Abstract
By using sample units (SUs), the generalized data envelopment analysis (DEA) method can evaluate the efficiency of decision making unit (DMU) through different reference sets, but the existing models are radial models, and the DMU is treated as a black box, rarely taking the operations of the internal divisions into account. This paper proposes a generalized network slacks-based measure (SBM) approach based on the SUs. First, the generalized network SBM approach for a basic two-stage structure is proposed. This paper considers the intermediate products in calculating the divisional efficiency for each DMU. Overall efficiency of DMU is a weighted average of the divisional efficiency. The weight of each division does not need to be given in advance. Since the DMUs set and SUs set are not necessarily the same, this paper proposes an improved generalized network SBM approach for a basic two-stage structure to solve the problem that the original model may be infeasible. Then, the approach for basic two-stage structure is extended to general multi-stage structure. Finally, an example is given to show the practicability of the generalized network SBM approach.
Highlights
Data envelopment analysis (DEA) as proposed by Charnes, Cooper, and Rhodes [1], is an approach for measuring the relative efficiency of a set of homogenous decision making units (DMUs) with multiple inputs and multiple outputs [2]
In traditional DEA approaches, DMUs are treated as a whole unit, or a black box, and only the inputs supplied from the outside and the outputs sent to the outside are considered in measuring efficiency, ignoring the intermediate products produced and consumed within the system, without taking the operations of the internal divisions into account [8]
We have proposed generalized network slacks-based measure (SBM) approach based on sample units (SUs) to extend the study of Ma [48]
Summary
Data envelopment analysis (DEA) as proposed by Charnes, Cooper, and Rhodes [1], is an approach for measuring the relative efficiency of a set of homogenous decision making units (DMUs) with multiple inputs and multiple outputs [2]. Fukuyama et al [38] proposed an improved two-stage network SBM, which includes the slack variables of intermediate products in the formula for calculating the overall efficiency of DMU, but the weight of each division in the formula needs to be given in advance according to its importance to DMU. Kao [39] proposed a general SBM model for network systems, and decomposed the overall efficiency into a weighted average of the divisional efficiencies. Since the DMUs set and SUs set are not necessarily the same, an improved generalized network SBM model for basic two-stage structure is proposed, the relationship between overall and divisional efficiency is derived.
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