Sequential data envelopment analysis

We consider a new class of Data Envelopment Analysis (DEA) modeling, which we call ‘sequential DEA’. This new approach is a relatively simple generalization of the standard and popular in practice DEA. It allows for analyzing efficiency of the decision making units that consist of a sequence of sub-DMUs (e.g., branches of banks, hospital holding company running a number of hospitals at different locations, hotel chains, etc.). The approach is embedded in the Hilbert sequence space (ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell ^{2}$$\end{document}) and therefore it allows for potentially different numbers of the sub-DMUs as well as different numbers of inputs and outputs used by different decision making units. We hope this approach will open up a new stream of literature in the sense that many existing variations from the already rich literature on DEA can be adapted to this approach.