Modelling efficiency in the presence of shared inputs within groups of DMUs

Data envelopment analysis (DEA) is a methodology for evaluating efficiencies of decision-making units (DMUs) with each unit having its own set of inputs and outputs. However, there are situations where there can be an interdependence among the units. In a previous paper the authors examine efficiency measurement in a situation where university departments are grouped by faculty and share a single resource at the faculty level. Furthermore, the shared resource is assumed to be one which cannot be split up and allocated to the group members. The current paper generalizes that earlier work by considering decision-making units grouped according to multiple attributes and with multiple shared inputs. In addition, the problem of overlapping groups is investigated. A DEA-like methodology is developed for deriving efficiency scores in this multiple attribute situation. Further, we present a methodology for evaluating efficiency at the level of the groups, e.g. the level of the faculty, as well as at the level of the members within the groups. To further demonstrate the need for such methodologies, we present a number of real-world problem settings where shared factors and groupings of DMUs need to be dealt with.