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Resource Allocation Based on DEA and Non-Cooperative Game

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Abstract

Resource allocation is one of the most important applications of data envelopment analysis (DEA). Usually, the resource to be allocated is directly related to the interests of decision-making units (DMUs), thus the dynamic non-cooperative game is one of the representative behaviours in the allocation process. However, it is rarely considered in the previous DEA-based allocation studies, which may reduce the acceptability of the allocation plan. Therefore, this paper proposes a DEA-based resource allocation method considering the dynamic non-cooperative game behaviours of DMUs. The authors first deduce the efficient allocation set under the framework of variable return to scale (VRS) and build the allocation model subjecting to the allocation set. Then an iteration algorithm based on the concept of the non-cooperative game is provided for generating the optimal allocation plan. Several interesting characteristics of the algorithm are proved, including i) the algorithm is convergent, ii) the optimal allocation plan is a unique Nash equilibrium point, and iii) the optimal allocation plan is unique no matter which positive value the initial allocation takes. Some advantages of the allocation plan have been found. For example, the allocation plan is more balanced, has more incentives and less outliers, compared with other DEA-based allocation plans. Finally, the proposed method is applied to allocate the green credit among the 30 Chinese iron and steel enterprises, and the results highlight the applicability of the allocation method and solution approach. Therefore, the approach can provide decision makers with a useful resource allocation tool from the perspective of dynamic non-cooperative game.

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References

  1. Charnes A, Cooper W W, and Rhodes E, Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2(6): 429–444.

    Article  MathSciNet  MATH  Google Scholar 

  2. Li Y, Lei X, and Morton A, Performance evaluation of nonhomogeneous hospitals: The case of Hong Kong hospitals. Health Care Management Science, 2019, 22: 215–228.

    Article  Google Scholar 

  3. Sotiros D, Koronakos G, and Despotis D K, Dominance at the divisional efficiencies level in network DEA: The case of two-stage processes, Omega, 2019, 85: 144–155.

    Article  MATH  Google Scholar 

  4. Guo C, Shureshjani R A, Foroughi A A, et al., Decomposition weights and overall efficiency in two-stage additive network DEA, European Journal of Operational Research, 2017, 257(3): 896–906.

    Article  MathSciNet  MATH  Google Scholar 

  5. Dai Q, Li L, Lei X, et al., Considering monopoly maintenance cost for an automobile purchase in China: A DEA-based approach, Journal of Systems Science and Complexity, 2019, 32(4): 1167–1179.

    Article  Google Scholar 

  6. Pan W, Huang L, and Zhao L, An integrated DEA model allowing decomposition of eco-efficiency: A case study of China, Journal of Systems Science and Information, 2017, 5(5): 473–488.

    Article  Google Scholar 

  7. Lei X, Li L, Zhang X, et al., A novel ratio-based parallel DEA approach for evaluating the energy and environmental performance of Chinese transportation sectors, Journal of Systems Science and Systems Engineering, 2019, 28: 621–635.

    Article  Google Scholar 

  8. Lin B, Song D, and Liu Z, A model of aircraft support concept evaluation based on DEA and PCA, Journal of Systems Science and Information, 2018, 6(6): 563–576.

    Article  Google Scholar 

  9. Xi W and Cheng X, The difference of capital input and productivity in service industries: Based on four stages bootstrap-DEA model, Journal of Systems Science and Information, 2018, 6(4): 320–335.

    Article  Google Scholar 

  10. Liu J and Wang X, A dynamic multi-player bargaining game with veto players, Journal of Systems Science and Complexity, 2021, 34(2): 673–691.

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu C, Gao H, Petrosian O, et al., A class of general transformation of characteristic functions in dynamic games, Journal of Systems Science and Complexity, 2020, 33(6): 1997–2012.

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang G and Zhang S, A mean-field linear-quadratic stochastic stackelberg differential game with one leader and two followers, Journal of Systems Science and Complexity, 2020, 33(5): 1383–1401.

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang X and Liu J, A dynamic bargaining game with externalities, Journal of Systems Science and Complexity, 2018, 31(6): 1591–1602.

    Article  MathSciNet  MATH  Google Scholar 

  14. Cook W D and Kress M, Characterizing an equitable allocation of shared costs: A DEA approach, European Journal of Operational Research, 1999, 119: 652–661.

    Article  MATH  Google Scholar 

  15. Cook W D and Zhu J, Allocation of shared costs among decision making units: A DEA approach, Computers & Operations Research, 2005, 32: 2171–2178.

