# Mathematical Programming (ΣΕΕ3)

### General

School School of Science Department of Mathematics Graduate ΣΣΕ3 1 Mathematical Programming Lectures (Weekly Teaching Hours: 3, Credits: 7.5) Special Background - Greek Yes (in English) 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) 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
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.