Multiobjective centralized DEA approach to Tokyo 2020 Olympic Games

"Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License...."There exist two types of Data Envelopment Analysis (DEA) approaches to the Olympic Games: conventional and fixed-sum outputs (FSO). The approach proposed in this paper belongs to the latter category as it takes into account the total number de medals of each type awarded. Imposing these constraints requires a centralized DEA perspective that projects all the countries simultaneously. In this paper, a multiobjective FSO approach is proposed, and the Weighted Tchebychef solution method is employed. This approach aims to set all output targets as close as possible to their ideal values. In order to choose between the alternative optima, a secondary goal has been considered that minimizes the sum of absolute changes in the number of medals, which also renders the computed targets to be as close to the observed values as possible. These targets represent the output levels that could be expected if all countries performed at their best level. For certain countries, the targets are higher than the actual number of medals won while, for other countries, these targets may be lower. The proposed approach has been applied to the results of the Tokyo 2020 Olympic Games and compared with both FSO and non-FSO DEA method

A critical review of the main methods to treat undesirable outputs in DEA

The treatment of undesirable outputs in Data Envelopment Analysis (DEA) has received great research attention recently. As such and as are presented in this work, there are four possible options to deal with those: first ignoring them from the production function; second treating them as regular inputs; third treating them as normal outputs and fourth performing necessary transformations to take them into account. Also new model propositions for their treatment are being presented. Each method brings with it, benefits and drawbacks which each researcher should take into account at every stage of their research and assess which method is more appropriate to be used

A critical review of the main methods to treat undesirable outputs in DEA

The treatment of undesirable outputs in Data Envelopment Analysis (DEA) has received great research attention recently. As such and as are presented in this work, there are four possible options to deal with those: first ignoring them from the production function; second treating them as regular inputs; third treating them as normal outputs and fourth performing necessary transformations to take them into account. Also new model propositions for their treatment are being presented. Each method brings with it, benefits and drawbacks which each researcher should take into account at every stage of their research and assess which method is more appropriate to be used

The linear formulation of the ZSG-DEA models with different production technologies

International audienceThe zero sum gains data envelopment analysis models (ZSG-DEA models) are non-linear. In this paper, we first show that the ZSG-DEA models can be transformed to linear or parametric linear models and discuss the feasible domains of the parameters. Second, we show that the linear formulations of ZSG-DEA models under the equal output reduction strategy and the proportional output reduction strategy in a single output case are equivalent to the output-oriented super-efficiency model under variable returns-to-scale (VRS) assumption. As a matter of course, the models may encounter infeasibility. Third, we propose the linear transformations of ZSG-DEA models under constant returns-to-scale (CRS) assumption and compare them with the VRS models. In the end, we evaluate the participant countries at the Olympic Games by the linear equivalent models with multiple outputs under different weight restrictions. Our results are compared with the efficiencies obtained from the original ZSG-DEA model with an aggregated output under both CRS and VRS assumptions. It is found that the original method with aggregated output tends to underestimate the efficiencies of DMUs