    Article  MATH  Google Scholar 

  16. Jahanshahloo G R, Hosseinzadeh Lotfi F, Shoja N, et al., An alternative approach for equitable allocation of shared costs by using DEA, Applied Mathematics and Computation, 2004, 153: 267–274.

    Article  MathSciNet  MATH  Google Scholar 

  17. Lin R, Allocating fixed costs and common revenue via data envelopment analysis, Applied Mathematics and Computation, 2011, 218: 3680–3688.

    Article  MathSciNet  MATH  Google Scholar 

  18. Yan H, Wei Q, and Hao G, DEA models for resource reallocation and production input/output estimation, European Journal of Operational Research, 2002, 136: 19–31.

    Article  MathSciNet  MATH  Google Scholar 

  19. An Q, Wang P, Emrouznejad A, et al., Fixed cost allocation based on the principle of efficiency invariance in two-stage systems, European Journal of Operational Research, 2020, 283(2): 662–675.

    Article  MathSciNet  MATH  Google Scholar 

  20. Beasley J E, Allocating fixed costs and resources via data envelopment analysis, European Journal of Operational Research, 2003, 147: 198–216.

    Article  MATH  Google Scholar 

  21. Avellar J V G, Milioni A Z, and Rabello T N, Spherical frontier DEA model based on a constant sum of inputs, Journal of the Operational Research Society, 2007, 58: 1246–1251.

  22. Milioni A Z, Avellar J V G, Gomes E G, et al., An ellipsoidal frontier model: Allocating input via parametric DEA, European Journal of Operational Research, 2011, 209: 113–121.

    Article  MATH  Google Scholar 

  23. Bernardo M, Souza M A M, Lopes R S M, et al., University library performance management: Applying zero-sum gains DEA models to resource allocation, Socio-Economic Planning Sciences, 2020, 100808, https://doi.org/10.1016/j.seps.2020.100808.

    Google Scholar 

  24. Si X, Liang L, Jia J, et al., Proportional sharing and DEA in allocating the fixed cost, Applied Mathematics and Computation, 2013, 219: 6580–6590.

    Article  MathSciNet  MATH  Google Scholar 

  25. Dai Q, Li Y, Xie Q, et al., Allocating tradable emissions permits based on the proportional allocation concept to achieve a low carbon economy, Mathematical Problems in Engineering, 2014, 462705, https://doi.org/10.1155/2014/462705.

    Google Scholar 

  26. Hosseinzadeh Lotfi F, Hatami-Marbini A, Agrell P J, et al., Allocating fixed resources and setting targets using a common-weights DEA approach, Computers & Industrial Engineering, 2013, 64(2): 631–640.

    Article  Google Scholar 

  27. Li Y, Yang M, Chen Y, et al., Allocating a fixed cost based on data envelopment analysis and satisfaction degree, Omega, 2013, 41: 55–60.

    Article  Google Scholar 

  28. Xie Q, Xu Q, Zhu D, et al., Fair allocation of wastewater discharge permits based on satisfaction criteria using data envelopment analysis, Utilities Policy, 2020, 66: 101078, https://doi.org/10.1016/j.jup.2020.101078.

    Article  Google Scholar 

  29. Du J, Cook W D, Liang L, et al., Fixed cost and resource allocation based on DEA cross-efficiency, European Journal of Operational Research, 2014, 235(1): 206–214.

    Article  MathSciNet  MATH  Google Scholar 

  30. Li F, Zhu Q, and Chen Z, Allocating a fixed cost across the decision making units with two-stage network structures, Omega, 2019, 83: 139–154.

    Article  Google Scholar 

  31. Li Y, Lin L, Dai Q, et al., Allocating common costs of multinational companies based on the arm’s length principle and the nash non-cooperative game, European Journal of Operational Research, 2020, 283(3): 1002–1010.

    Article  MathSciNet  MATH  Google Scholar 

  32. Chu J, Wu J, Chu C, et al., DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches, Omega, 2020, https://doi.org/10.1016/j.omega.2019.03.012.

    Google Scholar 

  33. An Q, Wang P, Shi S, Fixed cost allocation for two-stage systems with cooperative relationship using data envelopment analysis, Computers & Industrial Engineering, 2020, 145, https://doi.org/10.1016/j.cie.2020.106534.

    Google Scholar 

  34. Dai Q, Li Y, Lei X, et al., A DEA-based incentives approach for allocating common revenues or fixed costs, European Journal of Operation Research, 2021, 292(2): 675–686.

