American Institute of Mathematical Sciences

Advanced
January  2016, 12(1): 211-228. doi: 10.3934/jimo.2016.12.211

A new approach for allocating fixed costs among decision making units

Ruiyue Lin 1, , Zhiping Chen 1, and  Zongxin Li 1,

1. 

Department of Computing Science, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China, China, China

Received  March 2014 Revised  January 2015 Published  April 2015

How to equitably distribute a common fixed cost among decision making units (DMUs) of an organization is a typical problem in organization management. Based on the data envelopment analysis technique, this paper proposes a new proportional sharing model to determine a unique fixed cost allocation under two assumptions: efficiency invariance and zero slack. It is noteworthy that the fixed cost allocation determined by our proportional sharing model is a feasible solution to the model proposed by Cook and Zhu [Cook and Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers & Operations Research, 32 (2005) 2171-2178]. To ensure the uniqueness of the fixed cost allocation, three algorithms are proposed under the new model. Different from current fixed cost allocation methods under the efficiency invariance assumption, our approach can generate a fixed cost allocation that is unique, partially dependent of DMUs' inputs and units-invariant, and thus is more effective. Numerical examples are used to illustrate the validity and superiorities of our approach.
Keywords: units-invariance., efficiency invariance, Data envelopment analysis, fixed cost allocation, uniqueness.
Mathematics Subject Classification: Primary: 91B32, 90B50; Secondary: 90C2.
Citation: Ruiyue Lin, Zhiping Chen, Zongxin Li. A new approach for allocating fixed costs among decision making units. Journal of Industrial & Management Optimization, 2016, 12 (1) : 211-228. doi: 10.3934/jimo.2016.12.211
References:
[1]

A. Amirteimoori and S. Kordrostami, Allocating fixed costs and target setting: A DEA-based approach,, Applied Mathematics and Computation, 171 (2005), 136.  doi: 10.1016/j.amc.2005.01.064.  Google Scholar

[2]

J. E. Beasley, Allocating fixed costs and resources via data envelopment analysis,, European Journal of Operational Research, 147 (2003), 198.  doi: 10.1016/S0377-2217(02)00244-8.  Google Scholar

[3]

A. Cadena, A. Marcucci, J. F. Pérez, H. Durán, H. Mutis, C. Taútiva and F. Palacios, Efficiency analysis in electricity transmission utilities,, Journal of Industrial and management optimization, 5 (2009), 253.  doi: 10.3934/jimo.2009.5.253.  Google Scholar

[4]

A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units,, European Journal of Operational Research, 2 (1978), 429.  doi: 10.1016/0377-2217(78)90138-8.  Google Scholar

[5]

W. D. Cook and M. Kress, Characterizing an equitable allocation of shared costs: A DEA approach,, European Journal of Operational Research, 119 (1999), 652.  doi: 10.1016/S0377-2217(98)00337-3.  Google Scholar

[6]

W. D. Cook and J. Zhu, Allocation of shared costs among decision making units: A DEA approach,, Computers & Operations Research, 32 (2005), 2171.  doi: 10.1016/j.cor.2004.02.007.  Google Scholar

[7]

W. W. Cooper, L. M. Seiford and K. Tone, Data Envelopment Analysis,, 2nd edition, (2007).   Google Scholar

[8]

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

[9]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja and M. Sanei, An alternative approach for equitable allocation of shared costs by using DEA,, Applied Mathematics and Computation, 153 (2004), 267.  doi: 10.1016/S0096-3003(03)00631-3.  Google Scholar

[10]

M. Khodabakhshi and K. Aryavash, The fair allocation of common fixed cost or revenue using DEA concept,, Annals of Operational Research, 214 (2014), 187.  doi: 10.1007/s10479-012-1117-2.  Google Scholar

[11]

Y. Li, F. Yang, L. Liang and Z. Hua, Allocating the fixed cost as a complement of other cost inputs: A DEA approach,, European Journal of Operational Research, 197 (2009), 389.  doi: 10.1016/j.ejor.2008.06.017.  Google Scholar

