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OPERATIONAL RESEARCH (502SM)

A.Y. 2020 / 2021

Professor 
Period 
First semester
Credits 
6
Duration/Length 
48
Type of Learning Activity 
Related/additional subjects
Study Path 
[PDS0-2018 - Ord. 2018] common
Mutuazione 
Mutuato: IN05 - 035IN - RICERCA OPERATIVA
Syllabus 
Teaching language 

Italian

Learning objectives 

Knowledge and understanding: capability of understanding (a) the conceptual approach of Operations Research as a tool for formulating, solving and evaluating decision-makimg problems related to complex systems, (b) the methodologies for the formalization of quantitative models and algorithmic solutions, and (c) the theoretical aspects underlying the solution techniques, their mathematical justifications and their implications and applicative potentialities.

Applying knowledge and understanding: capability of actually applying the solution techniques and algorithms, by executing the necessary procedures to attain the solution of numerical problems and being able to critically analyze the solutions obtained.

Making judgments: capability of applying the acquired knowledge to autonomously formulate quantitative models and solve the associated optimization problems, by also manually executing the appropriate solution algorithms.

Communication skills: capability of introducing decision-making problems and their possible solutions, both in written and oral form, and to critically discuss the validity and the limits of formulations and solutions.

Learning skills: capability of gathering information from textbooks, scientific papers and other material for the formulation and autonomous solution of decision-making problems.

Prerequisites 

Knowledge of the linear algebra formalism (vectors, matrices, their operations and space representations) and of the graph theory (classification, properties, trees, paths, circuits) can favor the understanding. However, it is not an essential condition.

No strict prerequisite.

Contents 

1. Introduction to Operations Research
Decision problems
Application areas (Activity management, resource planning and management. manufacturing, logistics & transportation, economy, finance, healthcare services, public administration)

2. Linear programming (LP)
Properties, characteristics and applicability of LP.
LP models formulation: decision variables, objective, constraints.

Geometric interpretation for problems in two dimensions.
Geometric solution.
Possible outcomes for a PL problem: feasibility, unique and multiple optimality.

Algebraic formulation.
Standard form, slack and surplus variables.
Generality of the standard form.

Simplex method.
Base solution. Basic and non basic solutions.
Optimality criterion
Improvement of a non optimal basic solution.
Examples.

3. DUALITY in PL.
Multipliers, dual variables, constraints and problem.
Examples.
Duality theorems.
Weak and strong duality.
Complementary slackness.
Relations between primal and dual solutions.

4. POSTOPTOMALITY
Postoptimality and sensitivity analysis.
Modifying rhs terms, objective function.

5. NONLINEAR PROGRAMMING
Examples and graphical representation of nonlinear programming problems

Unconstrained optimization (one variable)
Bisection method
Newton method

Unconstrained optimization (multiple variables)
Gradient method

Karush-Kuhn-Tucker (KKT) conditions for constrained optimization

Quadratic programming

Separable programming

Convex programming

Examples

Teaching format 

Lectures and Exercises.

Extended Programme 
End-of-course test 

The final exam consists of a written test that involves the resolution of exercises and possibly the answer to theoretical questions. This will verify both the knowledge of the topics covered during the course and students' ability of understanding and autonomy of judgment.

Any changes to the information presented here, which are necessary to ensure the application of the safety protocols related to the COVID19 emergency, will be communicated on the Department, Study Program and teaching website.

Other information 
Texts/Books 

F. S. Hillier and G. J. Liebermann: Ricerca Operativa, 9th Ed. McGraw-Hill


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