Abstract
The problem of ranking efficient decision making units (DMUs) is of interest from both theoretical and practical points of view. In this paper, we propose an integrated data envelopment analysis and mixed integer non-linear programming (MINLP) model to find the most efficient DMU using a common set of weights. We linearize the MINLP model to an equivalent mixed integer linear programming (MILP) model by eliminating the non-linear constraints in which the products of variables are incorporated. The formulated MILP model is simpler and computationally more efficient. In addition, we introduce a model for finding the value of epsilon, since the improper choice of the non-Archimedean epsilon may result in infeasible conditions. We use a real-life facility layout problem to demonstrate the applicability and exhibit the efficacy of the proposed model.
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Acknowledgements
The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. This research was supported in part by the European Social Fund (CZ.1.07/2.3.00/20.0296) and the Czech Science Foundation (GAČR16-17810S).
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Toloo, M., Tavana, M. & Santos-Arteaga, F.J. An integrated data envelopment analysis and mixed integer non-linear programming model for linearizing the common set of weights. Cent Eur J Oper Res 27, 887–904 (2019). https://doi.org/10.1007/s10100-017-0510-y
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DOI: https://doi.org/10.1007/s10100-017-0510-y