AHP - TWO DIMENSIONAL COST BENEFIT

1. THE HOSPICE PROBLEM (BY T.L. SATY) SOLVED USING 2 DIMENSIONS (BENEFIT AND COST) USING AHP
To choose the best of the alternatives for terminally ill patient by the county hospital of Pensylvania from the standpoint of the patient, the hospital, the community, and society at large.
Decision is given based on costs and benefits and benefit to cost ratio for each alternative is identified . Here risk factor is not considered
Benefits Costs Models
Recepient
Physical
Direct care
Commun
ity Model 1 Model II Model III
Palliative care
The hospital provided full care to the patients
The family cares for the
patient at home and the
hospital provides only
emergency treatment
The hospital and the home share
patient care Formulas used : To make the
matrix normalized the following
steps were carried out
Recipient Benefit Cell = Cell
value/sum of that column
Weight – average of each row
WS = cell value of each criteria in
the original matric * weight in
each cell of the column(Weight
sums vector) Consis/Lambda =
WS*1/W CI = (λmax -n)/n-1 CR
= CI/R,I RI value to be taken
from external source
Psycho-social
Volunteer
support
Instituti
onal
Capital
0.43 0.12 0.45
Post death
distress relief
Decision making
Emotional
support
Plausible questions
Whether institutional benefit should be accorded more benefit than societal or
recipient benefit
Family
networking
Which criterion is a more important determinant of the cost or benefit of a hospice
model?
Guilt
alleviation Finally from the best of the alternatives finding Benefit to Cost ratio
Economic
Reduced Cost
Operating
THE SOLUTION
Bad Debt
Matrix 1 -Judgment matrix for the criteria of the benefits hierarchy
Institutio
nal
Psycho-social
Publicity and
Public relations
Choosing best hospice
Recipient
benefits
Institutio
nal
benefits
Social
benefit
s
Prioritie
s
Normali
zed
Recipie
nt
benefits
Institutiona
l benefits Weights
Weight
sums
vector 1/W
Consi
s/La
mbda
Volunteer
recruitment
Professional
recruitment Recipient benefits 1 3 5 0.64 0.65 0.69
0.63
1.94 1.58 3.07
Economic
Reduced length
of stay
Education
Community Institutional benefits 0.33 1 3 0.26 0.22 0.23
0.26
0.79 3.85 3.03
Optimum
utilization of
resources Training staff Social benefits 0.20 0.33 1 0.11 0.13 0.08
0.11
0.32 9.43 3.01
Professional
recruitment
and support
Recruitment
Volunteers Sum 1.53 4.33 9 1 1
Societal
Rehumanizatio
n of medical
and health instt Staff
Lamb
da 3.03
Death as a
social issue
Societal
Consistency index(Matrix 1) 0.02
Normalized
Consistency ratio(Matrix 1)
0.03
CR = CI/RI

2. Matrix 2 -Judgment of subcriteria with respect to institutional benefits Normalized Matrix 2 -Judgment of subcriteria with respect to institutional benefits
stitutional
enefits
Psycho-
social Economic Priorities
Institutional
benefits
Psycho-
