# Operational Research (Engineering Courses)

## Objectives

In this course Engineering students are introduced to the first concepts of Operations Research. The course will introduce students to the following O.R. subjects: Linear Programming, Project Management, Decision Theory and Simulation.

## General characterization

10361

6.0

##### Responsible teacher

Manuel Valdemar Cabral Vieira

##### Hours

Weekly - 4

Total - Available soon

Português

### Prerequisites

Students should have strong knowledge of Probability Theory and matricial calculus.

### Bibliography

1. F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, 2015, 10ª Ed., McGraw-Hill.

2. L. V. Tavares, F. N. Correia, I. H.l Themido e R. C. Oliveira, Investigação Operacional, 1996, McGraw-Hill.

3. Wayne L. Winston, Operations Research, 2003, Duxbury Press.

### Teaching method

Basic concepts will be introduced in lectures ("aulas teóricas") and problems will be solved in problem solving classes ("Aulas práticas").

### Evaluation method

Students should attend at least 2/3 of the practical lessons.There are 2 Tests during the semester and one Exam afterwards.

For further information, you should contact Prof. Manuel Vieira, mvcv@fct.unl.pt .

## Subject matter

1.

Introduction to Linear Programming
 1.1. Linear Programming Formulations 1.2. The Simplex method 1.3. The Revised Simplex method 1.4. Duality
1.5.   Sensitivity Analysis
2.
Project Management
 2.1. Critical Path Method 2.2. Construction of the Time Chart and Resource Leveling 2.3. Reduction of the project duration 2.4. PERT technique

3.
Decision Theory
 5.1. Decisions under risk and under uncertainty 5.2. Utility. Introduction to the multicriteria decision 5.3. Decision Trees

4.
Simulation
 4.1. Generating random numbers: mixed congruential method, inverse transformation, acceptance-rejection method 4.2. Duration of the simulation/Results precision 4.3. Applications: project management, inventory management, Markov chains, models of visual simulation, introduction to the simulation of queuing systems

## Programs

Programs where the course is taught: