© j. christopher beck 20081 lecture 25: hospital scheduling

© J. Christopher Beck 2008 1

Lecture 25: Hospital Scheduling


Outline Healthcare & Scheduling Operating room scheduling at Mt.

Sinai Problem Models Results


Readings

Blake & Donald,Mount Sinai Hospital Uses IntegerProgramming to Allocate Operating Room Time, Interfaces, pp 63-87, 32(2), 2002.


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


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


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


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


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


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


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)


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


Model

sj+ – amount of oversupply for dept j

sj- – amount of undersupply for dept j


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


bounds on number of specific type of room assigned to a dept in a week

arbitrary bound on max. under allocation


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


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


What Do I Have to Know about this Paper?

As this is a fairly simple, mostly non-technical paper, you should have a detailed understanding of both the problem and the model I could give you an OR scheduling

problem and ask you to give me a MIP model for it

© j. christopher beck 20081 lecture 25: hospital scheduling

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