msci 332 presentation - minimizing elderly care wait list time
TRANSCRIPT
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NURSING CAREUsing optimization to minimize
w a i t l i s t t i m e
By Nor Hameed, Merisa Lee, Masa Shaban & Yahya Wahbeh
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Between 2005 and 2012, the median wait time for people trying to get into an Ontario nursing home almost tripled —from 36 to 98 days.
15% of people on nursing home wait lists die before they can be placed.
PROBLEM
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Life expectancy is steadily increasing due to improved health services and the retirement of baby boomers.
Projected number of Canadians over 65 in percentage
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DEMAND IS GOING UP FASTWhereas supply is going up a mere 3%
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HOW DO WE FIX THIS?
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Basic Deluxe Private
LicensedBeds
# on Waitlist
Average days
waiting
# on Waitlist
Average days waiting
# on Waitlist
Average days waiting
Cambridge Country Manor
79 6 55 0 34 0 26
Chateau Gardens Elmira
48 14 151 14 102 28 199
Columbia Forest Centre
156 79 672 0 0 79 580
Derbecker’sHeritage House
72 21 536 13 138 26 0
Fairview Mennonite
Home84 121 1352 0 0 70 1079
…
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22 elderly homes in four different cities within KW region
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Elmira(3)
Cambridge(8)
Waterloo(3)
Kitchener(8)
Split into 4 different clusters based on location
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Basic Deluxe Private
ClusterTotal #
available beds
# waitingAverage waiting
time# waiting
Average waiting
time# waiting
Average waiting
time
Cambridge 336 486 917 29 190 180 591
Kitchener 468 1178 917 85 331 912 679
Waterloo 108 268 677 2 168 311 1305
Elmira 60 36 357 12 127 12 171
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Objective function:
Minimize waiting time
0<x T<0.4*total capacityx B*c B + xD*cD + x P*c P <x T
c B + cD + c P = 1
subject to:
𝑖=0
2
𝑗=0
𝑛
𝐷𝑊𝑖𝑗
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M2M1
1AB0
W0
DW0
D0
0
AB1
W1
DW1
D1
ABi = average of available beds at year iWi = average number of waiting days at year iDWi = average days waiting per patient at year iDi = demand at year iMi = mortality at year i
XT
M0
2
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What percentage for new capacity added should we allocate each bed type?
? ? ?
Demand Capacity
xB
xD xP
xB
xD
xP
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Demand Mortality
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Thank you!