The operational environment can heavily influence the efficiency scores of the evaluated observations. If heterogeneity among entities is neglected, the efficiency evaluation is strongly biased. In this paper, we discuss five methodologies to incorporate heterogeneity in non-parametric frontier models which are robust for outlying observations. In particular, we examine the frontier separation approach, the all-in-one model, the two-stage model, the multi-stage approach and the conditional efficiency measures. We discuss their appropriateness on a simulated and a real-world drinking water data set. Although, the outcomes are closely related on average, the robust conditional efficiency procedure seems to be superior.