Network optimization

The objectives of the course are as follows:

• 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.

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:

• being able to transform real situations of maximization of profits, minimization of costs and risks, ... into mathematical models;
• possess knowledge and ability to understand texts.

Applying knowledge and understanding:

The theoretical and practical knowledge acquired during the course will allow the student to:

• critically analyze various business situations;
• propose optimal solutions to complex problems;
• identify the essence of a problem and apply general principles to specific cases.

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:

• pass on their experience and knowledge to others;
• confronting others, especially in the development of projects in which you work in a team.

Learning skills:

• The student will acquire the ability to learn, even independently, additional knowledge on applied mathematics problems. These skills will allow him to face and solve concrete optimization problems.

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.

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.

1. P. Daniele, “Dynamic Networks and Evolutionary Variational Inequalities", Edward Elgar Publishing, 2006.
2. A. Nagurney, J. Dong, "Supernetworks", Edward Elgar Publishing, 2002.
3. Papers on STUDIUM