THE INTERNATIONAL UNIVERSITY (IU) Course: MCDM
Department of Industrial System Engineering
FINAL EXAMINATION
MCDM Duration:
120 minutes
Head of School of Industrial Lecturer: Student ID: Date:
& Engineering Management 8 Jan, 2020
Name:
Dr. Nguyen Van Hop Phan Nguyen Ky Phuc
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 (30pts)
Given following problem:
max z 1=2 x 1+3 x 2
max z 2=3 x 1−x 2
Subject to
2 x1 −x2 ≥ 0
3 x 1−2 x 2 +1 ≥0
x 1+ 2 x 2−13 ≤ 0
x 1+ x2−9 ≤0
3 x 1−x 2−15 ≤0
Solve the problem for goal z 1 (10 pts)
MCDM-Final Exam 8,Jan, 2020 1
, THE INTERNATIONAL UNIVERSITY (IU) Course: MCDM
Department of Industrial System Engineering
Then the vertices of polyhedron is
(1,2) (3,5) (5,4) (6,3) (0,5)
max z 1=2 x 1+3 x 2
Insert into the objective function
(1,2)=> z 1=8
(3,5)=> z 1=21
(5,4)=> z 1=22
(6,3)=> z 1=21
(0,5)=> z 1=15
z1 obtains max at (5,4)
Solve the problem for goal z 2 (10 pts)
Then the vertices of polyhedron is
(1,2) (3,5) (5,4) (6,3) (0,5)
max z 2=3 x 1−x 2
Insert into the objective function
(1,2)=> z 2=1
(3,5)=> z 2=4
(5,4)=> z 2=11
(6,3)=> z 2=15
(0,5)=> z 2=−5
z2 obtains max at (6,3)
Use the compromise method to solve two goals at the same time (10 pts)
The compromise
MCDM-Final Exam 8,Jan, 2020 2
Department of Industrial System Engineering
FINAL EXAMINATION
MCDM Duration:
120 minutes
Head of School of Industrial Lecturer: Student ID: Date:
& Engineering Management 8 Jan, 2020
Name:
Dr. Nguyen Van Hop Phan Nguyen Ky Phuc
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 (30pts)
Given following problem:
max z 1=2 x 1+3 x 2
max z 2=3 x 1−x 2
Subject to
2 x1 −x2 ≥ 0
3 x 1−2 x 2 +1 ≥0
x 1+ 2 x 2−13 ≤ 0
x 1+ x2−9 ≤0
3 x 1−x 2−15 ≤0
Solve the problem for goal z 1 (10 pts)
MCDM-Final Exam 8,Jan, 2020 1
, THE INTERNATIONAL UNIVERSITY (IU) Course: MCDM
Department of Industrial System Engineering
Then the vertices of polyhedron is
(1,2) (3,5) (5,4) (6,3) (0,5)
max z 1=2 x 1+3 x 2
Insert into the objective function
(1,2)=> z 1=8
(3,5)=> z 1=21
(5,4)=> z 1=22
(6,3)=> z 1=21
(0,5)=> z 1=15
z1 obtains max at (5,4)
Solve the problem for goal z 2 (10 pts)
Then the vertices of polyhedron is
(1,2) (3,5) (5,4) (6,3) (0,5)
max z 2=3 x 1−x 2
Insert into the objective function
(1,2)=> z 2=1
(3,5)=> z 2=4
(5,4)=> z 2=11
(6,3)=> z 2=15
(0,5)=> z 2=−5
z2 obtains max at (6,3)
Use the compromise method to solve two goals at the same time (10 pts)
The compromise
MCDM-Final Exam 8,Jan, 2020 2
