# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2020/2021
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT ENGINEERING
Location:
Napoli
Disciplinary sector:
OPERATIONAL RESEARCH (MAT/09)
Credits:
6
Year of study:
2
Teachers:
Cycle:
Second semester
Hours of front activity:
48

Italian

### Course description

Objectives.
The course aims to provide the main concepts, models and tools of Operational Research that allow to solve a wide spectrum of complex decision problems.

Dublin descriptors.
Knowledge and understanding
The student must demonstrate knowledge and understanding of:
a) the main aspects of optimization problems;
b) the methodologies and software tools for solving optimization problems

Applying knowledge and understanding
The student must demonstrate to be able:
a) to know a set of methods and understand their use in different contexts;
b) to formulate problems analytically;
c) to select the most suitable methods for solving the problems;
d) to use software tools to solve decision problems.

Making judgments
The student must be able:
a) to know how to evaluate the resolution methodologies in relation to the considered problem;
b) to implement the most suitable algorithms needed for solving the problems

Communication skills
The student must have the ability to explain in a simple way the main methods of linear programming and the network models .

Learning skills
The student must be able to:
a) elaborate, organize, summarize the acquired course contents;
b) continuously update his/her knowledge by consulting texts and publications to solve decision making problems that are typical of Management Engineering.

### Prerequisites

Basics of linear algebra.

### Syllabus

Introduction to Operations Research (CFU 0.5 - 4 hours):
Decision problem solving, optimization and mathematical programming problems.
Continuous one-dimensional optimization problems (CFU 2 - 16 hours):
Main methods to solve one-dimensional nonlinear optimization problems (bisection method, Newton’s method and dichotomous research) (1.25 CFU - 10 hours).
Exercises in the classroom and in the computer lab (0.75 CFU - 6 hours).
Continuous linear optimization (CFU 2.5 - 20 hours):
Basics of linear algebra and polyhedral geometry; formulation of linear problems; graphic representation of a linear optimization problem (0.75 CFU - 6 hours).
Standard simplex algorithm; sensitivity analysis and BigM algorithm; post-optimal analysis (1 CFU - 8 hours).
Exercises in the classroom and in the computer lab (0.75 CFU - 6 hours).
Network optimization models (1 CFU - 8 hours):
Basic definitions of graph theory; the shortest-path problem: Dijkstra algorithm. Exercises.
Optimization of complex systems (3 CFU - 24 hours):
Nonlinear multidimensional optimization problems. Method of Lagrange multiplier. Karush-Kuhn-Tucker conditions (1.5 CFU - 12 hours).
Applications to complex system management (0.75 CFU - 6 hours).
Exercises in the classroom and in the computer lab (0.75 CFU - 6 hours)

The contents of lessons include the main methodologies to solve typical optimization problems of Operations Research. Particular attention is paid to main models and algorithms that allows to address a wide range of complex decision problems. The topics covered are: one-dimensional optimization, the fundamental elements of linear programming; the simplex method; the graphical analysis and geometric interpretation of the simplex method; post-optimal analysis; the formulation and resolution of linear optimization problems in Matlab; the network models; nonlinear multidimensional optimization; applications to complex system management.

### Teaching Methods

Lectures, exercises and laboratory sessions.

### Textbooks

Book
Hamdy A. Taha, Operations Research: An Introduction Prentice-Hall, Inc. Upper Saddle River, NJ, USA 2006

Notes and slides provided by teacher available on website:
http://edi.uniparthenope.it/course/index.php?categoryid=20

### Learning assessment

The objective of the exam is to check the level of achievement of the objectives previously indicated.
The exam is divided into two parts.
The first part is based on a question that requires to resolve numerical exercises with the aim of assessing whether the student is able to apply the methodologies studied during the course. The question includes the solution of exercises on the topics: nonlinear optimization, linear optimization, network optimization models, optimization for complex systems. It is mandatory for the student to pass the exercise part in order to continue the exam.
In the second part the level of knowledge of the topics covered during the course will be evaluated. This part typically consists of two questions, one dealing with linear optimization methods and one dealing with the remaining arguments of course.
The exam is usually completed in about 60 minutes. The final grade is the average value of the two grades achieved by the student in the two parts of the exam.