ISTITUZIONI DI RICERCA OPERATIVA

12 CFU - 1° and 2° Semester

Teaching Staff

PATRIZIA DANIELE - MODULO I - MAT/09 - 6 CFU
TEACHER NOT YET ALLOCATED - MODULO II - MAT/09 - 6 CFU

Learning Objectives

MODULO I
The objectives of the course Networks and Supernetworks are as follows:
- to determine paths of minimum and maximum length starting from a root node;
- to apply the concepts of generalized derivatives to functions;
- to apply the Lagrange theory to constrained optimization problems;
- to formulate an equilibrium problem as an evolutionary variational inequality;
- to solve evolutionary variational inequalities.
Knowledge and understanding: the aim of the course is to be able in recognizing constrained optimization problems and in formulating real life problems in mathematical terms

Applying knowledge and understanding: students will be able to identify the functional characteristics of the data, to analyze various optimization situations, to propose optimal solutions to complex problems.

Making judgments: students will be able to analyze the data.

Communication skills: students will be able to communicate their experience and knowledge to other people.

Learning skills: students will have acquired the ability to learn, even autonomously, further knowledge on the problems related to applied mathematics.
MODULO II
The objectives of the course Networks and Supernetworks are as follows:
- to determine paths of minimum and maximum length starting from a root node;
- to formulate equilibrium traffic problems in the dynamic case using networks, including also capacity constraints, additional restrictions and delay terms;
- to evaluate the importance of the single components of a network;
- to build a multi-tiered network for production and distribution problems, for electrical models and in the case of merger of companies;
- to apply theoretical models to business cases.

Course Structure

MODULO I
The course will be taught through lectures and exercises in the classroom and at the computer labs.
MODULO II
The course will be taught through lectures and exercises in the classroom and at the computer labs.

Detailed Course Content

MODULO I
Graph theory (about 12 hours):

Graphs and digraphs: Definitions and preliminary notions, associated matrices. Kruskal's algorithm and its variant. Dijkstra's algorithm and its variant. Ford algorithm. Bellman-Kalaba’s algorithm. The traveling salesman problem.

Generalized derivatives (about 10 hours)

Directional derivatives, Gâteaux and Fréchet derivatives. Subdifferential.

Computational methods (about 8 hours)

The subgradient method. The discretization method.

Network models (about 17 hours)

Traffic networks. The Braess' paradox. Efficiency measure of a network. Supernetworks with three levells of decision-makers.
MODULO II
Graph theory:

Graphs and digraphs: Definitions and preliminary notions, associated matrices. Kruskal's algorithm and its variant. Dijkstra's algorithm and its variant. Ford algorithm. Bellman-Kalaba’s algorithm. The traveling salesman problem.

Networks:

• Traffic networks in the static case: the model; Wardrope’s principle; model with capacity constraints. Traffic networks in the dynamic case: the model; equilibrium conditions; variational formulations; existence theorems; model with additional constraints. Traffic networks with delay terms. Directional derivative: definition and properties. Subdifferential of a convex function: definition and properties. Subgradient method, discretization method. Braess’ paradox in the static case and in the dynamic case. The efficiency of a network: Latora-Marchiori measure and Nagurney-Qiang measure. Importance of the components in a network. Applications to Braess network. Identification of critical elements in networks.

• Spatially distributed networks of economic markets in the static case in the presence of production and demand excesses. Variational formulation and Lagrangian theory.

• Horizontal mergers: the models before and after the merger; associated optimization problems; synergy. Models with environmental interests.

• Variational inequalities for auction problems: the model, equilibrium conditions and equivalent variational formulations.

Supernetworks:

• Supply chain networks with three levels of decision-makers: economic model in the presence of manufacturers, retailers and consumers with e-commerce; optimality conditions and equivalent variational inequality for the representatives of all levels and for the entire chain. Dynamic case: model with production and demand excesses.

• Networks with critical needs with external sources: optimization problem and variational formulation.

• Supply chains for food: optimality conditions and variational formulation.

• Electricity supply chain networks: the model with electric power producers, energy providers, transmission service providers and demand markets; optimality conditions and equivalent variational formulation for the representatives of all levels and for the entire network. Presentation of the model with non-renewable fuel suppliers and optimality conditions.

• closed loop supply chains: direct chain and reverse chain. Behavior of raw material suppliers, producers, retailers, demand markets, the recovery centers. Variational formulation.

• The model of cybercrime in financial services.

Textbook Information

MODULO I
1. L. Daboni, P. Malesani, P. Manca, G. Ottaviani, F. Ricci, G. Sommi, “Ricerca Operativa”, Zanichelli, Bologna, 1975.
2. P. Daniele, “Dynamic Networks and Evolutionary Variational Inequalities", Edward Elgar Publishing, 2006.
3. J. Jahn, "Introduction to the Theory of Nonlinear Optimization", Springer, 1996.
4. Papers on STUDIUM http://studium.unict.it
MODULO II
1. L. Daboni, P. Malesani, P. Manca, G. Ottaviani, F. Ricci, G. Sommi, “Ricerca Operativa”, Zanichelli, Bologna, 1975.
2. P. Daniele, “Dynamic Networks and Evolutionary Variational Inequalities", Edward Elgar Publishing, 2006.
3. A. Nagurney, J. Dong, "Supernetworks", Edward Elgar Publishing, 2002.
4. Papers on STUDIUM

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