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 Programing
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)	-

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

Suggested bibliography:

1. Bellman, R.E.. Dynamic Programming, Princeton University Press, 1957, Princeton, NJ. Republished 2003
2. Bertsekas D.P. Dynamic Programming and Optimal Control, Vols I and II, Athena Scientific, 1995, (3rd Edition Vol. I, 2005, 4th Edition Vol. II, 2012),
3. Bertsimas D. and J.N. Tsitsiklis Introduction to Linear Optimization, Athena Scientific 1997.
4. Gass S. Linear Programming Methods and Applications, McGraw-Hill 1985
5. Hadley G. Linear Programming, Addison-Wesley Publishing Company, INC, 1965
6. Taha H., Επιχειρησιακή Έρευνα Εκδόσεις Α. Τζιολα & ΥΙΟΙ Α.Ε., 2011
7. Hillier F.S. and G.J. Lieberman Introduction Operations research. The McGraw-Hill Companies, 2001
8. Johnson L. A. and D. C Douglas, Operations research in production planning scheduling and inventory control. John Willey and Sons, New-York, 1974
9. Silver E. A., D.F. Pyke and R. Peterson, Inventory Management and Production Planning and Scheduling. John Willey and Sons, New-York, 3rd Edition, 1998
10. Tersine R.J., Principles of inventory and material management, Prentice Hall International Inc, New Jersey, 4rd Edition, 1994
11. Wagner H.M and T.M Within (1958) Dynamic version of the economic lot size model. Management Science, 5(1), 89-96
12. Winston W.L., Operations Research (Applications and algorithms), Duxbury Press (International Thomson Publishing) 1994.
13. Βασιλειου Π. και Τσαντας Ν., Εισαγωγή στην επιχειρησιακή έρευνα, Εκδόσεις ΖΗΤΗ 2000.
14. Κολετσος Ι., και Στογιαννης Δ. Εισαγωγή στην επιχειρησιακή έρευνα, Εκδόσεις Συμεών, 2012.
15. Κουνιας Σ. και Φακινος Δ., Γραμμικός Προγραμματισμός, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη 1999.
16. Λουκακης M., Επιχειρησιακή έρευνα γραμμικός προγραμματισμός, Εκδοτικό Κέντρο Βορείου Ελλάδας, 1994.
17. Παπαρριζος Κ., Γραμμικός Προγραμματισμός. Εκδόσεις Ζυγός, Θεσσαλονίκη 1999.
18. Σισκος Γ., Γραμμικός Προγραμματισμός, Εκδόσεις Νέων Τεχνολογιών, Αθήνα 1998.
19. Φακινου Δ. και Οικονόμου Α., Εισαγωγή στην επιχειρησιακή έρευνα - Θεωρία και Ασκήσεις, Αθήνα 2003.

Related academic journals:

1. Mathematical Programming Journal, Series A and Series B
2. INFORMS Transactions on Education (ITE)
3. Interfaces

Related academic journals: