This paper proposes a new efficiency measure that aims at capturing the overall distance to the efficient frontier and not the distance corresponding to a specific projection, as most oriented and non‐oriented methods compute. The proposed approach uses a grid‐based method to sample all possible improvement directions from a given operating point and for each direction it computes a directional efficiency score solving a directional distance function model. This provides information about the distribution of the distance to the efficient frontier. Therefore, the proposed multidirectional efficiency measure does not provide a single efficiency score but a distribution of efficiency scores. The minimum, the median, the Q1 and Q3 quartiles and the maximum can be singled out as representatives of that distribution. The latter corresponds to the closest among the computed efficient targets. In addition to the efficiency score distribution, the associated efficient targets are also provided. The proposed approach can take into account integer and nondiscretionary variables and a preference structure. An application of the method to assess the efficiency of material recovery facilities is presented.
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.
This paper presents a new Data Envelopment Analysis (DEA) target setting approach that uses the Compromise Programming (CP) method of multiobjective optimization. This method computes the ideal point associated to each Decision Making Unit (DMU) and determines an ambitious, efficient target that is as close as possible (using an lp metric) to that ideal point. The specific cases p=1, p=2 and p= are separately discussed and analyzed. In particular, for p=1 and p=, a lexicographic optimization approach is proposed in order to guarantee uniqueness of the obtained target. The original CP method is translation invariant and has been adapted so that the proposed CP-DEA is also units invariant. An lp metric-based efficiency score is also defined for each DMU. The proposed CP-DEA approach can also be utilized in the presence of preference information, non-discretionary or integer variables and undesirable outputs. The proposed approach has been extensively compared with other DEA approaches on a dataset from the literature.
The goal in efficiency analysis is not only to evaluate a Decision Making Unit (DMU) performance, but also to find an efficient target which provides information on inputs reduction and outputs increment values that are necessary to remove inefficiencies for each inefficient DMU. In Data Envelopment Analysis (DEA) the target unit is located on the efficient frontier and possibly far from the unit under assessment. Therefore, in practice performance improvement seems to be disappointing or even impossible to achieve in only one step for some inefficient DMUs. In this regard, finding intermediate targets is of great importance in benchmarking literature. In this paper we find a sequence of targets instead of a single target for each inefficient unit. In our method, the intermediate target at each step has three properties:(I) the intermediate targets and the unit under evaluation are all similar in size; (II) efficiency scores are ascending through the sequence of targets; (III) the target unit at each step is close to the special part of the efficient frontier as much as possible. These properties lead to finding a target that is more achievable in real applications.
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