Competing DEA procedures: analysis, testing, and comparisons (2407.15585v1)
Abstract: Reducing the computational time to process large data sets in Data Envelopment Analysis (DEA) is the objective of many studies. Contributions include fundamentally innovative procedures, new or improved preprocessors, and hybridization between - and among - all these. Ultimately, new contributions are made when the number and size of the LPs solved is somehow reduced. This paper provides a comprehensive analysis and comparison of two competing procedures to process DEA data sets: BuildHull and Enhanced Hierarchical Decomposition (EHD). A common ground for comparison is made by examining their sequential implementations, applying to both the same preprocessors - when permitted - on a suite of data sets widely employed in the computational DEA literature. In addition to reporting on execution time, we discuss how the data characteristics affect performance and we introduce using the number and size of the LPs solved to better understand performances and explain differences. Our experiments show that the dominance of BuildHull can be substantial in large-scale and high-density datasets. Comparing and explaining performance based on the number and size of LPS lays the groundwork for a comparison of the parallel implementations of procedures BuildHull and EHD.
- I. Ali. Streamlined computation for data envelopment analysis. European Journal of Operational Research, 64:61–7, 1993.
- Some models for estimating technological and scale inefficiencies in Data Envelopment Analysis. Management Science, 30:1078–1092, 1984.
- Parallel and hierarchical decomposition approaches for solving large scale Data Envelopment Analysis models. Annals of Operations Research, 73:339–372, 1997.
- A. Bessent and W. Bessent. Determining the comparative efficiency of schools through Data Envelopment Analysis. Education Administration Quarterly, 16:57–75, 1980.
- Measuring the efficiency of decision making units. European Journal of Operational Research, 2:429–444, 1978.
- A procedure for large-scale DEA computations. Computers & Operations Research, 36:1813 – 1824, 2009.
- Determining radial efficiency with a large data set by solving small-size linear programs. Annals of Operations Research, 250:147–166, 2017.
- J.H. Dulá. A computational study of dea with massive data sets. Computers & Operations Research, 35:1191 – 1203, 2008.
- J.H. Dulá. An algorithm for Data Envelopment Analysis. INFORMS Journal on Computing, 23:284–296, 2011.
- Preprocessing dea. Computers & Operations Research, 36:1204–1220, 2009.
- Competing output-sensitive frame algorithms. Computational Geometry: Theory and Applications, 45:186–197, 2012.
- T. Jie. Parallel processing of the build hull algorithm to address the large-scale dea problem. Annals of Operations Research, 295(1):453–481, 2020.
- Data envelopment analysis and big data. European Journal of Operational Research, 274:1047–1054, 2019.
- Dariush Khezrimotlagh. Parallel processing and large-scale datasets in data envelopment analysis. In Data-Enabled Analytics: DEA for Big Data, pages 159–174. Springer, 2021.
- Using lexicographic parametric programming for identifying efficient units in dea. Computers & Operations Research, 34(7):2177–2190, 2007.
- A dimensional decomposition approach to identifying efficient units in large-scale dea models. Computers & Operations Research, 36(1):234–244, 2009.
- T. Sueyoshi. A special algorithm for an additive model in data envelopment analysis. Journal of the Operational Research Society, 41(3):249–257, 1990.
- T. Sueyoshi and Y.L. Chang. Efficient algorithm for additive and multiplicative models in Data Envelopment Analysis. Operations Research Letters, 8:205–213, 1989.