Mathematical Programming (ΣΕΕ3)

Graduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΣΣΕ3
Semester	1
Course Title	Mathematical Programming
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The course learning outcomes are: the presentation of mathematical programming problems, the presentation of their solution techniques and their applications in several areas such as production, distribution, routing, etc. Upon successful completion of the course the student will be able to: model complex systems comprehend the mathematical foundation of the Simplex method and the dual theory select the appropriate algorithm for a particular optimization problem understand and apply the appropriate techniques required to solve linear optimization problems understand the principles of dynamic programming and apply dynamic programming solution techniques recognize and apply the appropriate inventory management policies (depending, each time, on underlying assumptions of the system)
General Competences	Working independently Decision-making Adapting to new situations Production of free, creative and inductive thinking Synthesis of data and information, with the use of the necessary technology Project planning and management

Syllabus

Linear programming problems formulation. The Simplex algorithm. Big M-method. Two-Phase method. Revised Simplex method. Duality theory. Dual Simplex algorithm. Sensitivity analysis. Parametric analysis. Transportation problem. Transhipment problem. Assignment problem. Dynamic programming: Bellman principle of optimality, finite and infinite horizon problems. Applications of dynamic programming. Inventory control.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology

Lindo/Lingo Software, Mathematica, Email, Class Web

Teaching Methods

Activity	Semester Workload
Lectures	39
Study and analysis of bibliography	78
Preparation of assignments and interactive teaching	70.5
Course total	187.5

Student Performance Evaluation

LANGUAGE OF EVALUATION: Greek
METHODS OF EVALUATION: Written work (30%), Final exam (70%).

Attached Bibliography

Καρακώστας, Κ. (2002). Γραμμικά Μοντέλα: Παλινδρόμηση και Ανάλυση Διακύμανσης. Πανεπιστήμιο Ιωαννίνων.
Λουκάς, Σ. (2014). Γενικό Γραμμικό Μοντέλο. Πανεπιστήμιο Ιωαννίνων.
Οικονόμου, Π. και Καρώνη, Χ. (2010). Στατιστικά Μοντέλα Παλινδρόμησης, Εκδόσεις Συμεών.
Draper, N.R. and H. Smith, (1998). Applied Regression Analysis, Third Edition, Wiley,
Searle, S.R., (1997). Linear Models, Wiley Classics Library, Wiley,
Seber, G.A.F. and A.J. Lee, (2003). Linear Regression Analysis, 2nd Edition, Wiley.