  We present a simple and at the same time fficient algorithm to compute all
nondominated extreme points in the outcome set of multi-objective mixed integer
linear programmes in any dimension. The method generalizes the well-known
dichotomic scheme to compute the set of nondominated extreme points in the
outcome set of a bi-objective programme based on the iterative solution of
weighted sum scalarizations. It uses as a main routine a convex hull algorithm.
The algorithm is illustrated with, and numerically tested on, instances of
multi-objective assignment and knapsack problems. Experimental results confirm
the computational efficiency of the approach. Finally, an implementation in
incremental polynomial time with respect to the number of computed nondominated
extreme points is possible, under the assumption that the lexicographic version
of the problem can be solved in polynomial time.
