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Allocating fixed costs with considering the return to scale: A DEA approach

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Abstract

When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis (DEA) researches have ignored the effect of the return to scale (RTS) in fixed cost allocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale (VRS) efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation. To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finally propose a fixed cost allocation approach in terms of principles as: (i) The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and (ii) the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.

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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. 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 

  3. Wu J and Liang L, A DEA model for identifying critical input-output performance measures, Journal of Systems Science and Complexity, 2012, 25(2): 275–286.

    Article  MathSciNet  MATH  Google Scholar 

  4. Wei Q and Yan H, The data envelopment analysis model with intersection form production possibility set, Journal of Systems Science and Complexity, 2010, 23(6): 1086–1101.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cooper W W, Sieford L M, and Tone K, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA Solver Software, Springer-Verlag, New York, 2007.

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  8. Jahanshahloo G R, Hosseinzadeh Lotfi F, and Moradi M, A DEA approach for fair allocation of common revenue, Applied Mathematics and Computation, 2005, 160: 160–719.

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  11. Lin R, Allocating fixed costs or resources and setting targets via data envelopment analysis, Applied Mathematics and Computation, 2011, 217: 217–6349.

    MathSciNet  MATH  Google Scholar 

  12. Amirteimoori A and Shafiei M, Characterizing an equitable omission of shared resources: A DEA-based approach, Applied Mathematics and Computation, 2006, 177: 177–18.

    MathSciNet  MATH  Google Scholar 

  13. Amirteimoori A and Kordrostami S, Allocating fixed costs and target setting: A DEA-based approach, Applied Mathematics and Computation, 2005, 171: 171–136.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. 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: 58–1246.

    MATH  Google Scholar 

  17. Guedes E C C, Milioni A Z, de Avellar J V G, and Silva R C, Adjusted spherical frontier model: Allocating input via parametric DEA, Journal of the Operational Research Society, 2012, 63: 63–406.

    Article  Google Scholar 

  18. Milioni A Z, Avellar J V G, Gomes E G, and Mello J C C B S, An ellipsoidal frontier model: Allocating input via parametric DEA, European Journal of Operational Research, 2011, 209: 209–113.

    Article  MATH  Google Scholar 

  19. Lozano S and Villa G, Centralized resource allocation using data envelopment analysis, Journal of Productivity Analysis, 2004, 22: 22–143.

    Article  Google Scholar 

  20. Li Y J, Yang M, Chen Y, Dai Q Z, and Liang L, Allocating a fixed cost based on data envelopment analysis and satisfaction degree, OMEGA-International Journal of Management Science, 2013, 41: 41–55.

    Article  Google Scholar 

  21. Si X, Liang L, Jia J, Yang L, Wu H, and Li Y, Proportional sharing and DEA in allocating the fixed cost, Applied Mathematics and Computation, 2013, 219: 219–6580.

    Article  MathSciNet  MATH  Google Scholar 

  22. Du J, Cook W D, Liang L, and Zhu J, Fixed cost and resource allocation based on DEA crossefficiency, European Journal of Operational Research, 2013, 235: 235–206.

    MathSciNet  Google Scholar 

  23. Golany B and Tamir E, Evaluating efficiency-effectiveness-equality trade-offs: A data envelopment approach, Management Science, 1995, 41: 41–1172.

    Article  MATH  Google Scholar 

  24. 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 

  25. Li Y, Yang F, Liang L, and Hua Z, Allocating the fixed cost as a complement of other cost inputs: A DEA approach, European Journal of Operational Research, 2009, 197: 197–389.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  29. Pachkova E V, Restricted reallocation of resources, European Journal of Operational Research, 2009, 196: 196–1049.

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  31. Korhonen P and Syrjänen M, Resource allocation based on efficiency analysis, Management Science, 2004, 50: 50–1134.

    Article  MATH  Google Scholar 

  32. Hosseinzadeh Lotfi F, Hatami-Marbini A, Agrell P J, Aghayi N, and Gholami K, Allocating fixed resources and setting targets using a common-weights DEA approach, Computers & Industrial Engineering, 2013, 64: 64–631.

