Allocation of Fixed Costs in the Presence of Production Trade-offs in Data Envelopment Analysis

Authors

https://doi.org/10.22105/raise.v2i2.47

Abstract

In this paper, we present a new case for the topic of fixed cost allocation in the presence of production trade-offs in Data Envelopment Analysis (DEA). To this end, we use the principle of unchanged efficiency and propose a fixed cost allocation model in such a way that the efficiency scores of Decision Making Units (DMUs) do not change before and after the allocation of fixed costs. By considering production trade-offs on the input and output components, we incorporate the importance of these inputs and outputs in the fixed cost allocation model. By treating fixed costs as a new input, we incorporate the importance of this new input by defining production trade-offs. According to the proposed fixed cost allocation plan, costs are allocated among efficient and inefficient units. An application of approximation for the data set is employed in the petrochemical industry, and the results of the models are presented.

Keywords:

Data envelopment analysis, Fixed cost allocation, Production trade-offs

References

  1. [1] Du, S., Nie, T., Chu, C., & Yu, Y. (2014). Reciprocal supply chain with intention. European journal of operational research, 239(2), 389–402. https://doi.org/10.1016/j.ejor.2014.05.032
  2. [2] An, Q., Wang, P., & Shi, S. (2020). Fixed cost allocation for two-stage systems with cooperative relationship using data envelopment analysis. Computers & industrial engineering, 145, 106534. https://doi.org/10.1016/j.cie.2020.106534
  3. [3] Chu, J., Su, W., Li, F., & Yuan, Z. (2023). Individual rationality and overall fairness in fixed cost allocation: An approach under DEA cross-efficiency evaluation mechanism. Journal of the operational research society, 74(3), 992–1007. https://doi.org/10.1080/01605682.2022.2079434
  4. [4] Cook, W. D., & Zhu, J. (2005). Allocation of shared costs among decision making units: A DEA approach. Computers & operations research, 32(8), 2171–2178. https://doi.org/10.1016/j.cor.2004.02.007
  5. [5] Lin, R. (2011). Allocating fixed costs or resources and setting targets via data envelopment analysis. Applied mathematics and computation, 217(13), 6349–6358. https://doi.org/10.1016/j.amc.2011.01.008
  6. [6] Mostafaei, H., & Ghaffari Hadigheh, A. (2014). A general modeling framework for the long-term scheduling of multiproduct pipelines with delivery constraints. Industrial & engineering chemistry research, 53(17), 7029–7042. https://doi.org/10.1021/ie4038032
  7. [7] Jahanshahloo, G. R., Sadeghi, J., & Khodabakhshi, M. (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, 85, 223–240. https://doi.org/10.1007/s00186-016-0563-z
  8. [8] Li, F., Zhu, Q., & Liang, L. (2019). Allocating a fixed cost based on a DEA-game cross efficiency approach. Annals of operations research, 274, 347–372. https://doi.org/10.1007/s10479-018-2819-x
  9. [9] Yang, J., Li, D., & Li, Y. (2024). A generalized data envelopment analysis approach for fixed cost allocation with preference information. Omega, 122, 102948. https://doi.org/10.1016/j.omega.2023.102948
  10. [10] An, Q., Wang, P., Emrouznejad, A., & Hu, J. (2020). Fixed cost allocation based on the principle of efficiency invariance in two-stage systems. European journal of operational research, 283(2), 662–675. https://doi.org/10.1016/j.ejor.2019.11.031
  11. [11] Li, Y., Yang, M., Chen, Y., Dai, Q., & Liang, L. (2013). Allocating a fixed cost based on data envelopment analysis and satisfaction degree. Omega, 41(1), 55–60. https://doi.org/10.1016/j.omega.2011.02.008
  12. [12] 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. https://doi.org/10.1016/j.omega.2019.03.012
  13. [13] Xu, G., Wu, J., & Zhu, Q. (2022). Fixed cost allocation in two-stage system: A data-driven approach from the perspective of fairness concern. Computers & industrial engineering, 173, 108647. https://doi.org/10.1016/j.cie.2022.108647
  14. [14] Cook, W. D., & Kress, M. (1999). Characterizing an equitable allocation of shared costs: A DEA approach. European journal of operational research, 119(3), 652–661. https://doi.org/10.1016/S0377-2217(98)00337-3
  15. [15] Podinovski, V. V. (2004). Production trade-offs and weight restrictions in data envelopment analysis. Journal of the operational research society, 55(12), 1311–1322. https://doi.org/10.1057/palgrave.jors.2601794
  16. [16] Podinovski, V. V. (2007). Computation of efficient targets in DEA models with production trade-offs and weight restrictions. European journal of operational research, 181(2), 586–591. https://doi.org/10.1016/j.ejor.2006.06.041
  17. [17] Podinovski, V. V. (2016). Optimal weights in DEA models with weight restrictions. European journal of operational research, 254(3), 916–924. https://doi.org/10.1016/j.ejor.2016.04.035
  18. [18] Podinovski, V. V, & Bouzdine-Chameeva, T. (2013). Weight restrictions and free production in data envelopment analysis. Operations research, 61(2), 426–437. https://doi.org/10.1287/opre.1120.1122
  19. [19] Podinovski, V. V, & Bouzdine-Chameeva, T. (2015). Consistent weight restrictions in data envelopment analysis. European journal of operational research, 244(1), 201–209. https://doi.org/10.1016/j.ejor.2015.01.037
  20. [20] Atici, K. B., & Podinovski, V. V. (2015). Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture. Omega, 54, 72–83. https://doi.org/10.1016/j.omega.2015.01.015
  21. [21] Podinovski, V. V, Wu, J., & Argyris, N. (2024). Production trade-offs in models of data envelopment analysis with ratio inputs and outputs: An application to schools in England. European journal of operational research, 313(1), 359–372. https://doi.org/10.1016/j.ejor.2023.08.019
  22. [22] Podinovski, V. (2002). Weight restrictions and radial measures of efficiency. https://B2n.ir/f12475

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Published

2025-05-12

Issue

Vol. 2 No. 2 (2025): Research Annals of Industrial and Systems Engineering

Section

Articles

How to Cite

Allocation of Fixed Costs in the Presence of Production Trade-offs in Data Envelopment Analysis. (2025). Research Annals of Industrial and Systems Engineering, 2(2), 93-102. https://doi.org/10.22105/raise.v2i2.47

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