Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Systems of linear equations, Convex analysis

The course aims allowing students to acquire the basic knowledge on the mathematical programming models for decision optimization problems in the company management. It gives the necessary mathematical and application basis for solving linear programming problems with particular reference to both the algorithmic and the computational aspects. The knowledge transmitted will provide students with the methodological instruments for developing both optimization models and methods based on linear programming and on the related solution algorithms.

The student will be able to mathematically formulate the company management problems. Moreover, he/she will acquire the capability of using the optimization software and of interpreting the obtained results through simulations run on computers.

The presentation and the discussion of the application problems of Operations Research, during the written and the oral test, will allow students to improve their autonomous judgment degree and their communication skills. The learning capability will be developed by applying the acquired knowledge to contests that differ from the ones presented during the course and by examining in depth through an autonomous search. The presentation and the discussion of the application problems of Operations Research will allow students to improve their autonomous judgment degree, their communication skills and their capability of applying the acquired knowledge to contests that differ from the ones presented during the course.

- Introduction to optimization problems - Mathematical programming models - Formulation of linear programming models - Graphical solution of linear programming in two variables - Review of linear algebra and convex analysis - Simplex method in tableau form - Pivot matrix method - Simplex in matrix form - Revised simplex methods - Two-phase simplex method - Duality theory and primal-dual relationships: dual variables and duality theorems - Dual simplex method - Stability analysis of the optimal solution - Linear Programming applications to production planning problems - Transportation problems: mathematical model - Assignment problems : mathematical model - Software LINDO (Linear INteractiver Discrete Optimization)

The evaluation of the studentsÂ’ learning level consists of: -- A written examination that requires solving a linear programming problem via several solution methods, studied during the course. Its duration is two hours. -- An oral examination that requires discussing two or more themes, analyzed during the course. Only the students who have reached a sufficient level in the written examination are allowed accessing the oral one. The students have to do the oral test in the same exam of the writing one. In the case of the oral examination is negatively evaluated, the result of the writing test will be maintained only for the next exam.

In order to pass the learning evaluation, the student, through both the examination tests, has to prove that he/she has understood the arguments, addressed during the course, among which: --Linear Programming model and its applications to some decisional problems; --Linear Programming theory and the solution proprieties; - Simplex method and its different versions; --Theorems of the Dual Theory and the Stabiltity Analysis; --Linear Programming applications to some production planning problems

Both the writing and the oral examination are scored out of a maximum of thirty points (i.e., the score is between zero and thirty). The total score, for a maximum of thirty points, is the rounded up average value of the previous two scores .

The result of the learning evaluation will be positive if the student reaches a sufficient level (equal to eighteen points) in both the two examinations (such as in both the writing and the oral test). The evaluation of thirty points is reached by proving, in both the examinations, a deep knowledge of the arguments, addressed during the course, together with the ability to efficiently solve the Linear Programming problems. The evaluation of thirty points cum laude is for students who have carried out both the examinations in a correct and complete way, showing a particular clarity during the oral discussion and in the writing test.

- Educational material provided by the teacher on Learning Management System - MOODLE - F. Pezzella, Elementi di Programmazione Lineare, Liguori Editore, Napoli

- Ingegneria Biomedica (Corso di Laurea Triennale (DM 270/04))
- Ingegneria Informatica e dell'Automazione (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

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