© j. christopher beck 20081 lecture 25: hospital scheduling
TRANSCRIPT
© J. Christopher Beck 2008 2
Outline Healthcare & Scheduling Operating room scheduling at Mt.
Sinai Problem Models Results
© J. Christopher Beck 2008 3
Readings
Blake & Donald,Mount Sinai Hospital Uses IntegerProgramming to Allocate Operating Room Time, Interfaces, pp 63-87, 32(2), 2002.
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Healthcare & Scheduling
A growth opportunityfor scheduling research Staff scheduling (nurses,
doctors, orderlies) Operating room scheduling Patient scheduling
operations, clinics, … Therapy (e.g., radiation)
Historically, much lessattention than manufacturing
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Healthcare & Scheduling
Challenges Uncertainty
ER, going into labour, complications in surgery, …
Large, interacting systems The law of unintended consequences
Complex “people” constraints in a high-stress job
Many stakeholders
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OR Room Scheduling
How to allocate OR time among different surgical specialties 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
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3-Step Process
Management: total number of OR hours available
Nurse manager: # of template schedules # of rooms and hours of opening each
day must meet total hours must be feasible with nurses’ collective
agreement
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3-Step Process
Nurse manager: using template, assign available time to departments Competing objectives:
hospital wants to reduce cost fewer hours
doctors want to maximize income more hours
equity among surgical departments
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Constraints & Preferences
One department per day share by assigning alternate weeks to
different departments 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
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Model
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
(long, short) X (main, EOPS)
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Model
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 target time for dept j
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Model
sj+ – amount of oversupply for dept j
sj- – amount of undersupply for dept j
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minimize penalty
allocated time ± over/under supply
all available rooms are allocated
bounds on number of roomsassigned to a dept in a day
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
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Results
Full production since 1997 Time to produce schedule reduced
from days to 1 or 2 hours OR manager’s time reduced saving
$20K/year Faster scheduling more alternatives
investigated increased quality Objective measure of quality
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Other Points
Background section provides an interesting description of how & why the Canadian healthcare system is set-up economic incentives, etc.
Political realities old process (p. 68) objective criteria reduces conflict