Parallel processing of the Build Hull algorithm to address the large-scale DEA problem

Build Hull is currently one of the most efficient methods to address the large-scale data envelopment analysis problem. In this paper, the computational complexity of Build Hull is established, implying that the dimension of the data set has a strong influence on computational efficiency. Based on the complexity result, we find that the “worst density” of Build Hull monotonically increases with respect to dimension. In addition, a two-phase parallel Build Hull algorithm is proposed to enhance the computational efficiency of Build Hull. The parallel procedure is based on the minimum volume enclosing ellipsoid technique, which enables the exclusion of a large number of DMUs in the first phase. A sensitivity analysis-based technique is also proposed to substantially reduce computational time in the second phase. Numerical tests support our theoretical results.