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Over the last decade, many studies have adopted the data envelopment analysis (DEA)-type metafrontier framework to relax the constraint of technological heterogeneity. In conventional metafrontier analyses, either radial or nonradial DEA models are used in two separate DEA efficiency analyses. The results of a metafrontier analysis may be biased if this approach is adopted in a nonradial DEA model. One possible problem is that the value of the technology gap ratio is greater than one because the technology gaps to be estimated for decision-making units (DMUs) under different technology groups relative to the metatechnology have no connection between group frontiers and metafrontiers. Furthermore, the direction of projection of each DMU onto the metafrontier is totally independent of the direction to the efficiency frontier of the respective group frontier. Our proposed integration of group technology and metatechnology constraints into a union model offers a possible solution to the existing metafrontier problem and provides more robust metafrontier results regardless whether radial or nonradial DEA models are used. Four numerical examples and one empirical application are demonstrated, and the results appear to support the use of our proposed model.

While the assessment of higher education systems is informative to both policy makers and individuals, it is subjective and performed according to experts' judgment. The present study proposes a relatively objective approach, hierarchical data envelopment analysis (H-DEA), to rank higher education systems. Unlike the subjective approach, H-DEA utilizes endogenous weight determination, allowing assessors to identify the relative importance of each attribute and subattribute. Utilizing the U21 Ranking of National Higher Education System 2020 data, our analysis indicates that the output attribute is a crucial factor influencing the overall performance of higher education systems, even considering countries' stage of development and culture. The computed weights of the H-DEA framework show various attributes' different contributions by group. Resources allocated to the higher education system are important for developing countries, while a high degree of internationalization and a strong link between academia and industry matter for advanced countries. Surprisingly, Asian and Western cultures experience similar performance in their higher education systems, reflecting the Asian higher education system's development toward the Western style. The performance of countries with non-Asian-non-Western cultures, as expected, lags behind, and putting more resources into these countries' higher education system is a way to enhance the overall performance.

Medication management is a complex but critical process within the healthcare delivery system. The pharmacy department in healthcare facilities is responsible for acquisition, distribution and dispensing of medication to patients that involves a series of network process. This process can be categorized into two main subprocesses: i) pharmacy store and ii) patient services (i.e., ambulatory and inpatient pharmacy). The objective of this study was to investigate the relative efficiency level of the two subprocesses of pharmacy services in Malaysia's public hospitals. We used a nonconvex metafrontier technology to estimate technical efficiency of hospital pharmacies between specialist and nonspecialist hospital categories under the dynamic network data envelopment analysis (DNDEA) framework. For overall efficiency, both specialist and nonspecialist categories had similar mean efficiency scores. However, when measuring the efficiency level according to pharmacy store and patient services separately, the nonspecialist category had a higher mean efficiency score in pharmacy store, whereas for patient service efficiency, both categories had similar results. The patient service efficiency level was lower consistently over time, suggesting that the overall inefficiency of hospital pharmacy is greatly influenced by the inefficiency of the patient service. This suggests that systematic improvements in patient service efficiency should be a higher priority than pharmacy store efficiency to further increase the overall efficiency level. We believe that our findings will provide valuable information to policymakers towards achieving an efficient public healthcare service.