An Inverse Two-Stage FDH Model in the Presence of Shared Resources

Subject Areas : International Journal of Industrial Mathematics

فرزانه اسدی ¹ , سهراب کردرستمی ^{2 *} , علیرضا امیرتیموری ³ , مرتضی بذرافشان ⁴

1 - Department of Industrial Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
2 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
3 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
4 - Department of Industrial Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Received: 2022-02-25 Accepted : 2022-07-04 Published : 2023-07-01

Keywords: Free disposal hull (FDH), Two-stage system, Shared. resources, Data Envelopment Analysis, Inverse DEA,

Abstract :

In this research, two-stage networks are considered in which there are common resources between both stages. Also, there are links between the first and second stages that are undesirable for the first stage. Two models are rendered, the first is a model for calculating the efficiency of the mentioned two-stage processes under the non-convex technology and the second model is an inverse model for calculating output values through input changes. The changes are such that efficiency values remain constant. Actually, at first, a non-radial network free disposal hull (FDH) model is planned to evaluate the entire and stage efficiencies of two-stage processes with shared resources. The introduced framework is a mixed integer nonlinear programming plan and is computed using a heuristic approach. Then, an inverse two-stage FDH approach is presented to determine outputs related to two stages for perturbing inputs of each stage while the efficiency values remain unchanged. To clarify the proposed models, an application from the literature is used.