Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Linear programming

The course aims at the acquisition of advanced tools of optimization techniques: non-linear programming, graph theory and optimization methods on networks, integer linear programming and combinatorial optimization, as well as the knowledge of the modeling language LINGO and of the main optimization software.

The student will be able to identify the most appropriate methods and algorithms and develop exact and heuristic algorithms for solving problems in the large, typical of real production and distribution logistics problems that arise in business management. The student will also acquire the ability to design and implement optimization algorithms and interpret the results using computer simulations.

The preparation and oral discussion of a report on the application of optimization methods to problems of business decisions, which is done by deepening topics using materials other than those proposed, will help to improve the communication skills and the ability to learn independently of student. Judgement will be enhanced by the need to identify the most appropriate techniques for each application context.

- Transportation problems : mathematical model, constraint matrix, simplex method - Assignment problems : mathematical model, hungarian method - Network optimization methods: shortest path, minimum spanning tree - Project scheduling: PERT - Maximum flow problem : mathematical model, Ford and FulkersonÂ’s algorithm - Minimum cost flow problem on networks : mathematical model and simplex on networks - Linear integer programming models and combinatorial optimization - Gomory's cutting plane method - Branch and bound algorithms. - Applications of integer linear programming problems in production management - Applications of integer linear programming problems in logistics management - Combinatorial optimization problems and applications - Traveling salesman problem: mathematical models and related solution methods - Vehicle routing problems: mathematical models - Knapsack problems - Software LINGO ( Linear INteractive Global Optimization ) and Microsoft Excel Solver

The evaluation of the studentsÂ’ learning level consists of an oral examination that is characterized by: --the presentation and the dissertation of an individual essay concerning the arguments addressed during the course. In this essay, the student has to prove his/her ability to use optimization software for solving the problems of production management and logistics. --the discussion of one or two themes, addressed during the course.

In order to pass the learning evaluation, the student has to prove that he/she has understood the arguments, addressed during the course, among which: --Mathematical models together with the related solution methods of the most significant network optimization problems; --Network techniques for the projects management; --Mathematical models together with the related methods for solving Integer Linear Programming and combinatorial optimization problems; -- Some applications of the Integer Linear Programming in production management; --Solving some production management mathematical models through both the optimization software LINGO and the Excel Solver.

During the course the student has to show ability to both model and solve some real-world management decision-making problems through optimization software and the implementation of heuristic approaches.

The result of the learning evaluation will be positive if the student reaches a sufficient level (equal to eighteen points) during both the essay dissertation and the oral examination. The evaluation of thirty points is reached by proving a deep knowledge of the arguments, addressed during the course, together with a good ability to solve the optimization problems. The evaluation of thirty points cum laude is for students who have both showed a particular clarity during the oral examination and developed in the essay efficient computer programs for solving optimization problems

- Educational material provided by the teacher on Learning Management System - MOODLE - F. Pezzella, E. Faggioli, Ricerca Operativa: problemi di gestione della produzione, Pitagora, Bologna - M. Fischetti, Lezioni di Ricerca Operativa, Edizioni Libreria Progetto, Padova

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

**Università Politecnica delle Marche**

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