Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Fundamentals of Linear Programming and of duality theory.

The course allows students to acquire the necessary skills for designing, evaluating and using the automatic tools of mathematical optimization. In particular, they will study and examine in depth the algebraic languages for mathematically modeling and the main solvers (both commercial and not) of linear programming and integer linear programming, focusing attention on their use for solving problems of logistic production management. Such skills, by integrating the ones acquired during the course of Operations Research, will develop the knowledge in the field of Industrial Engineering (with regard to the production management, the sector of logistic and transport).

The knowledge acquired during the course will be expressed through a set of professional skills, among which: 1. the capability to properly model the optimization problems; 2. the capability to identify the solver to use; 3. the capability to interpret the obtained results and to perform sensitivity analysis.

The exercise to solve a problem, developed (eventually) in a group, will lead to the writing of a report by the students. In this way, the students will improve: 1) their degree of autonomous judgment and of presenting (also in a written form) the obtained results; 2) their communication skills (derived from the work done in group); 3. their autonomous capability of both learning and of concluding.

Review of Linear Programming (LP). Examples of LP models: the product mix problem, the transportation problem, the assignment problem. Models of Mathematical Programming (MP) for production planning and for optimal recource allocation. Models of MP for production scheduling and for lot sizing. Models of MP for facility location and for distribution. Models of MP for project management. Optimization software: LINGO and Solver of electronic spreedsheets.

The learning evaluation is based on the discussion of an essay and on an oral test. The essay, individually elaborated, concerns a specific argument addressed during the course, with application to a case study inspired by industrial contexts. The oral test consists of a discussion on two or more arguments addressed during the lessons.

In order to positively pass the learning evaluation, the student has to show to have better understood the arguments addressed during the course: on the mathematical models of problems concerning the production management, on reticular techniques for project management, on the use of optimization software.

The mark assigned to the discussion of the individual essay and the one given to the oral test vary between zero and thirty. The final mark, expressed in thirtieths, is obtained by rounding up the arithmetic mean of these two marks.

The learning evaluation is positive if the student reaches a sufficient level, equal to a score of eighteen, in both the discussion of the essay and the oral test. The evaluation equal to a score of thirty is reached by showing a detailed comprehension of the arguments addressed during the course. The laude is, instead, given to the students who show a particular clarity during the oral test and during the organization and presentation of the essay.

F.S. Hillier, G.J. Lieberman, Ricerca operativa 9/ed Fondamenti, McGraw-Hill (Italia), 2010; C. Vercellis, Ottimizzazione- Teoria, Metodi, Applicazioni, McGraw-Hill, 2008; F. Pezzella, E. Faggioli, Ricerca Operativa: problemi di gestione della produzione, Pitagora Editrice, Bologna.

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

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427