Linear Programming and Resource Allocation Modeling

14Data Envelopment Analysis (DEA)

14.1 Introduction

(Charnes et al. 1978; Banker et al. 1984; Seiford and Thrall 1990; and Banker and Thrall 1992)

In this chapter we shall examine an important applications area of linear programming, namely the technique of data envelopment analysis (DEA) that was first introduced by Charnes, Cooper, and Rhodes (1978). Generally speaking, DEA is a computational procedure used to estimate multiple‐input, multiple‐output production correspondences so that the productive efficiency of decision making units (DMUs) can be scrutinized. It accomplishes this by using linear programming modeling to measure the productive efficiency of a DMU relative to that of a set of baseline DMUs. In particular, linear programming is used to estimate what is called a best‐practice extremal frontier. It does so by constructing a piecewise linear surface, which essentially “rests on top” of the observations. This frontier “envelops” the data and enables us to determine a set of efficient projections to the envelopment surface. The nature of the projection path to the said surface depends on whether the linear program is input‐oriented or output‐oriented:

• Input‐oriented DEA – the linear program is formulated so as to determine the amount by which input usage of a DMU could be contracted in order to produce the same output levels as best practice DMUs.
• Output‐oriented DEA – the linear program is formulated so as to determine a DMU’s potential output given its inputs ...