    Article  MathSciNet  MATH  Google Scholar 

  35. Li X and Cui J, A comprehensive DEA approach for the resource allocation problem based on scale economies classification, Journal of Systems Science and Complexity, 2008, 21(4): 540–557.

    Article  MathSciNet  MATH  Google Scholar 

  36. Li Y, Yang F, Liang L, et al., Allocating the fixed cost as a complement of other cost inputs: A DEA approach, European Journal of Operational Research, 2009, 197: 389–401.

    Article  MathSciNet  MATH  Google Scholar 

  37. Dai Q, Li Y, and Liang L, Allocating fixed costs with considering the return to scale: A DEA approach, Journal of Systems Science and Complexity, 2016, 29(5): 1320–1341.

    Article  MathSciNet  MATH  Google Scholar 

  38. Amirteimoori A and Tabar M M, Resource allocation and target setting in data envelopment analysis, Expert Systems with Applications, 2010, 37(4): 3036–3039.

    Article  Google Scholar 

  39. Bi G, Ding J, Luo Y, et al., Resource allocation and target setting for parallel production system based on DEA, Applied Mathematical Modelling, 2011, 35: 4270–4280.

    Article  MathSciNet  MATH  Google Scholar 

  40. Lozano S, Villa G, and Canca D, Application of centralised DEA approach to capital budgeting in Spanish ports, Computers & Industrial Engineering, 2011, 60(3): 455–465.

    Article  Google Scholar 

  41. Khodabakhshi M and Aryavash K, The fair allocation of common fixed cost or revenue using DEA concept, Annals of Operations Research, 2014, 214: 187–194.

    Article  MathSciNet  MATH  Google Scholar 

  42. Li F, Zhu Q, and Liang L, Allocating a fixed cost based on a DEA-game cross efficiency approach, Expert Systems with Applications, 2018, 96: 196–207.

    Article  Google Scholar 

  43. Xiong B, Wu J, An Q, et al., Resource allocation of a parallel system with interaction consideration using a DEA approach: An application to Chinese input-output table, INFOR: Information Systems and Operational Research, 2018, 56(3): 298–316.

    Google Scholar 

  44. Lai K K, Cheung M T, and Fu Y, Resource allocation in public healthcare: A team-DEA model, Journal of Systems Science and Complexity, 2018, 31(2): 463–472.

    Article  MathSciNet  Google Scholar 

  45. Yang M, An Q, Ding T, et al., Carbon emission allocation in China based on gradually efficiency improvement and emission reduction planning principle, Annals of Operations Research, 2019, 278(1–2): 123–139.

    Article  MathSciNet  MATH  Google Scholar 

  46. Banker R D, Charnes A, and Cooper W W, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 1984, 30(8): 1078–1092.

    Article  MATH  Google Scholar 

  47. Charnes A and Cooper W W, Programming with linear fractional functions, Naval Research Logistics Quarterly, 1962, 9: 181–185.

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhou Z, Wu H, Ding T, et al., Nonradial directional distance function for measuring the environmental efficiency of the Chinese iron and steel industry, Tropical Conservation Science, 2019, 12: 1–12.

    Article  Google Scholar 

  49. Wu H, Lü K, Liang L, et al., Measuring performance of sustainable manufacturing with recyclable wastes: A case from China’s iron and steel industry, Omega, 2017, 66: 38–47.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics and Finance, The School of Management, University of Science and Technology of China, Hefei, 230026, China

    Menghan Wang

  2. Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, 100190, China

    Lin Li

  3. School of Economics, Hefei University of Technology, Hefei, 230009, China

    Qianzhi Dai & Fangnan Shi

  4. Center for Industrial Information and Economic Research, Hefei University of Technology, Hefei, 230009, China

    Qianzhi Dai

Authors
  1. Menghan Wang
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  2. Lin Li
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  3. Qianzhi Dai
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  4. Fangnan Shi
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Corresponding author

Correspondence to Qianzhi Dai.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71701060, 71801075, and 71904186, the Fundamental Research Funds for the Central Universities (JZ2021HGTB0071), and Projects of National Social Science Foundation of China under Grant No. 18ZDA064.

This paper was recommended for publication by Editor ZHANG Xinyu.

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Wang, M., Li, L., Dai, Q. et al. Resource Allocation Based on DEA and Non-Cooperative Game. J Syst Sci Complex 34, 2231–2249 (2021). https://doi.org/10.1007/s11424-021-0259-1

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  • DOI: https://doi.org/10.1007/s11424-021-0259-1

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