Operations Research ΙΙ

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Title: 
Operations Research ΙΙ
Course ID: 
ΓΕ0128
Course Description: 
Semester: 
7th
Διδάσκων: 
ΕCTS: 
5
Track course
Management Engineering
Track course
Financial Engineering
Description: 

 

The main contribution of operational research in management is the mathematical modeling of management problems in order to optimize the procedure of decision making. The course analyzes further the scientific area of mathematical programming by presenting some techniques and models that standardize product, management,, resource assignment, optimization of investment decisions, workflow programming, management of supply chain and other problems.

Specifically, the course deals with the following issues:

Introduction to Dynamic Programming, network ant equipment replacement problems, stochastic network problems, stochastic problems on replacing and maintaining equipment, assignment problems, optimal load, travel salesman problem, introduction to Integer Programming, branch and bound, methods of bounding the feasible region , introduction to non-linear programming, non-constrained and constrained (equality constrains) non-linear programming, Kuhn-Tucker conditions.

 

Module Contents (Syllabus):

 

  • Introduction to Dynamic Programming
  • A Prototype Example for Dynamic Programming
  • Optimal Policy-Shortest path problem in Dynamic Programming-Exercises
  • Dynamic Programming for equipment replacement
  • Resource allocation- Knapsack problem-Exercises
  • Stochastic shortest path problem -Exercises
  • Stochastic Dynamic Programming
  • Travel Salesman Problem-Exercises
  • Introduction to Integer Programming, Branch & Bound, Modeling Dynamic Programming problems-Exercises
  • Introduction to Non-Linear Programming: Problems without constraints-Exercises
  • Non-Linear Programming: Problems without equality constraints-Exercises
  • Νon-Linear Programming: Problems without inequality constraints, Kuhn-Tucker
  • Exercises in Non-linear Programming

 

 

 

Assessment methods: 

Midterm exam (optional) and final exams in Greek

Recommended Reading:

A)Suggested Bibliography

[Option 1] Εφαρμοσμένος Μαθηματικός Προγραμματισμός, 1η έκδ./2001, Βασιλείου Παναγιώτης – Χρήστος, Ζήτη Πελαγία & Σια Ι.Κ.Ε., Κωδικός Βιβλίου στον Εύδοξο: 11031. (in Greek)

[Option 2] Εισαγωγή στην Επιχειρησιακή Έρευνα, 11η έκδ./2022, Hillier Frederick S., Lieberman Gerald J., Διαμαντίδης Αλέξανδρος (Επιστ. Επιμέλεια), ΕΚΔΟΣΕΙΣ Α. ΤΖΙΟΛΑ & ΥΙΟΙ Α.Ε., Κωδικός Βιβλίου στον Εύδοξο: 102072205. (in Greek)

[Option 3] Εισαγωγή στην Επιχειρησιακή Έρευνα, 10η έκδ./2017, Taha A. Hamdy, ΕΚΔΟΣΕΙΣ Α. ΤΖΙΟΛΑ & ΥΙΟΙ Α.Ε., Κωδικός Βιβλίου στον Εύδοξο: 59415056. (in Greek)

[Option 4] Διοικητική Επιστήμη - Λήψη Επιχειρηματικών Αποφάσεων στην Κοινωνία της Πληροφορίας, 2η έκδ./2017, Πραστάκος Γρηγόρης Π., UNIBOOKS ΙΚΕ. Κωδικός Βιβλίου στον Εύδοξο: 68402209. (in Greek)

B)Additional Bibliography

 

  1. Operations Research – Applications and Algorithms, 3rd Edition, Winston W., Duxbury Press, 1994
  2. Dynamic programming : models and applications, E.V. Denardo, Englewood Cliffs, N.J. :Prentice-Hall, c1982,2003
  3. Integer Programming, Laurence A. Wolsey, ISBN: 978-0-471-28366-9, December 1998, Wiley.
  4. Nonlinear Programming, Dimitris P. Bertsekas, ISBN: 978-1-886529-05-2, 3rd Edition, Athena Scientific, Belmond, Massachusetts.

 

Εξεταστέα ύλη: 
  • Deterministic Model of Dynamic Programming
  • Optimal Policy-Shortest path problem in Dynamic Programming
  • Dynamic Programming for equipment replacement
  • Stochastic shortest path problem
  • Stochastic Dynamic Programming
  • Resource allocation- Knapsack problem
  • Travel Salesman Problem
  • Integer Programming, Branch & Bound, Modeling Dynamic Programming problems
  • Non-Linear Programming: Problems without constraints
  • Non-Linear Programming: Problems without equality constraints