Shortest path Ranking Model With the Ability to Change the Importance of Inputs and Outputs: Case Studies from Education

This paper presents a novel super efficiency model based on the Andersen-Petersen model, which serves as a bridge between input-oriented and output-oriented models. The proposed model defines a path from the deleted decision-making unit to the efficiency frontier with the shortest step length. Initially formulated as a nonlinear programming model, the developed model is transformed into a multi-objective linear programming model and then further simplified into a linear programming model through variable changes and the application of nonlinear programming solving methods. The feasibility of the proposed path is discussed, and a weighted version of the shortest path model is introduced to incorporate preferences regarding the relative importance of inputs or outputs. Addressing a weakness of the AP methods, the inability to prioritize weights is resolved in the developed model. Real case studies in the context of Iranian education are conducted, and the results of the AP and shortest path analyses are analyzed to validate the proposed method.