The objectives of the course Networks and Supernetworks are as follows:
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.
The objectives of the course are as follows:
Knowledge and understanding:
At the end of the course, the student, in addition to having acquired the basic knowledge and skills in the field of optimization and mathematical modeling, will demonstrate:
Applying knowledge and understanding:
The theoretical and practical knowledge acquired during the course will allow the student to:
Making judgements:
The student, by virtue of the acquired training, also of an analytical-quantitative type, will be able to critically analyze and interpret the data provided.
Communication skills:
At the end of the course the student will be able to:
Learning skills:
The course will be taught through lectures and exercises in the classroom and at the computer labs.
Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.
Learning assessment may also be carried out on line, should the conditions require it.
The course will be taught through lectures and exercises in the classroom and at the computer labs.
Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.
Learning assessment may also be carried out on line, should the conditions require it.
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.
Networks:
• 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.
Supply chain networks:
• 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.
• 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.
Matlab applications.