Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Elements of Linear Programming and duality theory. Elements of structured programming.

The course introduces to the main theoretical, modeling and methodological issues of the formulation and quantitative solution of decision problems that arise in the management of complex (manufacturing and service) systems, for which the organizational variable plays a quite critical role. In particular, the course illustrates the declarative paradigm of mathematical programming and, in general, the methods and techniques used for the design and the use of quantitative tools for supporting the decision-making process.

The student should be able a) to identify and understand decision-making problems even of high complexity, interdisciplinary nature and partially defined b) to analytically formulate such problems by mathematical programming techniques and c) to quantitatively solve such problems with advanced software tools. The student will have the skill of systematically view the decision problems arising in the context of organized systems and will be able to apply quantitative methods for their solution. Given the interdisciplinary nature of these activities, the student will be able to work within cross-functional teams, acting as an interface between the various professional 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 quantitative methods for supporting the decision-making process. In general, such activities will contribute to the improvement of both the degree of independence of judgment and the ability of applying mathematical tools for model and control the behavior of complex decision-making processes.

- Introduction to decision-making problems and decision support systems. - Mathematical programming as a declarative paradigm. - Linear programming (LP) and integer linear programming (ILP) models. - Modelling techniques for LP/ILP. - Software optimization tools and Algebraic Modelling Languages (AMPL). - Outline on linear programming and duality theory: main results and applications. - Primer to theory of computational complexity. - Introduction to graph theory and main graph optimization problems. - Problems and models for network optimization. shortest path, max-flow and min cost flow problems. - Implicit enumeration algorithms for Integer Linear Programming. - Discrete models for Scheduling and routing problems. - Applications of mathematical programming.

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 discrete optimization problems 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.

It is evaluated the ability to clearly and logically explain ideas, concepts and theoretical results of discrete optimization. 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 discrete optimization.

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 mathematical programming and discrete optimization 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.

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 discrete optimization, 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 discrete optimization.

1) C. Vercellis, Â“Ottimizzazione. Teoria, metodi, applicazioniÂ“, Mc Graw-Hill, 2008. 2) presentations, exercises and lecture notes

- Ingegneria Gestionale (Corso di Laurea Magistrale Fuori Sede (DM 270/04))

**Università Politecnica delle Marche**

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