# Matematica | OPERATIONS RESEARCH

## Matematica OPERATIONS RESEARCH

 0512300034 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2010 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/09 6 48 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 RAFFAELE CERULLI T FRANCESCO CARRABS
Objectives
Knowledge and understanding
Knowledge of the basic concepts of mathematical modeling of general decision problems. Knowledge of the basic methodologies to build a linear mathematical model. Knowledge of the basic tools for solving linear optimization problems with continuous variables. Knowledge of the basic concepts of network theory and graph theory and of the elementary algorithms for solving network optimization problems.

Applying knowledge and understanding
Knowledge of how to represent a simple optimization problem of process or decision using a linear mathematical model with continuous variables. Knowledge of how to solve linear mathematical programming problems. Knowledge of how to model simple problems using graphs and flow networks. Ability to solve simple network optimization problems.

Autonomy of judgment
Ability to assess and compare autonomously solutions of a mathematical problem of limited complexity.

Communication skills
Ability to organize themselves into working groups. Ability to communicate effectively in written and / or oral exam in English.

Learning skills
Ability to catalog, outline and revise the gained knowledge.
Prerequisites
Students should know basic concepts of mathematics analysis, discrete mathematics and linear algebra.
Contents
1. LINEAR PROGRAMMING (LP):
- ELEMENTAR OPERATIONS ON MATRICES AND VECTORS; POLIEDRONS; EXTREME DIRECTIONS, VERTICES; REPRESENTATION THEOREM; SIMPLEX METHOD: ESTREME POINTS, OPTIMALITY CONDITIONS. SIMPLEX METHOD ALGEBRA: INITIAL BASIC FEASIBLE SOLUTION, TWO-PHASES METHOD, BOG-M METHOD, SIMPLEX CONVERGENCY.
- DUALITY: DUAL PROBLEM FORMULATIN, REDUCED COSTS, THEOREM OF WEAK DUALITY, THEOREM OF STRONG DUALITY, COMPLEMENTARY SLACKNESS CONDITIONS, PRIMAL-DUAL RELATIONECOPNOMIC INTREPRETATION OF DUALITY.
- SENSITIVITY ANALYSIS: POST-OPTIMALITY ANALYSIS, OPTIMUM POINT VARIATION, OPTIMUM SOLUTION VALUE VARIATION.

2. NETWORK OPTIMIZATION:
- SHORTHEST PATH PROBLEMS, MAX FLOW PROBLEM, TRANSPORTATION PROBLEM, MINIMUM SPANNING TREE PROBLEM, ASSIGNEMENT PROBLEM.
Teaching Methods