Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale

This paper studies the inverse Data Envelopment Analysis (inverse DEA) for the case of variable returns to scale (inverse BCC). The developed inverse BCC model can preserve relative efficiency values of all decision making units (DMUs) in a new production possibility set composing of all current DMUs and a perturbed DMU with new input and output values. We consider the inverse BCC model for a resource allocation problem, where increases of some outputs and decreases of the other outputs of the considered DMU can be taken into account simultaneously. The inverse BCC problem is in the form of a multi-objective nonlinear programming model (MONLP), which is not easy to solve. We propose a linear programming model, which gives a Pareto-efficient solution to the inverse BCC problem. However, there exists at least an optimal solution to the proposed model if and only if the new output vector is in the set of current production possibility set. The proposed approach is illustrated via a case study of a motorcycle-part company.