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 𝑧1 = 2𝑥1 + 3𝑥2
max 𝑧2 = 3𝑥1 − 𝑥2
Subject to
2𝑥1 − 𝑥2 ≥ 0
3𝑥1 − 2𝑥2 + 1 ≥ 0
𝑥1 + 2𝑥2 − 13 ≤ 0
𝑥1 + 𝑥2 − 9 ≤ 0
3𝑥1 − 𝑥2 − 15 ≤ 0
Solve the problem for goal 𝑧1 (10 pts)
Solve the problem for goal 𝑧2 (10 pts)
Use the compromise method to solve two goals at the same time (10 pts)
MCDM-Final Exam 8,Jan, 2020 1
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 𝑧1 = 2𝑥1 + 3𝑥2
max 𝑧2 = 3𝑥1 − 𝑥2
Subject to
2𝑥1 − 𝑥2 ≥ 0
3𝑥1 − 2𝑥2 + 1 ≥ 0
𝑥1 + 2𝑥2 − 13 ≤ 0
𝑥1 + 𝑥2 − 9 ≤ 0
3𝑥1 − 𝑥2 − 15 ≤ 0
Solve the problem for goal 𝑧1 (10 pts)
Solve the problem for goal 𝑧2 (10 pts)
Use the compromise method to solve two goals at the same time (10 pts)
MCDM-Final Exam 8,Jan, 2020 1
