Hybrid Dynamic Network Data Envelopment Analysis

Abstract

Conventional DEA models make no hypothesis concerning the internal operations in a static situation. To open the "black box" and work with dynamic assessment issues synchronously, we put forward a hybrid model for evaluating the relative efficiencies of a set of DMUs over an observed time period with a composite of network DEA and dynamic DEA. We vertically deal with intermediate products between divisions with assignable inputs in the network structure and, horizontally, we extend network structure by means of a dynamic pattern with unrelated activities between two succeeding periods. The hybrid dynamic network DEA model proposed in this paper enables us to (i) pry into the internal operations of DEA by another network structure, (ii) obtain dynamic change of period efficiency, and (iii) gain the overall dynamic efficiency of DMUs over the entire observed periods. We finally illustrate the calculation procedure of the proposed approach by a numerical example.

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“…The DEA-BCC (The BCC model assumes that DMU is in the case of variable returns to scale, and is used to measure pure technology and scale efficiency) model divides technical efficiency into pure technical efficiency and scale efficiency under the premise of variable returns to scale. Suppose there are n decision-making units (DMU), each DMU j has m types of inputs and q types of outputs denoted as 35 The linear programming model of DMU is equivalently transformed and dually processed, and the resulting model is:…”

“…Suppose there are n decision‐making units (DMU), each DMU j has m types of inputs and q types of outputs denoted as X j = ( X 1 j , X 2 j , …, X mj ), Y j = ( Y 1 j , Y 2 j , …, Y qj ). 35 The linear programming model of DMU is equivalently transformed and dually processed, and the resulting model is: $$$$\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {max\left\{ \theta \right\}}\\[8pt] {s.t.\mathop \sum \limits_{i = 1}^n {X_{ij}}{\lambda _j} - {S^ + } = \theta {X_{ik}}\;i = 1,2, \ldots \ldots \;}\\[8pt] {\mathop \sum \limits_{r = 1}^n {Y_{rj}}{\lambda _j} - {S^ - } = \theta \;r = 1,2 \ldots \ldots }\\[8pt] {\mathop \sum \limits_{j = 1}^n {\lambda _j} = 1\;j = 1,2 \ldots \ldots }\\[8pt] {{\lambda _j} \ge 0}\\[8pt] {{S^ + } \ge 0,{S^ - } \ge 0} \end{array} } \right.\end{equation}$$$$…”