Network optimization

The objectives of the course Optimization on Networks 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.

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

Networks (about 20 hours):

• 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. Traffic networks with delay terms. 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.

• 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 (about 27 hours):

• 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.

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