A fair evaluation of certain stage in a two-stage structure: revisiting the typical two-stage DEA approaches |
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Affiliation: | 1. College of Auditing and Evaluation, Nanjing Audit University, Nanjing 211815, Jiangsu Province, China;2. Foisie Business School, Worcester Polytechnic Institute, Worcester, MA 01609, USA;1. School of Economics and Management, Beihang University, Beijing 100191, PR China;2. Foisie School of Business, Worcester Polytechnic Institute, Worcester, MA 01609, USA;1. International Center for Auditing and Evaluation, Nanjing Audit University, Nanjing 211815, PR China;2. Manning School of Business, University of Massachusetts at Lowell, Lowell, MA 01845, USA |
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Abstract: | The efficiency of decision processes with a two-stage structure has been studied by some modified versions of Data Envelopment Analysis (DEA) methodology, such as the relational or centralized model, and the non-cooperative model. After revisiting the rationale of the centralized model provided by the literature, we find that some unfairness exist in its efficiency evaluation of certain stage. This unfairness leads to the usual underestimation of the overall efficiency by the centralized model. Furthermore, because the independent DEA model for one stage ignores its relation and coordination with the other stage and the two-stage system, externalities between these members may arise and lead to the seeming contradiction in efficiencies derived by independent DEA models for the stages and the black box system. Therefore, we argue that the efficiency of certain stage in the context of a two-stage structure should be reevaluated instead of simply using the independent DEA model. A sequence of leader-follower procedures, with data adjustment on intermediates, is proposed to eliminate the externalities and to ensure a fair evaluation. We find that, after this data adjustment, the reevaluation of the second stage for a given Decision Making Unit (DMU) yields the same result as obtained by the standard DEA model regarding the two-stage as a black box. Moreover, some explicit relations are established between the black box model, the centralized model, and the non-cooperative model. Two typical examples taken from the literature illustrate our main results. Our findings also imply that more emphasis should be placed on the game theoretic DEA approach to model the efficiency evaluation of two-stage processes. |
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Keywords: | Data Envelopment Analysis Two-stage structure Fair evaluation Coordination Leader-follower procedures |
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