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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
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
Life expectancy is steadily increasing due to improved health services and the retirement of baby boomers.
Projected number of Canadians over 65 in percentage
DEMAND IS GOING UP FASTWhereas supply is going up a mere 3%
HOW DO WE FIX THIS?
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
…
22 elderly homes in four different cities within KW region
Elmira(3)
Cambridge(8)
Waterloo(3)
Kitchener(8)
Split into 4 different clusters based on location
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
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
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
What percentage for new capacity added should we allocate each bed type?
? ? ?
Demand Capacity
xB
xD xP
xB
xD
xP
Demand Mortality
Thank you!
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