently, these
numbers are the same.

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For example, ophthalmology
requires at most two operating

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rooms every day.

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And we see that they
have two surgery

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teams available every day.

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However, let's look at
the case of oral surgery.

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They require at most one
operating room every day.

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However, the oral
surgeon is only

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present on Tuesdays
and Thursdays.

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Additionally, each department
has weekly requirements

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on the number of
operating rooms they need.

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For example, gynecology needs
to have at least 12 operating

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rooms in a given
week and at most 18.

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The traditional
way of doing this

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was not by using
integer optimization.

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Before integer optimization
was implemented

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at Mount Sinai in 1999,
the operating room manager

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used graph paper
and a large eraser

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to try to assign the
operating room blocks.

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Any changes that
were necessary were

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incorporated by trial and error.

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The operating room
manager made a draft,

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and this schedule was circulated
to all of the surgical groups.

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However, incorporating
feedback from one department

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usually meant altering another
group's schedule leading

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to many iterations
of this process.

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In the next video, we'll
design an integer optimization

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formulation for this problem.