DEA target setting using lexicographic and endogenous directional distance function approaches

Abstract

Directional Distance Function (DDF) is an approach often used in Data Envelopment Analysis (DEA) due to its clear interpretation and to the flexibility provided by the possibility of choosing the projection direction towards the efficient frontier. In this paper two new DDF approaches are considered. The first one uses an exogenous directional vector and a multi-stage methodology that at each step uses the projection along the input and output dimensions of the directional vector that can be improved. This lexicographic DDF approach also computes a directional efficiency score and a directional inefficiency indicator for each input and output variable. The second approach is a non-linear optimization model that endogenously determines the directional vector so that the smallest improvement required to reach the efficient frontier is computed.

Interactive multiobjective DEA target setting using lexicographic DDF

“…A problem with this conventional DDF model is that it computes a weakly efficient target. To remedy that, Lozano and Soltani (2018) have proposed a lexicographic DDF approach which moves along the given direction  …”

“…However, the approach proposed in this paper does not use conventional DDF. Instead, it uses a Lexicographic DDF method, which is somewhat more complex but guarantees reaching the efficient frontier (see Lozano and Soltani 2018). A simpler alternative to the Lexicographic DDF method is to use DDF followed by a slacks-maximization phase (see Tavana et al 2018).…”

“…from the own DMU, and using a lexicographic DDF approach. The lexicographic DDF approach was proposed in Lozano and Soltani (2018) for DEA target setting when the DMU can articulate its preference a priori. It is an extension of the lexicographic radial approach of Korhonen et al (2018) to any given directional vector.…”

“…The contributions of the paper are, therefore, twofold: it is the first IMO DEA approach that uses an iterative direction-sampling approach analogous to the method of Steuer and Choo (1983) but projecting not from an outside operating point like the ideal point but from the own DMU. Also, it computes the targets using the lexicographic DDF method (Lozano and Soltani 2018), which is more complex but also more effective than conventional DDF.…”

“…The structure of the paper is the following. In Section 2 the IWT method of Steuer and Choo (1983) and the lexicographic DDF approach of Lozano and Soltani (2018) are briefly reviewed.…”