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Ricerca Operativa (GEST)
Operations Research
Fabrizio Marinelli

Seat Ingegneria
A.A. 2016/2017
Credits 9
Hours 72
Period II
Language ENG

Prerequisites
Elements of linear algebra and convex analysis.

Learning outcomes
KNOWLEDGE AND UNDERSTANDING:
The course introduces the mathematical modeling and shows the basic topics, the methodological approaches and the solution techniques for linear and integer linear programming problems. The teaching describes the nature of the decision problems that particularly arise in production and service systems and illustrates the main techniques for their modeling and solution.
CAPACITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
The student will be able to formulate and quantitatively solve decision problems that arise within production and service systems. Such skills mainly consist in the ability of a) correctly identify the decisional aspects of a decision-making problem, b) define suitable measures of performance indicators, c) identify the physical and operational constraints and finally d) encoding and solving problems by suitable software tools. Given the interdisciplinary nature of these activities, the student will be able to work within cross-functional teams, acting as interface between the various professional skills.
TRANSVERSAL SKILLS:
The student skills will be checked through modeling exercises and the application of algorithms and solution techniques illustrated in the course, as well as by a final test, in which students must demonstrate sufficient knowledge of the theoretical principles and the optimization methods for linear and integer linear programming. In general, these activities will contribute to the improvement of both the degree of independence of judgment, and the ability of analysis, abstraction, modeling, interpretation and communication of the quantitative results related to decision-making problems.

Program
- Organized systems and decision-making problems. - Linear and integer linear programming models. - AMPL: an algebraic modeling language. - Basic topics in convex analysis and linear algebra. - Theory of Linear Programming. - Simplex algorithm and revised simplex algorithm. - Duality theory: motivations and main results. - Dual simplex algorithm. - Sensitivity analysis and economic interpretation. - Integer Linear Programming. - ILP models for noteworthy combinatorial optimization problems on graphs. - The method of cutting planes. Gomory cuts and cover inequalities for Knapsack 0-1. - Applications.

Development of the examination
LEARNING EVALUATION METHODS
The assessment of the level of learning includes both a written and an oral exam. The written lasts 2 hours and is composed by a first part with multiple-choice tests and a second part with one or more exercises on mathematical modeling and/or solution of (integer) linear programming models by means of the techniques presented in the course. During the exam students cannot use notes and books. The access to the oral exam is reserved to students that achieve a written rating of at least 18 points. The oral exam consists of the discussion of the written exam and the solution of one or more questions in order to verify the logical deductive skills and the understanding of the course topics.

LEARNING EVALUATION CRITERIA
It is evaluated the ability to clearly and logically explain ideas, concepts and theoretical results of linear programming. It is also assessed the ability to independently set and solve decision problems by correctly using appropriate methods, models and tools of mathematical programming and in particular od linear programming.

LEARNING MEASUREMENT CRITERIA
Knowledge of ideas, concepts and theoretical results is analytically measured by a score assigned to the first part of the written exam that ranges between -7 and 14 points. The ability to formulate and solve decision-making problems by means of the tools of linear programming is analytically measured by a score assigned to the second part of the written that ranges between 0 and 14 points. the capability of synthesis, logical and clear exposition is measured analytically by a score assigned to the oral exam that ranges between 0 and 30 points.

FINAL MARK ALLOCATION CRITERIA
The final grade is equal to half the sum of the scores awarded to the two parts of the written exam and to the oral exam. The maximum grade, equal to thirty points with honors, is awarded to students who demonstrate total mastery of the theoretical and methodological tools of linear programming, and full autonomy and logical accuracy in setting and solving the proposed problems. The minimum grade, equal to eighteen, is assigned to students who demonstrate to be able to solve the proposed problems and to sufficiently know of the theoretical and methodological tools of linear programming.

Recommended reading
a) C. Vercellis, “Ottimizzazione. Teoria, metodi“, applicazioni, Mc Graw-Hill, 2008. b) S. Martello, D. Vigo, “Esercizi di Ricerca Operativa“, Progetto Leonardo, Bologna, 2001. c) presentations, exercises and lecture notes.

Courses

• Ingegneria Gestionale (Corso di Laurea Triennale Fuori Sede (DM 270/04))