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Proposing a method for fixed cost allocation using DEA based on the efficiency invariance and common set of weights principles

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  • Gholam Reza Jahanshahloo

    (Kharazmi University)

  • Jafar Sadeghi

    (Kharazmi University)

  • Mohammad Khodabakhshi

    (Shahid Beheshti University, G.C.)

Abstract

One of the applications of data envelopment analysis is fixed costs allocation among homogenous decision making units. In this paper, we first prove that Beasley’s method (Eur J Oper Res 147(1):198–216, 2003), whose infeasibility has been claimed by Amirteimoori and Kordrostami (Appl Math Comput 171(1):136–151, 2005), always has a feasible solution and the efficiency invariance principle does not necessarily satisfy in Amirteimoori and Kordrostami’s method (Appl Math Comput 171(1):136–151, 2005). Hence, we present two equitable methods for fixed cost allocation based on the efficiency invariance and common set of weights principles such that, if possible, they help meet these two principles. In the first method, the costs are allocated to DMU in such a way that the efficiency score of DMUs does not change, and simultaneously this allocation has the minimum distance from the allocation that has been obtained with a common set of weights. However, in the second method, the costs are allocated in such a way that input and output of all units have a common set of weights and it has the minimum distance from the allocation that satisfies the efficiency invariance principle. Moreover, both methods, consider the satisfaction of each unit of the allocated cost. Finally, the proposed method is illustrated by two real world examples.

Suggested Citation

  • Gholam Reza Jahanshahloo & Jafar Sadeghi & Mohammad Khodabakhshi, 2017. "Proposing a method for fixed cost allocation using DEA based on the efficiency invariance and common set of weights principles," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 223-240, April.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-016-0563-z
    DOI: 10.1007/s00186-016-0563-z
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    2. Li, Feng & Zhu, Qingyuan & Chen, Zhi, 2019. "Allocating a fixed cost across the decision making units with two-stage network structures," Omega, Elsevier, vol. 83(C), pages 139-154.
    3. Yu, Ming-Miin & Chen, Li-Hsueh & Hsiao, Bo, 2018. "A performance-based subsidy allocation of ferry transportation: A data envelopment approach," Transport Policy, Elsevier, vol. 68(C), pages 13-19.
    4. Chao, Shih-Liang & Yu, Ming-Miin, 2022. "Applying data envelopment analysis to allocate incentive bonuses for container terminal operators," Transport Policy, Elsevier, vol. 125(C), pages 231-240.
    5. An, Qingxian & Wang, Ping & Emrouznejad, Ali & Hu, Junhua, 2020. "Fixed cost allocation based on the principle of efficiency invariance in two-stage systems," European Journal of Operational Research, Elsevier, vol. 283(2), pages 662-675.
    6. An, Qingxian & Tao, Xiangyang & Xiong, Beibei & Chen, Xiaohong, 2022. "Frontier-based incentive mechanisms for allocating common revenues or fixed costs," European Journal of Operational Research, Elsevier, vol. 302(1), pages 294-308.

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