MaxDEA Update History
Non-convex Frontier (FDH, ERH): algorithm update.
EBM： updated algorithm for calculating the epsilon values in models with non-orientation, super-efficiency, or undesirable outputs.
Code signed (digital certificate).
Minor improvements in data importing and processing.
Sequential Malmquist (1-TFP Index) model: algorithm optimized, 30% faster than before
Security update
The traditional DEA model allows the DMUs to evaluate their maximum efficiency scores using their most favourable weights. This kind of evaluation with total weight flexibility may prevent the DMUs from being fully ranked and make the evaluation results unacceptable to the DMUs. To solve these problems, Wu et al (2016) introduce a common weights model with the concept of satisfaction degree of a DMU in relation to a common set of weights. The common-weight evaluation approach can generate for the DMUs a set of common weights that maximizes the least satisfaction degrees among the DMUs, and can ensure that the generated common set of weights is unique and that the final satisfaction degrees of the DMUs constitute a Pareto-optimal solution. All of these factors make the evaluation results more satisfied and acceptable by all the DMUs.
The traditional DEA model seeks to maximize the efficiency score of the evaluated DMU using the most favorable set of input and output weights under the constraint that the efficiency scores of all DMUs are less than or equal to one.
Entani et al (2002) put forth a minimum efficiency model (a pessimistic DEA model). On the contrary, the minimum efficiency model seeks to minimize the efficiency score of the evaluated DMU using the most unfavorable set of input and output weights under the constraint that the maximum efficiency of all DMUs is equal to one.
Two options added under the option “Node Score Including Intermediates”: “NonIncreasing intermediates treated as input only” and “NonDecreasing intermediates treated as output only”. In SBM Network model and SBM Dynamic model, when slacks of the intermediates are included in computing node scores, these two options can limit the node scores within 0-1, i.e., avoid the node scores greater than 1 or less than 0.
When the EBM model is combined with MetaFrontier, the EBM parameters (epsilon and weights) are calculated separately in the MetaFrontier and GroupFrontier models, i.e., the MetaFrontier model and the GroupFrontier model use their own parameters. The MetaFrontier scores and the GroupFrontier scores are computed using different EBM parameters, so they are not comparable, and the computed TGRs may be greater than 1.
For the same reason, when the EBM model is used to compute Scale Efficiency, The CRS scores and the VRS scores are computed using different EBM parameters, so they are not comparable, and the computed scale efficiency scores may be greater than 1.
And when the EBM model is combined with Fuzzy inputs/outputs, the upper bound score may be less than the lower bound score.
To avoid the above problems, the user must use the “Customized” epsilon and weights in the EBM model, i.e., the user need input the values of epsilon and weights, so that both models use these parameters.
From MaxDEA 6.15, we resolve the above problems as follows.
1) when the EBM model is combined with MetaFrontier, both the MetaFrontier model and the GroupFrontier model use the same EBM parameters--the parameters from the MetaFrontier model.
2) when the EBM model is used to compute Scale Efficiency, both the CRS model and the VRS model use the same EBM parameters--the parameters from the CRS model.
3) when the EBM model is combined with Fuzzy inputs/outputs, both the lower bound model and the upper bound model use the same EBM parameters--the parameters from the lower bound model.
The user can still use the “Customized” epsilon and weights in the EBM model to avoid the EBM problems, and for panel data (Malmquist or Window model), the “Customized” epsilon and weights must be used.
The two-stage network model defines a two-stage production system, in which all the outputs (intermediate) from the first stage go into the second stage as inputs (Inputs --> Intermediates --> Outputs). The two-stage DEA model provides not only an overall efficiency score for the entire system, but also yields efficiency scores for both the individual stages. Chiang Kao and Hwang (2008) developed an approach for the above two-stage network model where the overall efficiency score of the two-stage network can be decomposed into the product of the efficiency score of the first stage and the efficiency score the second stage.
MaxDEA results are sorted by DMU name, not the original order in the data. If you want the results to keep the original order, you can sort the results using this field, “DMU Order in Data”.
The conventional DEA requires accurate input and output data. However, the observed data in real world are sometimes imprecise. Imprecise or vague data is often expressed with bounded intervals.
In MaxDEA, the DEA model with fuzzy inputs/outputs with bounded intervals is converted into a pair of standard DEA models, so that the lower and upper bounds of the efficiency scores are obtained respectively.
In MaxDEA Pro, the detailed results of bootstrap models are saved in internal tables. Due to the limitations of Access on table columns (maximum 255) and file size (maximum 2G), the maximum number of periods is limited to about 50.
New data engine is used in importing Excel data: faster and more stable.
The bootstrap models use built-in statistical functions, instead of Excel statistical functions: bootstrapping is more stable.
Minimum Distance to Weak Efficient Frontier, Minimum Distance to Strong Efficient Frontier and EBM, now can be combined with Malmquist, Cluster, Customized Benchmarking.
In MaxDEA 6.0 or lower versions, the panel data for Malmquist models must be balanced, i.e., there must be equal number of DMUs in each period. If the values for some DMUs in one or more periods are missing, these DMUs must be deleted from the dataset. However in such cases, the Malmquist indices for the periods that have complete data should be computed, and the deleted DMUs may be used as benchmarks for other DMUs, so exclusion of the DMUs with missing values results in loss of information. In MaxDEA 6.1, the panel data for Malmquist models can be unbalanced. If the values for some DMUs in one or more periods are missing, the Malmquist indices for the relevant periods will not be computed, but the Malmquist indices for the periods that have complete data will be computed. In addition, the DMUs with missing values may serve as benchmarks for other DMUs at the periods that they have data.
The first version of MaxDEA has the following features: Distance: Radial, Non-radial (SBM) and Hybrid; Orientation: Input-, Output- and Non- oriented; RTS: CRS, VRS, NIRS, NDRS and GRS; FDH model; Super-efficiency; Nondiscretionary model; Bounded model; Preference (weighted) model; Malmquist model.