Fuzzy evaluation of fixed cost allocation in two-stage networks with undesirable outputs: Considering ideal and anti-ideal points
نویسندگان
1 Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Turkiye.
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
doi
10.22105/jfea.2025.490267.1710چکیده
Data Envelopment Analysis (DEA) is an effective method for evaluating the performance of organizations, providing a more accurate assessment by considering their internal relationships in a networked manner rather than treating them as black boxes. When considering many organizations, challenges often emerge, such as uncertainty, ambiguity, and undesirable factors in the data and indicators under study. Fuzzy logic, which accounts for both ideal and non-ideal Decision-Making Units (DMUs), offers a robust approach for effectively distinguishing the performance of fuzzy units. This paper examines fuzzy rather than deterministic data within a two-stage network with undesirable outputs. Two virtual fuzzy units are introduced to evaluate this network: the Fuzzy Ideal Decision-Making Unit (FIDMU) and the Fuzzy non-Ideal Decision-Making Unit (FADMU). By employing a lexicographic approach, the best and worst fuzzy efficiencies of FIDMU and FADMU are calculated. Subsequently, the best and worst efficiency values are computed for each unit under evaluation by determining a Common Set of Weights (CSWs) in Fuzzy Data Envelopment Analysis (FDEA). Furthermore, by integrating the obtained efficiency values with the efficiencies of the ideal and non-ideal points, a relative proximity index is calculated for overall evaluation. This index facilitates a better ranking of the units within the studied network. Additionally, to enhance the performance of fuzzy units, the allocation of fixed costs is implemented so that the fuzzy proximity index to the ideal unit does not worsen after allocation and improves, if possible. Thus, the primary innovation of this study lies in developing a resource allocation method specifically aimed at enhancing the fuzzy proximity index under conditions of uncertainty and the presence of undesirable outputs. The proposed model is applied to assess the performance of 20 commercial bank branches in Iran.