Inverse data envelopment analysis (DEA) represents a fascinating and applicable topic within the DEA field that provides a tool for decision-makers to set target efficiency levels and identify what needs to change to achieve them. One of the most prevalent strategies to boost the efficiency of units involves unit restructuring, a process capitalizing on the synergy of activities. The focus of this study is the application of inverse DEA to build both a theoretical and practical framework during the restructuring of units that handle both desirable and undesirable data. The framework proposed provides a method to identify the inherited inputs/outputs from units involved in the restructuring process, aiming to achieve optimal efficiency objectives amidst the coexistence of both desirable and undesirable factors. The construction of the framework relies on the principles of inverse DEA and the tool of multi-objective programming. Pareto solutions from multi-objective programming issues are utilized to determine a sufficient condition for estimating both desirable and undesirable data. The proposed approach is evaluated through a case study in the educational.