[12]

Y. Li, M. Yang, Y. Chen, Q. Dai and L. Liang, Allocating a fixed cost based on data envelopment analysis and satisfaction degree,, Omega, 41 (2013), 55.  doi: 10.1016/j.omega.2011.02.008.  Google Scholar

[13]

R. Lin, Allocating fixed costs or resources and setting targets via data envelopment analysis,, Applied Mathematics and Computation, 217 (2011), 6349.  doi: 10.1016/j.amc.2011.01.008.  Google Scholar

[14]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis,, Applied Mathematics and Computation, 218 (2011), 3680.  doi: 10.1016/j.amc.2011.09.011.  Google Scholar

[15]

M. Mahdiloo, A. Noorizadeh and R. Farzipoor Saen, Developing a new data envelopment analysis model for custer value analysis,, Journal of Industrial and management optimization, 7 (2011), 531.   Google Scholar

[16]

A. Z. Milioni, J. V. G. Avellar, E. G. Gomes and J. C. B. Soares de Mello, An ellipsoidal frontier model: Allocating input via parametric DEA,, European Journal of Operational Research, 209 (2011), 113.  doi: 10.1016/j.ejor.2010.08.008.  Google Scholar

[17]

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

[18]

H. Moulin and R. Stong, Fair queuing and other probabilistic allocation methods,, Mathematics of Operations Research, 27 (2002), 1.  doi: 10.1287/moor.27.1.1.336.  Google Scholar

[19]

X. Si, L. Liang, G. Jia, L. Yang, H. Wu and Y. Li, Proportional sharing and DEA in allocating the fixed cost,, Applied Mathematics and Computation, 219 (2013), 6580.  doi: 10.1016/j.amc.2012.12.085.  Google Scholar

[20]

R. C. Silva and A. Z. Milioni, The adjusted spherical drontier model with weight restrictions,, European Journal of Operational Research, 220 (2012), 729.  doi: 10.1016/j.ejor.2012.01.064.  Google Scholar

[21]

T. Sueyoshi and K. Sekitani, An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties,, European Journal of Operational Research, 196 (2009), 764.  doi: 10.1016/j.ejor.2008.01.045.  Google Scholar

[22]

Y. T. Wang and D. X. Zhu, Ordinal proportional cost sharing,, Journal of Mathematical Economics, 37 (2002), 215.  doi: 10.1016/S0304-4068(02)00016-2.  Google Scholar

show all references

References:
[1]

A. Amirteimoori and S. Kordrostami, Allocating fixed costs and target setting: A DEA-based approach,, Applied Mathematics and Computation, 171 (2005), 136.  doi: 10.1016/j.amc.2005.01.064.  Google Scholar

[2]

J. E. Beasley, Allocating fixed costs and resources via data envelopment analysis,, European Journal of Operational Research, 147 (2003), 198.  doi: 10.1016/S0377-2217(02)00244-8.  Google Scholar

[3]

A. Cadena, A. Marcucci, J. F. Pérez, H. Durán, H. Mutis, C. Taútiva and F. Palacios, Efficiency analysis in electricity transmission utilities,, Journal of Industrial and management optimization, 5 (2009), 253.  doi: 10.3934/jimo.2009.5.253.  Google Scholar

[4]

A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units,, European Journal of Operational Research, 2 (1978), 429.  doi: 10.1016/0377-2217(78)90138-8.  Google Scholar

[5]

W. D. Cook and M. Kress, Characterizing an equitable allocation of shared costs: A DEA approach,, European Journal of Operational Research, 119 (1999), 652.  doi: 10.1016/S0377-2217(98)00337-3.  Google Scholar

[6]

W. D. Cook and J. Zhu, Allocation of shared costs among decision making units: A DEA approach,, Computers & Operations Research, 32 (2005), 2171.  doi: 10.1016/j.cor.2004.02.007.  Google Scholar

