Use the game theory approach and data envelopment analysis to calculate cost efficiency in two-stage networks

Subject Areas : Industrial Management

Raheleh Mousavizadeh ¹ , Mehrzad Navabakhsh ² , Ashkan Hafezalkotob ³

1 - Industrial Engineering College, Islamic Azad University, South Tehran Branch, Tehran, Iran,
2 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
3 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2021-06-19 Accepted : 2021-10-16 Published : 2022-02-01

Keywords: Cost efficiency, Network Processes, Game Theory, Data envelopment analysis, Technical efficiency,

Abstract :

Performance evaluation in data envelopment analysis is obtained by using technical efficiency calculation. But what is not taken into account in this type of calculation is the price of model inputs. In calculating technical efficiency, the amount of output to the input is maximized, and the model can be used to identify efficient decision-making units, while it is possible to determine the decision-making unit that is at the efficiency limit and a reference for other units. Decision-making systems are efficient at a high cost, and it is possible to find decision-making units that are on the verge of efficiency at a lower production cost. Cost Efficiency seeks to find points that are on the edge of efficiency at the lowest cost. Given the importance of cost efficiency and the lack of attention to this concept in network and multi-stage structures, this study investigates cost efficiency in a purely two-stage process. In the present study, using the concept of game theory and data envelopment analysis in a centralized and decentralized state, we evaluate the performance of purely two-stage processes. In order to investigate the validity and efficiency of the models and their applicability, a case study has been used in the Iranian electricity industry and some management results are discussed.

References:

1. Charnes, A., et al. (1986). Two phase data envelopment analysis approaches to policy evaluation and management of army recruiting activities: Tradeoffs between joint services and army advertising. Research report CCS.


2. Färe, R. and S. Grosskopf. (1997). intertemporal production frontiers: with dynamic DEA. Journal of the Operational Research Society, 48(6): 656-656.


3. Färe, R., S. Grosskopf, and G. Whittaker. (2007). Network DEA, in Modeling data irregularities and structural complexities in data envelopment analysis. p. 209-240.


4. Prieto, A.M. and J.L. Zofío. (2007). Network DEA efficiency in input–output models: With an application to OECD countries. European Journal of Operational Research, 178(1): 292-304.


5. Jaenicke, E.C. (2000). Testing for intermediate outputs in dynamic DEA models: Accounting for soil capital in rotational crop production and productivity measures. Journal of Productivity Analysis, 14(3): 247-266.


6. Kao, C. (2009). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192(3): 949-962.


7. Kao, C. (2014). Network data envelopment analysis: A review. European Journal of OperationalResearch, 239(1): 1-16.


8. Shephard, R.W., D. Gale, and H.W. Kuhn. (1970). Theory of cost and production functions. Princeton University Press Princeton.


9. Shephard, R.W. and R. Fare. (2013). A Dynamic Theory of Production Correspondences. 1975, DTIC Document. Adler, N., V. Liebert, and E. Yazhemsky, Benchmarking airports from a managerial perspective. Omega, 41(2): 442-458.


10. Chen, Y., L. Liang, F. Yang, and J. Zhu. (2006). Evaluation of information technology investment: a data envelopment analysis approach. Computers & Operations Research, 33(5): 1368-1379.


11. Kao C, Hwang SN. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European journal of operational research. Feb 16; 185(1):418-29.


12. Liang, L., W.D. Cook, and Zhu., J. (2008). DEA models for two‐stage processes: Game approach and efficiency decomposition. Naval Research Logistics, 55(7): 643-653.


13. Chen, Y., L. Liang, F. Yang, and J. Zhu. (2006). Evaluation of information technology investment: a data envelopment analysis approach. Computers & Operations Research, 33(5): 1368-1379.


14. Du, J., L. Liang, Y. Chen, W.D. Cook, and J. Zhu. (2011). A bargaining game model for measuring performance of two-stage network structures. European Journal of Operational Research, 210(2): 390-397.


15. Mahmoudi R, Emrouznejad A, Rasti-Barzoki M. (2019). A bargaining game model for performance assessment in network DEA considering sub-networks: a real case study in banking. Neural Computing and Applications. Oct; 31(10): 6429-47.


16. Abdali E, Fallahnejad R. (2020). A bargaining game model for measuring efficiency of two-stage network DEA with non-discretionary inputs. International Journal of Computer Mathematics: Computer Systems Theory. Jan 2; 5(1): 48-59.


17. Tavana, M. and K. Khalili-Damghani. (2014). A new two-stage Stackelberg fuzzy data envelopment analysis model. Measurement, 53: 277-296.


18. Omrani, H., R. Gharizadeh Beiragh, and S. Shafiei Kaleibari. (2015). Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment analysis principal component analysis approach. International Journal of Electrical Power & Energy Systems, 64: 617-625.


19. Khalili-Damghani, K. and Z. Shahmir. (2015). Uncertain network data envelopment analysis with undesirable outputs to evaluate the efficiency of electricity power production and distribution processes. Computers & Industrial Engineering, 88: 131-150.


20. Khalili-Damghani, K., M. Taghavifard, L. Olfat, and K. Feizi. (2011). A hybrid approach based on fuzzy DEA and simulation to measure the efficiency of agility in supply chain: real case of dairy industry. International Journal of Management Science and Engineering Management, 6(3): 163-172.


21. Despotis, D.K., D. Sotiros, and G. Koronakos. (2016). A network DEA approach for series multistage processes. Omega, 61: 35-48.


22. Jahangoshai Rezaee, M., H. Izadbakhsh, and S. Yousefi. (2016). An improvement approach based on DEA-game theory for comparison of operational and spatial efficiencies in urban transportation systems. KSCE Journal of Civil Engineering, 20(4): 1526-1531.


23. Jahangoshai Rezaee, M. and M. Shokry. (2016). Game theory versus multi-objective model for evaluating multi-level structure by using data envelopment analysis. International Journal of Management Science and Engineering Management, 1-11.


24. Esfandiari, M., A. Hafezalkotob, K. Khalili-Damghani, and M. Amirkhan. (2017). Robust twostage DEA models under discrete uncertain data. International Journal of Management Science and Engineering Management, 12(3): 216-224.


25. Sadjadi, S.J. and M. Fathollah Bayati. (2016). Two-tier supplier base efficiency evaluation via network DEA: A game theory approach. International Journal of Engineering-Transactions A: Basics, 29(7): 931-939.


26. Wanke, P., Azad, M. A. K., Emrouznejad, A., & Antunes, J. (2019). A dynamic network DEA model for accounting and financial indicators: A case of efficiency in MENA banking. International Review of Economics & Finance, 61, 52-68.


27. Fukuyama, H., Matousek, R., & Tzeremes, N. G. (2020). A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system.Omega, 95, 102198.


28. Zhu, W., Zhang, Q., & Wang, H. (2019). Fixed costs and shared resources allocation in two-stage network DEA. Annals of Operations Research, 278(1), 177-194.


29. Chu, J., Wu, J., Chu, C., & Zhang, T. (2020). DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches. Omega, 94, 102054.


30. Toloo M, Ertay T. (2014). The most cost efficient automotive vendor with price uncertainty: A new DEA approach. Jun 1; 52: 135-44.


31. Farrell, M.J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 120(3): 253-281.