The CCR Model and Production Correspondence

In this chapter we described the CCR model in some detail in both its input-oriented and output-oriented versions. 1. We also relaxed assumptions of a positive data set to semipositivity. 2. We defined the production possibility set based on the constant returns-to-scale assumption and developed the CCR model under this assumption. 3. The dual problem of the original CCR model was introduced as (DLP o) in (3.6)–(3.9) and the existence of input excesses and output shortfalls clarified by solving this model. (To avoid confusion and to align our terminology with the DEA literature, we referred to the dual as the “envelopment model” and the primal (LP o) introduced in Chapter 2 as the “multiplier model.”) 4. In Definition 3.2 we identified a DMU as CCR-efficient if and only if it is (i) radial-efficient and (ii) has zero-slack in the sense of Definition 3.1. Hence a DMU is CCR-efficient if and only if it has no input excesses and no output shortfalls. 5. Improvement of inefficient DMUs was discussed and formulae were given for effecting the improvements needed to achieve full CCR efficiency in the form of the CCR-projections given in (3.22) and (3.23). 6. Detailed computational procedures for the CCR model were presented in Section 3.6 and an optimal multiplier values (v, u) were obtained as the simplex multipliers for an optimal tableau obtained from the simplex method of linear programming.