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!