Hierarchical models via optimal transport: locating, partitioning, pricing

"Hierarchical models via optimal transport: locating, partitioning, pricing", organizado polo CITMAga. Será impartido por Lina Mallozzi (University of Naples “Federico II”)

Data: venres 24 de marzo

Hora: 12:00 h.

Lugar: Aula Seminario 7, Facultade de Ciencias Económicas e Empresariais (UVigo)

Abstract:

Optimal transport theory is widely used to solve problems in mathematics and different areas of the sciences. We formulate some problems in applied economics as two-stage schemes studied by using optimal transport tools. More precisely, two-stage optimization models corresponding to economic equilibrium problems are presented. A distribution of citizens in an urban area, where a given number of services must be located, is given. Citizens are partitioned in service regions such that each facility serves the costumer demand in one of the service regions. At first, it is assumed that the demand is totally satisfied and in the spirit of a market survey, a social planner divides the market region into a set of service regions in order to minimize the total cost: the objective is to find the optimal location of the services in the urban area and the related costumers partition. Existence results are obtained by using optimal transport mass tools. Then, a bilevel formulation is considered related to an optimal monopoly pricing where customers have the option of not purchasing the good and the utility for purchasing the good at a given price may be random. In this case the problem is solved via partial transport mass theory