Identifying anchor points and determining adjustment bounds in data envelopment analysis with negative data

Identifying anchor points and determining their input and output adjustment bounds are significant topics in data envelopment analysis (DEA). An anchor point (AP) is an extremely efficient decision-making unit (DMU) positioned at the intersection of the strongly and weakly efficient frontiers of the technology. This implies that increasing at least one input or decreasing at least one output of an anchor point will not turn it into an interior point of the technology. However, such changes may result in the anchor point losing its efficiency. Existing DEA methods for identifying anchor points have focused on technologies with non-negative data. However, these methods may fail to properly identify anchor points, have limitations in doing so, are time-consuming, or lack applicability in the presence of negative data. Moreover, none of these methods determine the input and output adjustment bounds for anchor points. Input (or output) adjustment bounds represent the maximum increases in inputs (or decreases in outputs) that an anchor point can undergo while remaining efficient. This study addresses these gaps by proposing: (1) an integrated mixed-integer linear programming (MILP) model to identify anchor points in the presence of negative data, and (2) two linear models to determine the maximum allowable input increments and output decrements for anchor points. Additionally, this research illustrates the managerial and economic importance of anchor points and their adjustment bounds, providing three comparative and empirical examples to demonstrate the application and effectiveness of the proposed models.