Dual-role factors in data envelopment analysis

This paper presents a methodology for dealing with performance evaluation settings where factors can simultaneously play both input and output roles. Model structures are developed for classifying Decision-Making Units (DMUs) into three groups according to whether such a factor is behaving like an output, an input, or is in equilibrium, neither wanting to lose or gain any of the factors. We connect these ideas to those involving increasing, decreasing and constant returns to scale. Examples of factors that play this dual-role are: trainees in organizations, such as nurses, medical students, and doctoral students; awards to scholars or university departments; certain revenue-generating transactions in banks, and so on. We apply the model to the analysis of a set of university departments. In some settings, a dual-role factor may be one that can be reallocated, such as would be the case when DMUs are managed by a central authority. We develop the appropriate model structures to permit such a reallocation. We present two such structures, with the first involving reallocation from an existing allocation, and the second, a zero-base allocation.