Variational inequalities and networks for organ transplants and for humanitarian organizations

Abstract

In this thesis we focus our attention on two mathematical models applied to two real situations, both studied with the theory of variational inequalities. The first network-based model describes the organ transplant system with the aim of minimizing the total costs associated with this process. We find the related optimality conditions and the variational inequality formulation. Some existence and uniqueness results as well as the Lagrange formulation are stated and some numerical examples are studied. The second mathematical model presented is a Generalized Nash Equilibrium model for postdisaster humanitarian relief. We identify the network structure of the problem, with logistical and financial ows, and propose a variational equilibrium framework, which allows us to then formulate, analyze, and solve the model using the theory of variational inequalities. We then utilize Lagrange analysis and finally we illustrate the game theory model through a case study.