THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Industrial System Engineering
MIDTERM EXAMINATION
MCDM Duration:
120 minutes
Head of School of Industrial Lecturer: Student ID: Date:
& Engineering Management 6 Nov, 2019
Name:
Dr. Nguyen Van Hop
INSTRUCTIONS:
1. This is an open book examination. No laptops, PDA.
2. Use of calculator is allowed; discussion and material transfer are strictly prohibited.
Total pages: 2 (including this page)
PART I (100 %)
Question 1 (25pts)
A company want to identify which one among 4 designs namely, A, B, C, D are most preferred to come
up with the final selections. To obtain this, the company want to use the pairwise comparison to facilitate
the survey process. The final table is given as follows:
A B C D
A _ 1/5 1/5 1
B _ 1/3 5
C _ 9
D _
a) Using AHP approach to find the final weight of each design based on the above table (15pts)
The full matrix of the question above
MCDM-Midterm Exam 6,Nov, 2019 1
, THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Industrial System Engineering
A B C D
A 1 1/5 1/5 1
B 5 1 1/3 5
C 5 3 1 9
D 1 1/5 1/9 1
Sum 12 4.4 1.64 16
The eigen vector
Eig=[0.08 0.29 0.57 0.06]
Base on the result of eigen vector
w A=0.08, w B =0.29, w C =0.57 ,w D =0.06
b) Check the consistency ratio of the final result (7pts)
The λ max=0.08∗12+0.29∗4.4 +1.64∗0.57+0.06∗16=4.18
The consistency ratio
λmax −n
CI = =0.06
n−1
The survey result is consistent
c) Now assume that instead of directly pairwise comparison like the above, the company now add
more one layer of criteria between goal and alternatives. There are 3 criteria in this layer namely,
X, Y and Z. How many matrix of pairwise comparison need to be surveyed, the size of each matrix
and their meaning.(7pts)
From the view of Goal : it requires one 3x3 matrix to make pairwise comparisons among X,Y,Z
From the view of X : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
From the view of Y : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
From the view of Z : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
Question 2 (30pts)
Given the following alternatives and its respecting criterion as following tables:
C1 C2 C3 C4
A1 5 2 4 5
A2 6 8 7 4
A3 7 5 4 7
A4 3 6 8 6
Weight 0.35 0.25 0.25 0.15
MCDM-Midterm Exam 6,Nov, 2019 2
Department of Industrial System Engineering
MIDTERM EXAMINATION
MCDM Duration:
120 minutes
Head of School of Industrial Lecturer: Student ID: Date:
& Engineering Management 6 Nov, 2019
Name:
Dr. Nguyen Van Hop
INSTRUCTIONS:
1. This is an open book examination. No laptops, PDA.
2. Use of calculator is allowed; discussion and material transfer are strictly prohibited.
Total pages: 2 (including this page)
PART I (100 %)
Question 1 (25pts)
A company want to identify which one among 4 designs namely, A, B, C, D are most preferred to come
up with the final selections. To obtain this, the company want to use the pairwise comparison to facilitate
the survey process. The final table is given as follows:
A B C D
A _ 1/5 1/5 1
B _ 1/3 5
C _ 9
D _
a) Using AHP approach to find the final weight of each design based on the above table (15pts)
The full matrix of the question above
MCDM-Midterm Exam 6,Nov, 2019 1
, THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Industrial System Engineering
A B C D
A 1 1/5 1/5 1
B 5 1 1/3 5
C 5 3 1 9
D 1 1/5 1/9 1
Sum 12 4.4 1.64 16
The eigen vector
Eig=[0.08 0.29 0.57 0.06]
Base on the result of eigen vector
w A=0.08, w B =0.29, w C =0.57 ,w D =0.06
b) Check the consistency ratio of the final result (7pts)
The λ max=0.08∗12+0.29∗4.4 +1.64∗0.57+0.06∗16=4.18
The consistency ratio
λmax −n
CI = =0.06
n−1
The survey result is consistent
c) Now assume that instead of directly pairwise comparison like the above, the company now add
more one layer of criteria between goal and alternatives. There are 3 criteria in this layer namely,
X, Y and Z. How many matrix of pairwise comparison need to be surveyed, the size of each matrix
and their meaning.(7pts)
From the view of Goal : it requires one 3x3 matrix to make pairwise comparisons among X,Y,Z
From the view of X : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
From the view of Y : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
From the view of Z : it requires one 4x4 matrix to make pairwise comparisons among alternatives
A,B,C, D
Question 2 (30pts)
Given the following alternatives and its respecting criterion as following tables:
C1 C2 C3 C4
A1 5 2 4 5
A2 6 8 7 4
A3 7 5 4 7
A4 3 6 8 6
Weight 0.35 0.25 0.25 0.15
MCDM-Midterm Exam 6,Nov, 2019 2
