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BiLevel programming Data Envelopment Analysis with constrained resource

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  • Wu, Desheng Dash

Abstract

A new BiLevel programming Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the performance of a system with Stackelberg-game relationships. This new approach allows us to evaluate the firm performance in decentralized decisions, which consist of the objective(s) of the leader at its first level and that is of the follower at the second level. This approach can help decentralized companies to optimize their performance using multiple inputs to produce multiples outputs in a cost-effective way, where both the system "black-box" and subsystem performance are exposed in details. We show the algorithms and solutions to our new models. We illustrate and validate the proposed new approach using two case studies: a banking chain and a manufacturing supply chain. The computation shows that subsystem being efficient at all levels results in an overall efficiency achievement in a decentralized BiLevel structure.

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  • Wu, Desheng Dash, 2010. "BiLevel programming Data Envelopment Analysis with constrained resource," European Journal of Operational Research, Elsevier, vol. 207(2), pages 856-864, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:856-864
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    2. Juan Aparicio & Magdalena Kapelko & Juan F. Monge, 2020. "A Well-Defined Composite Indicator: An Application to Corporate Social Responsibility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 299-323, July.
    3. Yang, Feng & Wu, Desheng Dash & Liang, Liang & O'Neill, Liam, 2011. "Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 212(3), pages 560-569, August.
    4. Zhou, Xiaoyang & Luo, Rui & Tu, Yan & Lev, Benjamin & Pedrycz, Witold, 2018. "Data envelopment analysis for bi-level systems with multiple followers," Omega, Elsevier, vol. 77(C), pages 180-188.
    5. Nomita Pachar & Jyoti Dhingra Darbari & Kannan Govindan & P. C. Jha, 2022. "Sustainable performance measurement of Indian retail chain using two-stage network DEA," Annals of Operations Research, Springer, vol. 315(2), pages 1477-1515, August.
    6. Monge, Juan F. & Ruiz, José L., 2023. "Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1084-1096.
    7. Camanho, Ana Santos & Silva, Maria Conceicao & Piran, Fabio Sartori & Lacerda, Daniel Pacheco, 2024. "A literature review of economic efficiency assessments using Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 315(1), pages 1-18.
    8. Dariush Akbarian, 2015. "Ranking All DEA-Efficient DMUs Based on Cross Efficiency and Analytic Hierarchy Process Methods," Journal of Optimization, Hindawi, vol. 2015, pages 1-10, January.
    9. Aparicio, Juan & Cordero, Jose M. & Gonzalez, Martin & Lopez-Espin, Jose J., 2018. "Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries," Omega, Elsevier, vol. 79(C), pages 9-20.
    10. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    11. AGRELL, Per & HATAMI-MARBINI, Adel, 2011. "Frontier-based performance analysis models for supply chain management; state of the art and research directions," LIDAM Discussion Papers CORE 2011069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Chen, Zhongfei & Wanke, Peter & Antunes, Jorge Junio Moreira & Zhang, Ning, 2017. "Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model," Energy Economics, Elsevier, vol. 68(C), pages 89-108.
    13. Abd Hadi Mustaffa & Nur Zahidah Bahrudin & Zahariah Sahudin & Hasni Abdullah & Muhammad Ridzuan Abdul Aziz, 2023. "What have we Learned from Firm Efficiency Research for the Past 35 Years? A Bibliometric Analysis," Information Management and Business Review, AMH International, vol. 15(1), pages 216-227.
    14. Herrera-Restrepo, Oscar & Triantis, Konstantinos, 2019. "Enterprise design through complex adaptive systems and efficiency measurement," European Journal of Operational Research, Elsevier, vol. 278(2), pages 481-497.

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