    Article  Google Scholar 

  33. Cinca C S and Molinero C M, Selecting DEA specifications and ranking units via PCA, Journal of the Operational Research Society, 2004, 55: 55–521.

    Article  MATH  Google Scholar 

  34. Jenkins L and Anderson M, A multivariate statistical approach to reducing the number of variables in data envelopment analysis, European Journal of Operation Research, 2003, 147: 147–51.

    Article  MathSciNet  MATH  Google Scholar 

  35. Cook W D, Liang L, Zha Y, and Zhu J, A modified super-efficiency DEA model for infeasibility, Journal of the Operational Research Society, 2009, 60: 60–276.

    MATH  Google Scholar 

  36. Dyson R G, Allen R, Camanho A S, Podinovski V V, and Sarrico C S, Pitfalls and protocols in DEA, European Journal of Operational Research, 2001, 132: 132–245.

    MATH  Google Scholar 

  37. Adler N, Friedman L, and Sinuany-Stern Z, Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 2002, 140: 140–249.

    Article  MathSciNet  MATH  Google Scholar 

  38. Bal H, Örkcü H H, and Celebioglu S, A new method based on the dispersion of weights in data envelopment analysis, Journal of Computers Industrial Engineering, 2008, 54: 54–502.

    Article  Google Scholar 

  39. Wang Y M and Luo Y, A note on a new method based on the dispersion of weights in data envelopment analysis, Computers & Industrial Engineering, 2009, 56: 56–1703.

    Google Scholar 

  40. Jahanshahloo G R and Shahmirzadi P F, New methods for ranking decision making units based on the dispersion of weights and Norm 1 in Data Envelopment Analysis, Computers & Industrial Engineering, 2013, 65: 65–187.

    Article  Google Scholar 

  41. Majid Z A L, Adli M, and Ali E, Ranking efficient decision-making units in data envelopment analysis using fuzzy concept, Computers & Industrial Engineering, 2010, 59: 59–712.

    Google Scholar 

  42. Andersen P and Petersen N C, A procedure for ranking efficient units in data envelopment analysis, Management Science, 1993, 39: 39–1261.

    Article  MATH  Google Scholar 

  43. Chen Y, Measuring super-efficiency in DEA in the presence of infeasibility, European Journal of Operational Research, 2005, 161: 161–545.

    MathSciNet  MATH  Google Scholar 

  44. Lee H S, Chu C W, and Zhu J, Super-efficiency DEA in the presence of infeasibility, European Journal of Operational Research, 2011, 212: 212–141.

    Article  MathSciNet  MATH  Google Scholar 

  45. Chen Y and Liang L, Super-efficiency DEA in the presence of infeasibility: One model approach, European Journal of Operational Research, 2011, 213: 213–359.

    MathSciNet  MATH  Google Scholar 

  46. Lee H S and Zhu J, Super-efficiency infeasibility and zero data in DEA, European Journal of Operational Research, 2012, 216: 216–429.

    MATH  Google Scholar 

  47. Xie Q, Dai Q, Mita S, Long Q, and Li Y, Investigate the relationship between the super-efficiency and fixed input in the presence of infeasibility, Proceedings of the 16th International IEEE Annual Conference on Intelligent Transportation Systems (ITSC 2013), Hague, 2013, 2026–2032.

    Google Scholar 

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Correspondence to Qianzhi Dai.

Additional information

This research is supported by the China Postdoctoral Science Foundation under Grant Nos. 2015M571135, 2015M570155, and 2015M571134, the National Natural Science Foundation of China under Grant Nos. 71271196, 71201156, 71403055, and 21307150, and Science Funds for Creative Research Groups of the National Natural Science Foundation of China and University of Science and Technology of China under Grant Nos. 71121061 and WK2040160008.

This paper was recommended for publication by Editor ZHANG Xun.

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Dai, Q., Li, Y. & Liang, L. Allocating fixed costs with considering the return to scale: A DEA approach. J Syst Sci Complex 29, 1320–1341 (2016). https://doi.org/10.1007/s11424-015-4211-0

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  • DOI: https://doi.org/10.1007/s11424-015-4211-0

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