The Basic CCR Model

Abstract

In this chapter, we introduced the CCR model, which is a basic DEA model. 1. For each DMU, we formed the virtual input and output by (yet unknown) weights (v i) and (u r): $$ \begin{gathered} Virtual input = v_1 x_{1o} + \cdots + v_m x_{mo} \hfill \\ Virtual output = u_1 y_{1o} + \cdots + u_s y_{so} . \hfill \\ \end{gathered} $$ Then we tried to determine the weight, using linear programming so as to maximize the ratio $$ \frac{{Virtual output}} {{Virtual input}}. $$ The optimal weights may (and generally will) vary from one DMU to another DMU. Thus, the ?weights? in DEA are derived from the data instead of being fixed in advance. Each DMU is assigned a best set of weights with values that may vary from one DMU to another. Here, too, the DEA weights differ from customary weightings (e.g., as in index number constructions) so we will hereafter generally use the term ?multiplier? to distinguish these DEA values from the other commonly used approaches. 2. CCR-efficiency was defined, along with the reference sets for inefficient DMUs. 3. Details of the linear programming solution procedure and the production function correspondence are given in Chapter 3.