Decomposition of slacks-based efficiency measures in network data envelopment analysis

Abstract

One objective of the efficiency measurement of multi-division systems is to find the least efficient divisions such that making improvements to them will increase the efficiency of the system most effectively. To accomplish this task, it is desirable to find the relationship between the system and division efficiencies. This issue has been addressed for the radial efficiency measures. This paper explores the relationship for a non-radial efficiency measure known as the slacks-based measure. The idea is to transform the network system into an equivalent one that is composed of a series of subsystems with parallel structures. Based on the property that the system efficiency is the product of the division efficiencies adjusted by the linkage efficiencies for series systems and is a linear combination of the division efficiencies for parallel systems, the system efficiency can be decomposed into a function of the division and linkage efficiencies. The decomposition of the slacks-based efficiency measure works not only for the technology of constant returns to scale, but also for the case of variable returns to scale. In addition, the proposed model produces suitable efficiency scores for weakly efficient units and for those using weakly efficient units as the target to calculate efficiencies, which makes it possible to obtain reliable rankings for the assessed units.