Changes in the technical and scale efficiency of rice production activities in the Mekong delta, Vietnam

Agricultural and Food Economics

Table 1 A summary of input-oriented DEA models

Input-oriented constant returns to scale DEA (CRS): min_θ,λθ, subject to	Input-oriented variable returns to scale DEA (VRS): min_θ,λθ, subject to	Input-oriented non-increasing returns to scale DEA (NIRS): min_θ,λθ, subject to
− q_i + Qλ ≥ 0	− q_i + Qλ ≥ 0	− q_i + Qλ ≥ 0
θ x_i − Xλ ≥ 0	θ x_i − Xλ ≥ 0	θ x_i − Xλ ≥ 0
λ ≥ 0	N1 ’ λ = 1	N1 ’ λ ≤ 1
	λ ≥ 0	λ ≥ 0

Where θ is the total technical efficiency score of the ith firm and λ is a Nx1 vector of constants. The value of θ must satisfy the restriction: 0 ≤ θ ≤ 1. If θ = 1; it indicates that the firm is on the production frontier and is technically efficient. When θ ≤ 1, the firm is technically inefficient.
In the VRS DEA model, N1’λ = 1 is added to show a convexity constraint which ensures that an inefficient firm is only benchmarked against firms of a similar size. On the other hand, in the NIRS DEA model, N1’λ = 1 is replaced by N1’λ ≤ 1 to ensure that the ith firm is not “benchmarked” against firms that are substantially larger than it, but may be compared with firms smaller than it.
Source: Summarized from Coelli et al. (1998).