## Operational Research I NTUA

## Operational Research I (6th semester – compulsory), National Technical University of Athens – School of Mechanical Engineering

### COURSE DESCRIPTION

The objective of Operational Research is to help engineers solve practical problems by developing relevant mathematical models. Moreover, these models are used for selecting the optimum out of a set of potential solutions. During the course Operational Research I, students get familiar with specific type of operational research problems, learn how to model them and optimise their solutions.

The course is divided into two streams. The first one concerns Linear Programmimg (Model Formulation, Graphical Solution, Simplex Method), Sensitivity Analysis, Transportation Problems and Assignment Problems. The second part of the course concerns quantitative techniques in Project Management (CPM/PERT - Schedule/Cost Optimization), Monte Carlo Simulation, Shorter Route problems, Minimum Spanning Tree problems and Multi Criteria Decision Analysis.

### LEARNING OBJECTIVES

By the end of this course, students will be able to:

- Model a Linear Programming problem and solve it.
- Use the Simplex method
- Use and understand sensitivity analysis
- Model and solve Transportation problems
- Model and solve Assignment problems
- Calculate the duration of a project using the deterministic technique CPM.
- Calculate the duration of a project using the stochastic technique PERT.
- Optimise Schedule/Cost parameters in projects.
- Use Monte Carlo Simulation and interpret results.
- Model and solve Shorter Route problems.
- Model and solve Minimum Spanning Tree problems.
- Understand Multi Criteria Decision Analysis.

The course is based on the following books:

**Πραστάκος, Γ. 2006, Διοικητική Επιστήμη: Λήψη επιχειρησιακών αποφάσεων στην κοινωνία της πληροφορίας, Εκδόσεις Σταμούλη, Αθήνα.**

Bronson, R and Naadimuthu, G. 2010, *Schaums's Επιχειρησιακή Έρευνα*, Εκδόσεις Κλειδάριθμος, Αθήνα .

Suggested bibliography:

Taylor, B. 2007, *Introduction to Managment Science*, Prentice Hall, USA.

Course handouts.

### USEFUL FILES - ANNOUNCEMENTS

For files - announcements related to the course please visit this link (available only in greek)

Lecture notes for the minimum spanning tree problem (πρόβλημα ελάχιστα εκτεταμένου δένδρου).

Lecture notes for the shortest path problem (πρόβλημα συντομότερης διαδρομής).

Lecture notes for the maximum flow problem (πρόβλημα μέγιστης ροής).

Lecture notes for the travelling salesman problem (πρόβλημα περιοδεύοντος πωλητή)

Lecture notes for the analytic hierarchy process (AHP - αναλυτική ιεραρχική διεργασία)