Data Envelopment Analysis and Sequences in Hilbert Spaces

We introduce a new class of Data Envelopment Analysis modeling, which we call ‘sequential DEA’. This new approach allows for analyzing efficiency of the decision making units that consist of a sequence of sub-DMUs (e.g., branches of banks, hospital olding company running a number of hospitals at different locations, hotel chains, etc.). The approach is embedded in the Hilbert sequence space (l²) and therefore it allows for potentially different numbers of the sub-DMUs as well as different numbers of inputsand outputs used by different decision making units. This approach opens up a new stream of literature in the sense that many existing variations from the already rich literature on Data Envelopment Analysis can be adapted to this approach.