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Contruction of a smoothed DEA frontier

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Author(s): Mello João Carlos Correia Baptista Soares de | Lins Marcos Pereira Estellita | Gomes Eliane Gonçalves

Journal: Pesquisa Operacional
ISSN 0101-7438

Volume: 22;
Issue: 2;
Start page: 183;
Date: 2002;
Original page

Keywords: smoothed frontier | tradeoffs | Ritz method

ABSTRACT
It is known that the DEA multipliers model does not allow a unique solution for the weights. This is due to the absence of unique derivatives in the extreme-efficient points, which is a consequence of the piecewise linear nature of the frontier. In this paper we propose a method to solve this problem, consisting of changing the original DEA frontier for a new one, smooth (with continuous derivatives at every point) and closest to the original frontier. We present the theoretical development for the general case, exemplified with the particular case of the BCC model with one input and one output. The 3-dimensional problem is briefly discussed. Some uses of the model are summarised, and one of them, a new Cross-Evaluation model, is presented.
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