A note on robustness of the min-max solution to multi-objective linear programs

The challenge of using scalarising methods in multi-objective optimisation results from the choice of the method, which may not be apparent, and given that a method has been selected, from the choice of the values of the scalarising parameters. In general, these values may be unknown and the decision maker faces a difficult situation of making a choice possibly under a great deal of uncertainty. Due to its effectiveness, the robust optimisation approach of Ben-Tal and Nemirovski is applied to resolve the uncertainty carried in scalarised multi-objective linear programs (MOLPs). A robust counterpart is examined for six different scalarisations of the MOLP yielding robust (weakly) efficient solutions to the original MOLP. The study reveals that the min-max optimal solution emerges as a robust (weakly) efficient solution for five out of the six scalarisations. The implications of this result are also discussed.