Efficiency Aggregation in Generalized Network Data Envelopment Analysis with Slacks-Based Measure Based on Sample Units

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.

Keywords

• data envelopment analysis
• slacks-based measure
• efficiency
• basic two-stage structure
• general network structure
• sample unit