Cross efficiency measurement and decomposition in two basic network systems

The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship. (C) 2018 Elsevier Ltd. All rights reserved.