This article presents a systematic approach to analysing linear integer multi-objective optimization problems with uncertainty in the input data. The goal of this approach is to provide decision makers with meaningful information to facilitate the selection of a solution that meets performance expectations and is robust to input parameter uncertainty. Standard regularization techniques often deal with global stability concepts. The concept presented here is based on local quasi-stability and includes a local regularization technique that may be used to increase the robustness of any given efficient solution or to transform efficient solutions that are not robust (i.e. unstable), into robust solutions. An application to a multi-objective problem drawn from the mining industry is also presented.