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Imposing the Regular Ultra Passum law in DEA models

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  • Olesen, Ole Bent
  • Petersen, Niels Christian

Abstract

Recently there has been some discussion in the literature concerning the nature of scale properties in the Data Envelopment Model (DEA). It has been argued that DEA may not be able to provide reliable estimates of the optimal scale size. We argue in this paper that DEA is well suited to estimate optimal scale size, if DEA is augmented with two additional maintained hypotheses which imply that the DEA-frontier is consistent with smooth curves along rays in input and in output space that obey the Regular Ultra Passum (RUP) law, i.e. monotonically decreasing scale elasticities. A necessary condition for a smooth curve passing through all vertices to obey the RUP-law is presented. If this condition is satisfied then upper and lower bounds for the marginal product at each vertex are presented. It is shown that any set of feasible marginal products will correspond to a smooth curve passing through all points with a monotonic decreasing scale elasticity. The proof is constructive in the sense that an estimator of the curve is provided with the desired properties. A typical DEA based return to scale analysis simply reports whether or not a DMU is at the optimal scale based on point estimates of scale efficiency. A contribution of this paper is that we provide a method which allows us to determine in what interval optimal scale is located.

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  • Olesen, Ole Bent & Petersen, Niels Christian, 2013. "Imposing the Regular Ultra Passum law in DEA models," Omega, Elsevier, vol. 41(1), pages 16-27.
    • Handle: RePEc:eee:jomega:v:41:y:2013:i:1:p:16-27
    DOI: 10.1016/j.omega.2011.08.012
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    Cited by:

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    2. Tao, Xiangyang & An, Qingxian & Goh, Mark, 2024. "Plant capacity utilization with piecewise Cobb-Douglas technology: Definition and interpretation," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1034-1043.
    3. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    4. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.
    5. Olesen, Ole B. & Ruggiero, John, 2014. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 235(3), pages 798-809.
    6. An, Qingxian & Zhang, Qiaoyu & Tao, Xiangyang, 2023. "Pay-for-performance incentives in benchmarking with quasi S-shaped technology," Omega, Elsevier, vol. 118(C).

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