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A new data envelopment analysis based approach for fixed cost allocation

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Abstract

In many real applications, there exist situations where some independent and decentralized entities will construct a common platform for production processes. A natural and essential problem for the common platform is to allocate the fixed cost or common revenue across these entities in an equitable way. Since there is no powerful central decision maker, each decision-making unit (DMU) might propose an allocation scheme that will favor itself, giving itself a minimal cost and/or a maximal revenue. It is clear that such allocations are egoistic and unacceptable to all DMUs except for the distributing DMU. In this paper, we will address the fixed cost allocation problem in this decentralized environment. For this purpose, we suggest a non-egoistic principle which states that each DMU should propose its allocation proposal in such a way that the maximal cost would be allocated to itself. Further, a preferred allocation scheme should assign each DMU at most its non-egoistic allocation and lead to efficiency scores at least as high as the efficiency scores based on non-egoistic allocations. To this end, we integrate a goal programming method with data envelopment analysis methodology to propose a new model under a set of common weights. The final allocation scheme is determined in such a way that the efficiency scores are maximized for all DMUs through minimizing the total deviation to goal efficiencies. Finally, both a numerical example from prior literature and an empirical study of nine truck fleets are provided to demonstrate the proposed approach.

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Acknowledgements

The authors would like to thank the editor of Annals of Operations Research and two anonymous referees for their kind work and valuable suggestions. This research was financially supported by the Science Funds for Creative Research Groups of the National Natural Science Foundation of China (No. 71121061), the Fund for International Cooperation and Exchange of the National Natural Science Foundation of China (No. 71110107024), the National Natural Science Foundation of China (Nos. 71271196 and 71671172), the Youth Innovation Promotion Association of Chinese Academy of Sciences (CX2040160004), and the Science Funds for Creative Research Groups of University of Science and Technology of China (No. WK2040160008). This paper was finished when Feng Li was visiting the State University of New York at Buffalo with the financial support from the China Scholarship Council (No. 201606340017), and Qingyuan Zhu was visiting University of Illinois at Urbana-Champaign with financial support from the China Scholarship Council (No. 201606340054).

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Authors and Affiliations

  1. School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Feng Li

  2. School of Management, University of Science and Technology of China, Hefei, 230026, Anhui Province, China

    Feng Li, Qingyuan Zhu & Liang Liang

  3. Department of Business Administration, University of Illinois at Urbana-Champaign, Champaign, IL, 61822, USA

    Qingyuan Zhu

  4. School of Management, Hefei University of Technology, Hefei, 230009, Anhui Province, China

    Liang Liang

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  1. Feng Li
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Correspondence to Qingyuan Zhu.

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Li, F., Zhu, Q. & Liang, L. A new data envelopment analysis based approach for fixed cost allocation. Ann Oper Res 274, 347–372 (2019). https://doi.org/10.1007/s10479-018-2819-x

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