Computational Results for Four Exact Methods to Solve the Three-Objective Assignment Problem Anthony Przybylski 1 , Xavier Gandibleux 1 , and Matthias Ehrgott 1,2 1 LINA – FRE CNRS 2729, Universit´ e de Nantes. 2, rue de la Houssini` ere, BP 92208, F 44322 Nantes Cedex 03 – France FirstName.LastName@univ-nantes.fr 2 Department of Engineering Science, The University of Auckland. Private Bag 92019, Auckland 1142 – New Zealand m.ehrgott@auckland.ac.nz Most of the published exact methods for solving multi-objective combinato- rial optimization problems implicitely use properties of the bi-objective case and cannot easily be generalized to more than two objectives. Papers that deal explicitely with three (or more) objectives are relatively rare and often recent. Very few experimental results are known for these methods and no comparison has been done. We have recently developed a generalization of the two phase method that we have applied to the three-objective assignment problem. In order to evaluate the performance of our method we have imple- mented three exact methods found in the literatue. We provide an analysis of the performance of each method and explain the main difficulties observed in their application to the three-objective assignment problem. 1 The Multi-objective Assignment Problem Efficient algorithms to solve the single-objective assignment problem are well known. In this paper we consider the assignment problem with p objectives (pAP). It can be formulated as follows: “ min ”(z1(X),...,zp(X)) = n X i=1 n X j=1 c k ij xij k =1,...,p n X j=1 xij =1 i =1,...,n n X i=1 xij =1 j =1,...,n xij ∈{0, 1} i, j =1,...,n, (pAP)