social Economic
Weight
s (W) WS 1/W
Consis/L
ambda
sycho-social 1.00 7.00 0.88 Psycho-social 0.88 0.88 0.88 1.75 1.14 2
conomic 0.14 1.00 0.13 Economic 0.13 0.13 0.13 0.25 8.00 2
um 1.14 8 Sum 1.00 1.00 Lambda 2
Consistency
index(Matrix
2) 0
atrix 3 -Relative benefits of the models with respect to direct care of patients
Consistency
ratio(Matrix
2) 0
Column
Stochas
tic
irect care of
atient Model I Model II Model III Priorities
odel I: Unit
am 1.00 5.00 3.00 0.64 Normalized
Matrix 3 -Relative benefits of the models with respect to direct care of patients
odel II:
ixed/home
are 0.20 1.00 0.33 0.10
Direct care of
patient Model I Model II
Model
III Weights WS 1/W
Consis/La
mbda
odel III: Case
anagement 0.33 3.00 1.00 0.26
Model I: Unit
team 0.65 0.56 0.69 0.63 1.95 1.58 3.07
um 1.53 9.00 4.33
Model II:
Mixed/home
care 0.13 0.11 0.08 0.11 0.32 9.42 3.01
Matrix 4 - Cost alternative decision
Model III:
Case
management 0.22 0.33 0.23 0.26 0.79 3.84 3.03
Community
Costs
Institutional Costs
Societal
Costs
Priorities
Sum 1 1 1 Lambda 3.04
ommunity
osts 1 0.20 1 0.14
Consistency
index(Matrix
3) 0.02
stitutional
osts 5 1 5 0.71
Consistency
ratio(Matrix
3) 0.037
ocietal costs 1 0.20 1 0.14 Normalized
um 7 1.4 7 Matrix 4
Community
Costs
Institutiona
l Costs
Societa
l Costs Weights WS 1/W
Consis/La
mbda
Community
costs 0.14 0.14 0.14 0.14 0.42 7.00 2.97
Institutional
costs 0.71 0.71 0.71 0.71 2.12 1.41 2.99
Societal costs 0.14 0.14 0.14 0.14 0.42 7.14 3.03
Consistency
index(Matrix
4) 0.00 Lambda 3.00
atrix 5 - Finding the priority of the costs impacting the decision making
Consistency
ratio(Matrix
4) 0.00

3. Matrix 5 - Finding the priority of the costs impacting the decision making
Institutional
costs Capital Operating
Educatio
n Bad Debt Recruitment Priorities Normalized
Institutio
nal costs
Capit
al
Operat
ing
Educatio
n
Bad
Debt
Recruit
ment Weights 1/W
Consis/
Lambda
Capital 1 0.14 0.14 0.14 1 0.05 Capital 0.05 0.08 0.01 0.02 0.09 0.04 23.72 1.49
Operating 7 1.00 9.00 4.00 5 0.57
Operatin
g 0.35 0.59 0.68 0.67 0.45 0.57 1.75 1.04
Education 4 0.11 1.00 0.50 1 0.01
Educatio
n 0.20 0.07 0.08 0.08 0.09 0.11 9.41 0.73
Bad debt 7 0.25 2.00 1.00 3 0.21 Bad debt 0.35 0.15 0.15 0.17 0.27 0.20 4.90 0.83
Recruitmen
t 1 0.20 1.00 0.33 1 0.07
Recruitm
ent 0.05 0.12 0.08 0.06 0.09 0.07 13.37 1.28
Sum 20.00 1.70 13.14 5.98 11.00
Consiste
ncy
index(Ma
trix 5) -0.73 1.07
Matrix 6 Finding the alternative from models with respect to recruitment under
institutional cost
Consiste
ncy
ratio(Mat
rix 5)
-
0.658
9511
05 = 0
Model I Model II Model III Priorities Normalized
Model I Model II
Model III Weights 1/W WS
Consis/
Lambda
Model I:
Unit team 1.00 5.00 3.00 0.64
Model I:
Unit team 0.65 0.56 0.69 0.63 1.58 1.95 3.07
Model II:
Mixed/ho
me care 0.20 1.00 0.33 0.10
Model II:
Mixed/ho
