The efficacy of DEA in efficiency measurement is the primary reason why DEA has gained significant attentions from researchers across the world. The primary benefits of DEA include its ability to provide both efficiency scores and improvement targets for decision making units(DMUs) under measurement. The improvement targets suggest several ways to improve inefficient DMUs’ efficiency. An improvement target that is close to the DMU under measurement is considered to be easy-to-achieve in DEA. However, in previous studies, most conventional DEA models used for China’s efficiency measurement provided a far improvement targets that cannot be achieved immediately and would require several years. Thus, a least-distance DEA model that can provide a closer improvement target is used in our study. Furthermore, a conventional DEA model and a ratio type DEA model are used to study and compare the performances. All three DEA models are applied to the measurement of China’s energy efficiency in 1997, 2002, 2007, and 2012. The differences in the efficiency scores and improvement targets provided by the three models have been reviewed. Although the results show different improvement targets, it can be inferred that reducing the overall energy consumption and increasing the GDP are still two effective measures for inefficient provinces, districts, and cities according to the experimental results. 

Data envelopment analysis (DEA) is widely used to evaluate and improve the relative efficiency of decision making units (DMUs), which have multiple inputs and outputs. However, traditional DEA models can only handle a single perspective. We proposed a new approach for efficiency improvement under multiple perspectives based on the least-distance DEA.  The Nash bargaining game (NBG) theory has been used in extant studies to avoid conflicts and obtain a rational direction of efficiency improvement under multiple perspectives. Because of the practicality of the closest efficient target, we first proposed a least-distance DEA model incorporating NBG. A numerical experiment is conducted to compare the performance of our proposed approach with that of previous studies. The results reveal that our proposed approach can (1) evaluate the efficiency of DMUs under multiple perspectives, and (2) provide more easy-to-achieve efficiency improvement suggestions for the assessed DMUs. Thus, the proposed approach has remarkable potential applicability in decision making.

Data envelopment analysis(DEA) has been widely applied to evaluate relative efficiency and provide benchmarking information(efficient target) for decision making units(DMUs). Recently, the least-distance DEA has been extensively researched, and various corresponding models are proposed because of the practicability of the least-distance benchmarking information(closest efficient target). We have formulated the least-distance range adjusted measure (LRAM), which satisfies a set of desirable properties, as a new practical DEA model for efficiency evaluation and benchmarking. Based on more numerical experiments and deeper analysis, we found (1) that efficient targets provided by the LRAM match the evaluated DMUs more closely than those provided by the convention range adjusted measure(RAM) for most of the inputs and outputs, (2) although LRAM may suggest modifying a greater number of inputs and outputs than that suggested by the RAM, it optimizes the input-output modification to significantly reduce the total percentages of modifications required for each of the inefficient banks to achieve efficiency. Thus, the LRAM suggests the required modifications to achieve efficiency in a more equitable and balanced manner.

Dataenvelopment analysis (DEA) introduced in 1978 has been widely applied toevaluating the relative efficiency and providing efficient target for decisionmaking units (DMUs). The conventional range adjusted measure (RAM) in DEA actsas a well-defined measure satisfying a set of desirable properties, especiallythe strong monotonicity. However, because of the practicality of the closestefficient target, we focus on formulating the least-distance range adjustedmeasure (LRAM) and proposing the use of an efficient mixed integer programming(MIP) approach to compute it. Our formulated LRAM: (1) satisfies the desirableproperties as the conventional RAM; (2) provides the least-distance benchmarkinginformation for inefficient DMUs, which will make the efficiency improvementeasy, and (3) can be computed easily by using the proposed MIP approach. Here, weapply the LRAM to a Japanese banking data set corresponding to the period 2017-2019.Based on the results: the LRAM generates higher efficiency scores and allowsinefficient banks to improve their efficiency with a smaller extent ofinput-output modification than that required by the RAM, which indicates thatthe LRAM can provide more easy-to-achieve benchmarking information for inefficientbanks. Therefore, from the perspective of the managers of DMUs, we provide a valuableLRAM for efficiency evaluation and benchmarking analysis.

DataEnvelopment Analysis(DEA) has been widely used as a means of relativeefficiency evaluation since the first DEA model was introduced in 1978. It uses mathematicalprogramming techniques and models to evaluate the relative efficiency of decisionmaking units(DMUs) with multiple inputs and outputs. In DEA, an inefficient DMU’sefficiency can be improved by adjusting the inputs or outputs or both to reachthe projection target on the efficient frontier. In this research, we aim atsolving the lowest cost problem in DEA, which is to provide an efficient targetfor an inefficient DMU with the lowest adjustment costs. For this purpose, anew approach based on the least distance DEA model is proposed. Here, themarginal costs of adjusting the inputs and outputs are assumed to be known andsymmetrical. For the practical merit, different with the existing studies, our approachis able to increase inputs and decrease outputs. Numerical experiments are conductedto compare the performance of the proposed approach with previous existingstudies. The results show that the proposed approach can always provide anefficient target with no higher total adjustment costs than the costs oftargets provided by previous approaches. Therefore, this research’scontributions can be summarized as follows:　　• Propose an approach to DEA that minimizes the totaladjustment costs incurred when transitioning an inefficient DMU to an efficienttarget;• Enable the real world condition that some inputs couldbe increased or some outputs could be reduced to be reflected in the targetsetting process.Thus, the proposed approach is more practical and usefulfor decision makers.