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

  • Original-Comparative Computational Study
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Abstract

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.

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Notes

  1. Applying the simplex method to solve a standard linear program model:

    $$\begin{aligned} \begin{array}{cl}\min \limits _x &{} c^T x\\ \text {s.t.} &{} Ax=b,\\ \ &{} x\ge 0\\ \end{array} \end{aligned}$$

    with \(A\in \mathbb {R}^{m\times n}\), rank\((A)=m<n\), it needs at most \(n \atopwithdelims ()m\) iterations, and O(mn) flops are needed during each iteration.

  2. Let the MVEE of data set \(\mathcal {A}\) be E(H, c). Then, the homothetic ellipsoid \(\frac{1}{m} E(H,c)\) is contained in the convex hull of \(\mathcal {A}\).

  3. http://www.people.vcu.edu/~jdula/MassiveScaleDEAdata/.

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Acknowledgements

This research is supported by National Natural Science Foundation of China Grant No. 7160010139 and 71704101, Soft Science Foundation of Shanghai Grant No. 19692104600, and Humanities and Social Science Fund of Ministry of Education of China Grant No. 17YJC630094.

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  1. Business School, University of Shanghai for Science and Technology, No. 516 Jun Gong Road, Shanghai, 200093, China

    Tao Jie

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Correspondence to Tao Jie.

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In memory of my Mum, Wen Zonglan.

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Jie, T. Parallel processing of the Build Hull algorithm to address the large-scale DEA problem. Ann Oper Res 295, 453–481 (2020). https://doi.org/10.1007/s10479-020-03698-2

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