me care 0.13 0.11 0.08 0.11 9.42 0.32 3.01
Model III:
Case
manageme
nt 0.33 3.00 1.00 0.26
Model III:
Case
manageme
nt 0.22 0.33 0.23 0.26 3.84 0.79 3.03
Sum 1.53 9.00 4.33
Consistenc
y
index(Matr
ix 6) 0.02 3.04
Consistenc
y
ratio(Matr
ix 6) 0.03
Result Summary
As discussed in the 1st slide

4. 0.02 0.64 0.01 0.10 0.00 0.26 0.01 0.64 1.00 0.02 0.16 0.41
0.14 0.64 0.09 0.10 0.01 0.26 0.04 0.64 1.00 0.14 0.16 0.41
0.02 0.09 0.00 0.17 0.00 0.74 0.01 0.74 0.12 0.27 0.02 1.00
0.06 0.46 0.03 0.22 0.01 0.32 0.02 0.46 1.00 0.06 0.34 0.70
0.12 0.30 0.04 0.08 0.01 0.62 0.07 0.62 0.48 0.13 0.12 1.00
0.21 0.30 0.06 0.08 0.02 0.62 0.13 0.62 0.48 0.13 0.21 1.00
0.03 0.30 0.01 0.08 0.00 0.62 0.02 0.62 0.48 0.13 0.03 1.00
0.01 0.12 0.00 0.65 0.01 0.23 0.00 0.65 0.18 1.02 0.01 0.35
0.03 0.12 0.00 0.27 0.01 0.61 0.02 0.61 0.20 0.42 0.03 1.00
0.19 0.63 0.12 0.08 0.02 0.29 0.06 0.63 1.00 0.12 0.13 0.46
0.03 0.64 0.02 0.10 0.00 0.26 0.01 0.64 1.00 0.02 0.16 0.41
0.06 0.65 0.04 0.23 0.01 0.12 0.01 0.65 1.00 0.04 0.36 0.18
0.01 0.26 0.00 0.10 0.00 0.64 0.01 0.64 0.41 0.16 0.01 1.00
0.02 0.09 0.00 0.22 0.00 0.69 0.01 0.69 0.13 0.34 0.02 1.00
0.000 0.73 0.00 0.08 0.00 0.19 0.00 0.73 1.00 0.00 0.13 0.26
0.02 0.20 0.00 0.20 0.00 0.60 0.01 0.60 0.33 0.31 0.02 1.00
0.08 0.24 0.02 0.14 0.01 0.62 0.05 0.62 0.39 0.22 0.08 1.00
0.14 0.33 0.33 0.33 1 1 1
0.03 0.76 0.09 0.15 1 0.12 0.2
0.4 0.73 0.08 0.19 1 0.11 0.26
0.01 0.65 0.24 0.11 1 0.37 0.17
0.06 0.56 0.32 0.12 1 0.57 0.21
0.15 0.6 0.2 0.2 1 0.33 0.33
0.05 0.66 0.17 0.17 1 0.26 0.26
0.01 0.6 0.2
Distributive mode Ideal Mode
Models
Priorities 1 1"" (Validating) 2 2""(Validating) 3 3"(Validating) MaxBenefits
Synthesis
Costs
Synthesis
1 1" 2 2 " 3" 3
0.43 0.45 0.12 0.13 0.45 0.47 0.43 0.40 0.12 0.01 0.54 0.45
0.58 0.19 0.22 0.52 0.23 0.25
0.73 0.63 0.81 0.54
Direct care of patien
Palliative care
Volunteer support
Networking in fami
Relief of post death s
Emotional support o f a p
Alleviation of guilt
Reduced economic c f p
Improved productiv
Publicity and public r
Volunteer recruitme
Professional recruit a s
Reduced length of s
Better utilization of r
Increased monetary s
Death as a social iss
Rehumanization of i
Community costs
Institutional capital c
Institutional operati c
Institutional costs fo e t c
Institutional costs fo t s
Institutional bad de
Institutional costs o r s
Institutional costs o r v
Societal costs
Benefit/cost ratio
0.2 1 0.33 0.33
0.15 0.33 0.33 0.33 1 1 1
2.01 1.82
Distributive Mode - Existence of dependencies among criteria . Each row sums to 1considering the models The final
synthesis happens by multiplying weights to priorities and adding the sum.
Ideal Mode – One of the alternative is the best and is assigned a 1 and the rest is similar as in Distributive mode. Benefit and
Cost are assessed and Benefit to Cost Ratio shows model 3 is better.