  Data Envelopment Analysis (DEA) is a nonparametric, data driven technique
used to perform relative performance analysis among a group of comparable
decision making units (DMUs). Efficiency is assessed by comparing input and
output data for each DMU via linear programming. Traditionally in DEA, the data
are considered to be exact. However, in many real-world applications, it is
likely that the values for the input and output data used in the analysis are
imprecise. To account for this, we develop the uncertain DEA problem for the
case of box uncertainty. We introduce the notion of DEA distance to determine
the minimum amount of uncertainty required for a DMU to be deemed efficient.
For small problems, the minimum amount of uncertainty can be found exactly, for
larger problems this becomes computationally intensive. Therefore, we propose
an iterative method, where the amount of uncertainty is gradually increased.
This results in a robust DEA problem that can be solved efficiently. This study
of uncertainty is motivated by the inherently uncertain nature of the
radiotherapy treatment planning process in oncology. We apply the method to
evaluate the quality of a set of prostate cancer radiotherapy treatment plans
relative to each other.
