Measuring Performance of Dynamic and Network Structures by SBM Model

1. Introduction

Data envelopment analysis is a powerful instrument to measure the relative efficiency of decision making unites (DMU) which consume several inputs to produce several outputs Charnes et al. (1978) that these models do not consider the DMUs’ internal structure, including sub-DMUs and links that connect the sub-DMUs to form the basic DMU, is one of the problems of these models. DMUs can, in practice, be considered each as a set of different activities occurring in various sectors such as hospitals, universities, cities, countries, firms and the like. Therefore, in most cases, DMUs can be considered as having an internal or network structure. Models with DEA network structures have been suggested by Färe (1991), and Färe and Grosskopf (1996, 2000). Network models which consist of a two-stage structure have been proposed by Sexton and Lewis (2003) and expanded to multi-stage network models in Lewis and Sexton (2004). Indeed, Lewis and Sexton (2004) considered a set of DMUs witha structure of a network of sub-DMUs such that some DMU consume and produce resources that are produced and consumed by other sub-DMUs, respectively. They introduced a network-DEA model for the input and output orientationswith standard assumptions and incorporated reverse quantities as inputs, intermediate products and outputs. They also showed the advantages of the network-DEA models compared withstandard DEA models because of the ability to detect inefficiencies and to determine the efficiency score of any DMU by the efficiency of individual stages. Moreover, network models with parallel, series, and combinational structures have been suggested by some authors. Prieto and Zofío (2007) proposed a model to optimize the systems with multi-stage structures in which the input–output framework includes identifying the best practice economies. Regardingthe input–output framework, they argued that it is possible to optimize primary input allocation, intermediate production, and final demand production based on the non-parametric DEA approach. Kao (2009) presenteda relational network-DEA model to evaluate the efficiency of the network system and those of the processes at the same time such that the interconnection betweenthe processesis taken into consideration. In other words, this model is able to evaluate the aggregate performance of the component processes. In fact, the original system with the network structure can be converted into a series network where each stage in the series has a parallel structure. In this system, the efficiency scoreis calculated in two parts: 1. The product of the efficiencies of the stages in the series part of the system. 2. Inefficiency slack of each stage towardthe sum of the inefficiency slacks of its components in the parallel part of the system. Yu and Fan (2009) developed DEA models based upon mixed structure network data envelopment analysis (MSNDEA) to estimate the production efficiency, service effectiveness, and operational effectiveness of multimode transit firms simultaneously. The main applicability of this model is considering the internal linkage and shared inputs between DMUs. Network SBM is a new network DEA model based on the concept of slacksintroduced by Tone and Tsutsui (2009). They utilized this model to evaluate divisional efficiencies along with the overall efficiency of DMUs in systems with anetwork structure and intermediate products. In other words, the above-mentioned network-DEA models obtain the radial efficiency of DMUs, while Tone and Tsutsui (2009) suggested a network DEA model with the slack-based measure (SBM) that estimates the efficiency non-radially. In addition to reviewing, they considered the relationship between these models and established that all the existing approaches can be classified as utilizing either leader-follower or cooperative game concepts. Hsieh and Lin (2010) utilized a network DEA model to evaluate the efficiency and effectiveness of international tourist hotels (ITHs) with different production processes in Taiwan. They discussed and examined the relationships between efficiency, effectiveness, and overall performance of all hotels under evaluation and, on the basis of the results; they recommended ways of enhancing the overall performance of the hotel industry in Taiwan. Scale and cost efficiency analysis of network systems is an interesting problem in DEA that has beenconsidered by Lozano (2011). The structure of the given network systems consists ofa set of DMUs with some sub-processes and intermediate flows among them. Technical and cost efficiency network-DEA models introduced that any sub-process can have returns to scale corresponding to itself. Chen and Yan (2011) presented a new network model with an internal structure of supply chain based on the DEA approach. Indeed, they proposed three different network-DEA models under the concept of centralized, decentralized, and mixed organization mechanisms. Efficiency analysis, the relationship between supply chain and divisions, and therelationships among the three different organization mechanisms were examined in detail. Zhao et al. (2011) provided a network DEA evaluation of a downtown space reservation system (DSRS). They considered two types of network-DEA models, radial and slacks-based models, and showed that individual node performance drives network DEA performance. Fukuyama and Mirdehghan (2012) indicated some problems associated with existing network DEA models and identified the efficiency status in network DEA. Their method provided a practical computational procedure. Taiwan bank branches have their major profits from the internal fund transfers and a private bank may have remedial effects for improving the branch performance. Yang and Liu (2012) utilized the network DEA method toevaluate managerial efficiency in Taiwan bank branches. They proposed a network performance framework to measure bank branch performance and a network-DEA model to assess all bank branches on a common base.