Politecnico di Torino
Politecnico di Torino
Politecnico di Torino
Academic Year 2012/13
Operations research
1st degree and Bachelor-level of the Bologna process in Engineering And Management - Torino
1st degree and Bachelor-level of the Bologna process in Mathematics For Engineering - Torino
1st degree and Bachelor-level of the Bologna process in Engineering And Management - Torino
Teacher Status SSD Les Ex Lab Tut Years teaching
Della Croce Di Dojola Federico ORARIO RICEVIMENTO PO MAT/09 50 30 0 0 22
Norese Maria Franca ORARIO RICEVIMENTO     50 30 0 0 9
SSD CFU Activities Area context
MAT/09 8 A - Di base Matematica, informatica e statistica
Subject fundamentals
Operations Research consists in building up rational models for the representation of complex problems and in devising the related solution algorithms. The course intends to provide the student the basic tools to model and solve various complex engineering problems. Further objective of the course is to be able to adequately synthesize the necessary elements when coping with decisional problems.
Expected learning outcomes
At the end of the course the student must know a set of methods, understand the use of the methods in different problem contexts and must be able to a) structure singular problems of medium complexity, choose a particular method in relation to the characteristics of the problem, and use that method in the right way; b) use software tools to deal with more complex problems.
Prerequisites / Assumed knowledge
Elements of linear algebra
Linear programming: problems and models; base solutions; simplex method.
Duality: primal and dual models and their properties. Sensitivity analysis.
Integer linear programming.
Problems that can be represented and solved as a network and graph theory algorithms.
Elements of computational complexity.
Elements of Multiobjective optimisation. Elements of Multi-criteria analysis for the decision aid and outranking methods
Delivery modes
The exercise classes are related to the topics presented in the course.
Texts, readings, handouts and other learning resources
Textbooks that contain the topics presented in the course are:
- R. Tadei, F. Della Croce (2005), Elementi di Ricerca Operativa, Esculapio, Bologna
- R. Tadei, F. Della Croce, A. Grosso (2005), Fondamenti di Ottimizzazione, Esculapio, Bologna.
- M.F. Norese (2014), Strumenti di supporto alla decisione e metodi di analisi multicriteri. (dispense disponibili in rete).

Reference textbooks that contain part of the topics presented in the course are among others:
- P. Vincke (1992), Multicriteria decision-Aid, Wiley, Chichester.
- D.G. Luenberger (1984), Linear and Non Linear Programming, Addison Wesley
- C.H. Papadimitriou, K. Steiglitz (1982), Combinatorial Optimization. Algorithms and Complexity, Prentice Hall.
- L.A. Wolsey (1999), Integer Programming and Combinatorial Optimization, Wiley.
Assessment and grading criteria
Teacher: Maria Franca Norese
The final exam is a written test in relation to all the topics presented during the course. It is composed by two different parts. The first part lasts around one hour and includes only numerical exercises of method application.
The student has to demonstrate knowledge of the proposed methods and of their use in relation to problems of limited complexity.
The second part, which starts after the delivering of the work made in the first part, lasts around one hour and includes only two exercises of modelling and result analysis, in relation of problems that present some elements of complexity.
Texts and personal documentation can be used during both the parts of the written exam.
The final score can arrive to 30/30 with Laude. It is obtained by summing the results of the first and the second part, each one contributing in terms of approximately 50% of the final score.

Programma definitivo per l'A.A.2017/18

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