Abstract
Conventional data envelopment analysis evaluates the relative efficiency of a set of homogeneous decision making units (DMUs), where DMUs are evaluated in terms of a specified set of inputs and outputs. In some situations, however, a performance factor could serve as either an output or an input. These factors are referred to as dual-role factors. The presence of dual-role factor among performance factors gives rise to the issue of how to fairly designate the input/output status to such factor. Several studies have been conducted treating a dual-role factor in both methodological and applied nature. One approach taken to address this problem is to view the dual-role factor as being nondiscretionary and connect it to the returns to scale concepts. It is argued that the idea of classifying a factor as an input or an output within a single model cannot consider the causality relationships between inputs and outputs. In this paper we present a mixed integer linear programming approach with the aim at dealing with the dual-role factor. Model structure is developed for finding the status of a dual-role factor via solving a single model while considering the causality relationships between inputs and outputs. It is shown that the new model can designate the status of a dual-role factor with half calculations as the previous model. Both individual and aggregate points of view are suggested for deriving the most appropriate designation of the dual-role factor. A data set involving 18 supplier selections is adapted from literature review to illustrate the efficacy of the proposed models and compare the new approach with the previous ones.
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Acknowledgments
The research was supported by the Czech Science Foundation (GACR Project 14-31593S) and through European Social Fund within the Project CZ.1.07/2.3.00/20.0296.
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Toloo, M., Barat, M. On considering dual-role factor in supplier selection problem. Math Meth Oper Res 82, 107–122 (2015). https://doi.org/10.1007/s00186-015-0507-z
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DOI: https://doi.org/10.1007/s00186-015-0507-z