Lecture 25:
Hospital Scheduling
© J. Christopher Beck 2008
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Outline
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Healthcare & Scheduling
Operating room scheduling at Mt. Sinai
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Problem
Models
Results
© J. Christopher Beck 2008
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Readings
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Blake & Donald,
Mount Sinai Hospital Uses Integer
Programming to Allocate Operating
Room Time, Interfaces, pp 63-87,
32(2), 2002.
© J. Christopher Beck 2008
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Healthcare &
Scheduling
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A growth opportunity
for scheduling research
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Historically, much less
attention than
Staff scheduling (nurses,
manufacturing
doctors, orderlies)
Operating room scheduling
Patient scheduling
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operations, clinics, …
Therapy (e.g., radiation)
© J. Christopher Beck 2008
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Healthcare &
Scheduling
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Challenges
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Uncertainty
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Large, interacting systems
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ER, going into labour, complications in surgery,
…
The law of unintended consequences
Complex “people” constraints in a highstress job
Many stakeholders
© J. Christopher Beck 2008
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OR Room Scheduling
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How to allocate OR time among
different surgical specialties
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e.g., ophthalmology, gynecology, surgery,
oral surgery, …
Cyclical schedule
Number and type of ORs available
Assign specialties who will be given
priority at different times
© J. Christopher Beck 2008
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© J. Christopher Beck 2008
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3-Step Process
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Management: total number of OR hours
available
Nurse manager: # of template
schedules
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# of rooms and hours of opening each day
must meet total hours
must be feasible with nurses’ collective
agreement
© J. Christopher Beck 2008
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3-Step Process
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Nurse manager: using template, assign
available time to departments
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Competing objectives:
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hospital wants to reduce cost  fewer hours
doctors want to maximize income  more
hours
equity among surgical departments
© J. Christopher Beck 2008
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Constraints & Preferences
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One department per day
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share by assigning alternate weeks to
different departments
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i.e., alternate Mondays to different depts
Consistent schedule from week to week
Min/max bounds on number of blocks
assigned to each department in a given
day/week
© J. Christopher Beck 2008
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Model
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i – operating room type
j – department
k – day of week
xijk - # of blocks of type i assigned to
department j on day k
dik – duration of block i on day k
© J. Christopher Beck 2008
(long, short) X
(main, EOPS)
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Model
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Assign xijk such that the sum of the time
allocated for a department is equal to
their target number of hours
penalty for dept j
© J. Christopher Beck 2008
target time for dept j
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Model
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sj+ – amount of oversupply for dept j
sj- – amount of undersupply for dept j
© J. Christopher Beck 2008
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minimize penalty
allocated time ±
over/under supply
all available rooms are allocated
bounds on number of rooms
assigned to a dept in a day
© J. Christopher Beck 2008
bounds on number of specific type
of room assigned to a dept in a day
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bounds on number of specific type
of room assigned to a dept in a week
arbitrary bound on max.
under allocation
© J. Christopher Beck 2008
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Results
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Full production since 1997
Time to produce schedule reduced from
days to 1 or 2 hours
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OR manager’s time reduced saving
$20K/year
Faster scheduling  more alternatives
investigated  increased quality
Objective measure of quality
© J. Christopher Beck 2008
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Other Points
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Background section provides an
interesting description of how & why
the Canadian healthcare system is setup
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economic incentives, etc.
Political realities
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old process (p. 68)
objective criteria reduces conflict
© J. Christopher Beck 2008
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What Do I Have to Know
about this Paper?
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As this is a fairly simple, mostly nontechnical paper, you should have a
detailed understanding of both the
problem and the model
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I could give you an OR scheduling problem
and ask you to give me a MIP model for it
© J. Christopher Beck 2008
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