A Novel Framework for Efficiency Assessment in Multi-Divisional Systems: Application of Stackelberg Game Theory and Dynamic Network DEA
Subject Areas : International Journal of Mathematical Modelling & ComputationsAli Asghar Tatlari 1 , Farhad Hosenzadeh 2 * , Bijan Rahmani Parchikolaei 3
1 - Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 - Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Keywords: Dynamic Network DEA, Stackelberg Game theory, Intermediate measures, Carry-over activities, Hybrid DEA model.,
Abstract :
Intermediate products in network DEA interconnect the divisions that make up DMUs, while carry-over activities are responsible for establishing connections across multiple periods in dynamic DEA. These variables offer managers more detailed insights into inefficiencies within the organizations in different periods. A major challenge in performance evaluation is the dual role of these measures. Intermediate measures act as outputs for one division and inputs for another, creating a conflict that hinders managers from accurately assessing inefficiencies related to these measures. This paper proposes a novel approach to address this conflict in multi-divisional production systems by utilizing Stackelberg game theory. By employing this theory, we decompose the system's overall efficiency into leader’s and follower’s efficiencies, providing a more detailed evaluation of performance. Our model makes a significant contribution to the literature by developing a dynamic network DEA model. This model resolves conflicts arising from the dual role of connecting measures and establishes a Stackelberg-game dynamic between periods and divisions, ensuring continuity of flows. Additionally, in real-world problems, some data change proportionally (radially), while others change non-proportionally (non-radially). This paper applies a hybrid model, combining both radial and non-radial approaches, for efficiency evaluation. To verify the proposed model, we assess the performance of 14 petrochemical units over two years. The results show that the intermediate measures linking the followers to the leader need to be fully controlled by the leader.
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