Analysis and algorithms to solve the Bilevel Assignment Problem In this thesis, the Bilevel Assignment Problem (BAP) is analyzed, and different exact, metaheuristic and matheuristic approaches are developed and implemented to solve it. The Assignment Problem (AP) is well known in the literature and the typical problem consists of assigning n origins i to n destinations j, such that, given a costs matrix of size n x n in which each value corresponds to each cost cij (of assigning origin i to destination j) the total cost obtained as a linear sum is maximized/minimized. Each origin and each destination must be assigned once.