Open Access
Articles
Allocation of Fixed Costs in the Presence of Production Trade-offs in Data Envelopment Analysis
Downloads
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-offsReferences (22)
- [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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] Podinovski, V. (2002). Weight restrictions and radial measures of efficiency. https://B2n.ir/f12475