Benchmarking with quasiconcave production function under Variable returns to Scale: Exploration and empirical application

The variable returns to scale data envelopment analysis (VRS-DEA) benchmarking models are developed by assuming convexity on technology. However, this assumption may be not consistent with the classical microeconomic theory where marginal product initially increases but diminishing returns eventually set in. Accordingly, the selected benchmarks may aggregate best practices, which are less attainable in performance improvement. This paper thus proposes a VRS-DEA benchmarking model with quasiconcave production function, consistent with classical microeconomic theory. A novel approach for determining the returns to scale of Decision-Making Units (DMUs) is developed. The hyperplane of the quasiconcave production function is characterized. Benchmarks are selected by minimizing the weighted distance between the evaluated DMU and the hyperplane. An empirical application of China's tourism sector is used to validate the approach. The empirical results show that Mergers and Acquisitions are beneficial for smaller hotels as the production of most regions in China's tourism sector is subject to increasing returns to scale.