[7]

W. W. Cooper, L. M. Seiford and K. Tone, Data Envelopment Analysis,, 2nd edition, (2007).   Google Scholar

[8]

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

[9]

G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja and M. Sanei, An alternative approach for equitable allocation of shared costs by using DEA,, Applied Mathematics and Computation, 153 (2004), 267.  doi: 10.1016/S0096-3003(03)00631-3.  Google Scholar

[10]

M. Khodabakhshi and K. Aryavash, The fair allocation of common fixed cost or revenue using DEA concept,, Annals of Operational Research, 214 (2014), 187.  doi: 10.1007/s10479-012-1117-2.  Google Scholar

[11]

Y. Li, F. Yang, L. Liang and Z. Hua, Allocating the fixed cost as a complement of other cost inputs: A DEA approach,, European Journal of Operational Research, 197 (2009), 389.  doi: 10.1016/j.ejor.2008.06.017.  Google Scholar

[12]

Y. Li, M. Yang, Y. Chen, Q. Dai and L. Liang, Allocating a fixed cost based on data envelopment analysis and satisfaction degree,, Omega, 41 (2013), 55.  doi: 10.1016/j.omega.2011.02.008.  Google Scholar

[13]

R. Lin, Allocating fixed costs or resources and setting targets via data envelopment analysis,, Applied Mathematics and Computation, 217 (2011), 6349.  doi: 10.1016/j.amc.2011.01.008.  Google Scholar

[14]

R. Lin, Allocating fixed costs and common revenue via data envelopment analysis,, Applied Mathematics and Computation, 218 (2011), 3680.  doi: 10.1016/j.amc.2011.09.011.  Google Scholar

[15]

M. Mahdiloo, A. Noorizadeh and R. Farzipoor Saen, Developing a new data envelopment analysis model for custer value analysis,, Journal of Industrial and management optimization, 7 (2011), 531.   Google Scholar

[16]

A. Z. Milioni, J. V. G. Avellar, E. G. Gomes and J. C. B. Soares de Mello, An ellipsoidal frontier model: Allocating input via parametric DEA,, European Journal of Operational Research, 209 (2011), 113.  doi: 10.1016/j.ejor.2010.08.008.  Google Scholar

[17]

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

[18]

H. Moulin and R. Stong, Fair queuing and other probabilistic allocation methods,, Mathematics of Operations Research, 27 (2002), 1.  doi: 10.1287/moor.27.1.1.336.  Google Scholar

[19]

X. Si, L. Liang, G. Jia, L. Yang, H. Wu and Y. Li, Proportional sharing and DEA in allocating the fixed cost,, Applied Mathematics and Computation, 219 (2013), 6580.  doi: 10.1016/j.amc.2012.12.085.  Google Scholar

[20]

R. C. Silva and A. Z. Milioni, The adjusted spherical drontier model with weight restrictions,, European Journal of Operational Research, 220 (2012), 729.  doi: 10.1016/j.ejor.2012.01.064.  Google Scholar

[21]

T. Sueyoshi and K. Sekitani, An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties,, European Journal of Operational Research, 196 (2009), 764.  doi: 10.1016/j.ejor.2008.01.045.  Google Scholar

[22]

Y. T. Wang and D. X. Zhu, Ordinal proportional cost sharing,, Journal of Mathematical Economics, 37 (2002), 215.  doi: 10.1016/S0304-4068(02)00016-2.  Google Scholar

[1]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[2]

Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225
[3]

Habib Ammari, Josselin Garnier, Vincent Jugnon. Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 389-417. doi: 10.3934/dcdss.2015.8.389
[4]

A. Kochergin. Well-approximable angles and mixing for flows on T^2 with nonsingular fixed points. Electronic Research Announcements, 2004, 10: 113-121.

[5]

Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327
[6]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056
[7]

Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1
[8]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
[9]

Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034
[10]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825
[11]

Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (56)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences