  In this work, we present the first outer approximation algorithm for
multiobjective mixed-integer linear programming (MOMILP). The algorithm
produces the non-dominated extreme points for MOMILP, and the facets of the
convex hull of these points. Our algorithm uses an oracle which consists of
solving single-objective weighted-sum problems. We show that analogous to
existing outer approximation algorithms for multiobjective linear programming,
our algorithm needs a number of oracle calls, which is polynomial in the number
of facets of the convex hull of the non-dominated extreme points. As a
consequence, for problems for which the weighted-sum problem is solvable in
polynomial time, the facets can be computed in incremental polynomial time.
  From a practical perspective, due to its outer approximation nature, the
algorithm provides valid lower bound sets for use in multiobjective
branch-and-bound algorithms at any stage of its execution and thus allows for
early termination of such a bound computation. Moreover, the oracle produces
Pareto optimal solutions, which makes the algorithm also attractive from the
primal side. Finally, the oracle can also be called with any relaxation of the
original MOMILP, and the obtained points and facets still provide a valid lower
bound set. A computational study is done to assess the efficiency of our
algorithm.
