  This paper addresses the output-sensitive complexity for linear
multi-objective integer minimum cost flow (MOIMCF) problems and provides
insights about the time complexity for enumerating all supported nondominated
vectors. The paper shows that there can not exist an output-polynomial time
algorithm for the enumeration of all supported nondominated vectors that
determine the vectors in an ordered way in the outcome space unless NP = P.
Moreover, novel methods for identifying supported nondominated vectors in
bi-objective minimum cost flow (BOIMCF) problems are proposed, accompanied by a
numerical comparison between decision- and objective-space methods. A novel,
equivalent and more compact formulation of the minimum cost flow ILP
formulation used in the e-constrained-scalarization approach is introduced,
demonstrating enhanced efficiency in the numerical tests
