1	Course Title:	MATHEMATICAL PROGRAMMING
2	Course Code:	END 5101
3	Type of Course:	Compulsory
4	Level of Course:	Second Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	7,5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Doç. Dr. Fatih ÇAVDUR
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	hco@uludag.edu.tr 294-2082 Endüstri Mühendisliği Bölümü Görükle Bursa
18	Website:
19	Objective of the Course:	The objective of the course is to provide students with the Linear Algebra concepts and theorems that provide the basis for linear programming. After a brief review of undergraduate level methodologies, graduate level methods are conveyed to increase the level of knowledge
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Ability to understand the contraints and objective functions for various problems; 2 Ability to choose the most suitable optimization algorithm for real-life problems ; 3 Ability to understand the linear algebra and other mathematical theorems that provide the basis for optimization methodologies; 4 Ability to understand and build mathematical models of complex real life systems; 5 Ability to follow and present current Industrial Engineering literature;

22	Course Content:

Week	Theoretical	Practical
1	Fundamentals of linear programming, convexity and review of linear algebra
2	Mathematical models for linear programming
3	Finding solutions using graphicall approach and sensitivity
4	Simplex algorithm
5	Duality theorem and sensiivity analysis
6	M-method, two-phase method, artificial variable methods
7	Network models, uni-modularity
8	Network models and solution metholodlogies (shortest route, spanning tree, maximum flow, minimum cost capacity flow)
9	Repeating courses and midterm exam
10	Integer Linear Programming
11	Integer Linear Programming Algorithms (Branch-and-Bound, Cutting Plane)
12	Simplex method for the bounded variables
13	Nonlinear optimizastion
14	Project presentations

23	Textbooks, References and/or Other Materials:	1. Bazaraa, S.M., Jarvis, J.J. and Sherali, H.D., Linear Programming and Network Flows, Second edition, Wiley, 1990. 2. Strang, G., Linear Algebra and Its Applications, Third Edition, Saunders HBJ, 1998. 3. Peressini, A.L., Sullivan F.E., and Uhl, J.J.,Jr. The Mathematics of Nonlinear Programming, Springer – Verlag, 1998.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	30
Quiz	0	0
Homeworks, Performances	2	20
Final Exam	1	50
Total	4	100
Contribution of Term (Year) Learning Activities to Success Grade		50
Contribution of Final Exam to Success Grade		50
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	13	10	130
Homeworks, Performances	2	7	14
Projects	1	36	36
Field Studies	0	0	0
Midtermexams	1	3	3
Others	0	0	0
Final Exams	1	3	3
Total WorkLoad			228
Total workload/ 30 hr			7,6
ECTS Credit of the Course			7,5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 PQ11 PQ12 PQ13 LO1 5 5 4 0 0 0 0 0 0 0 0 0 0 LO2 5 5 4 0 0 3 3 0 3 0 0 0 0 LO3 5 5 4 0 0 0 0 0 0 0 0 0 0 LO4 0 0 3 3 2 5 5 5 5 5 0 5 0 LO5 0 0 3 3 2 5 5 5 5 5 0 5 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High