, 44:11 | Cite as

A data envelopment analysis approach for resource allocation with undesirable outputs: an application to home appliance production companies

  • Mohammad Nemati
  • Reza Kazemi MatinEmail author


Traditional data envelopment analysis (DEA) models use all multiple inputs and outputs to estimate efficiency scores of decision-making units (DMUs). Each unit may consist of several subunits in cases such as manufacturing systems, and each subunit may produce both desirable and undesirable outputs. Providing information about the proportion of resources for each subunit could assist managers in making better decisions for increasing the efficiency of production systems. The current study proposes a new approach for resource allocation and efficiency estimation of production units by considering partial impacts among inputs and outputs in the DEA framework. A weak disposable technology is used in these evaluations, and an empirical application of the proposed approach for obtaining performance of home appliances production companies is provided for illustration purposes.


Data envelopment analysis (DEA) partial impacts undesirable outputs weak disposability resource allocation 

List of Symbols

\( j \in J, j = 1, \ldots ,n \)

collection of DMUs

\( m = 1, \ldots ,M \)

set of good outputs

\( s = 1, \ldots ,S \)

set of bad outputs

\( i = 1, \ldots ,I \)

set of inputs

\( k = 1, \ldots ,K \)

number of bundles

\( {\text{DMU}}_{o} \)

DMU under evaluation

\( v_{mj} \)

mth good output of jth DMU

\( w_{sj} \)

sth bad output of jth DMU

\( x_{ij} \)

ith input of jth DMU

\( v_{mo} \)

mth good output of DMUo

\( w_{so} \)

sth bad output of DMUo

\( x_{io} \)

ith input of DMUo

\( \mu_{m} \)

weight for the rth good output

\( \theta_{s} \)

weight for the sth bad output

\( \rho_{i} \)

weight for the ith input

\( \beta_{ik} \)

split variable for \( x_{ij} \) in kth bundle

\( I_{k} \)

set of inputs in kth bundle

\( T_{i} \)

set of all k bundles that have i as a member

\( R_{k} \left( {O_{G} , O_{B} } \right) \)

kth bundle that has good or bad outputs

\( \varepsilon \)

non-Archimedean and very small number

\( H_{kj} \)

convex combination of k bundles’ efficiencies

\( e_{agg} \)

aggregate efficiency

\( e_{ove} \)

overall efficiency


  1. 1.
    Charnes A, Cooper W W and Rhodes E 1978 Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2: 429–444MathSciNetCrossRefGoogle Scholar
  2. 2.
    Wu J, An Q, Ali S and Liang L 2012 DEA based resource allocation considering environmental factors. Math. Comput. Model. 58: 1128–1137CrossRefGoogle Scholar
  3. 3.
    Hailu A and Veeman T S 2001 Non-parametric productivity analysis with undesirable outputs: an application to the Canadian pulp and paper industry. Am. J. Agric. Econ. 83: 605–616CrossRefGoogle Scholar
  4. 4.
    Chavas J P and Cox T L 1997 Production analysis: a non-parametric time series application to U.S. agriculture. Am. J. Agric. Econ. 48: 330–348CrossRefGoogle Scholar
  5. 5.
    Kuosmanen T 2005 Weak disposability in non-parametric production analysis with undesirable outputs. Am. J. Agric. Econ. 87: 1077–1082CrossRefGoogle Scholar
  6. 6.
    Zhou Y P, Poh K L and Ang B W 2008 Measuring environmental performance under different environmental DEA technologies. Energy Econ. 30: 1–14CrossRefGoogle Scholar
  7. 7.
    Bain Y and Yang F 2010 Resource and environment efficiency analysis of provinces in China: a DEA approach based on Shannon’s entropy. Energy Policy 38: 1909–1917CrossRefGoogle Scholar
  8. 8.
    Hosseinzadeh Lotfi F, Nematollahi N, Behzadi M H, Mirbolouki M and Z Moghaddasa 2012 Centralized resource allocation with stochastic data. J. Comput. Appl. Math. 236: 1783–1788MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mandal S K 2010 Do undesirable output and environmental regulation matter in energy efficiency analysis? Evidence from Indian cement industry. Energy Policy 38: 6076–6083CrossRefGoogle Scholar
  10. 10.
    Dakpo K H, Jeanneaux P and Latruffe L 2015 Modelling pollution-generating technologies in performance benchmarking: recent developments, limits and future prospects in the nonparametric framework. Eur. J. Oper. Res. 250: 347–359MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yan H, Wei Q L and Hao G 2002 DEA models for resource reallocation and production input/output estimation. Eur. J. Oper. Res. 136: 19–31MathSciNetCrossRefGoogle Scholar
  12. 12.
    Färe R and Grosskopf S 2004 Modeling undesirable factors in efficiency evaluation: comment. Eur. J. Oper. Res. 157: 242–245CrossRefGoogle Scholar
  13. 13.
    Basso A and Peccati L A 2001 Optimal resource allocation with minimum activation levels and fixed costs. Eur. J. Oper. Res. 131: 536–549MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hadi-Vencheh A, Foroughi A A and Soleimani-damaneh M 2008 A DEA model for resource allocation. Econ. Model. 25: 983–993CrossRefGoogle Scholar
  15. 15.
    Cecilio M M and Diego P 2006 On centralised resource allocation using DEA. Working Paper, Kent Business School, University of Kent, UK, pp. 146–154Google Scholar
  16. 16.
    Gomes E G and Lins M P E 2008 Modelling undesirable outputs with zero sum gains data envelopment analysis models. J. Oper. Res. Soc. 59: 616–623CrossRefGoogle Scholar
  17. 17.
    Lin R C, Mustafa Y S and Pasupathy K S 2013 Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: specific application to determining optimal resource levels in surgical services. Omega 41: 881–892CrossRefGoogle Scholar
  18. 18.
    Korhonen P and Syrjanen M 2004 Resource allocation based on efficiency analysis. Manag. Sci. 50: 1134–1144CrossRefGoogle Scholar
  19. 19.
    Yang T, Wang P and Li F 2018 Centralized resource allocation and target setting based on data envelopment analysis model. Math. Prob. Eng. 2018: 1–10MathSciNetGoogle Scholar
  20. 20.
    Amirteimoori A, Toloie-Eshlaghi A and Homayoonfar M 2014 Efficiency measurement in two-stage network structures considering undesirable outputs. Int. J. Ind. Math. 6: 65–71Google Scholar
  21. 21.
    Ming-Miin Y 2004 Measuring physical efficiency of domestic airports in Taiwan with undesirable outputs and environmental factors. J. Air Transp. Manag. 10: 295–303CrossRefGoogle Scholar
  22. 22.
    Fukuyama H and Weber W L 2010 A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega 38: 398–409CrossRefGoogle Scholar
  23. 23.
    Wu J, Zhu Q, Ji X, Chu J and Liang L 2016 Two-stage network processes with shared resources and resources recovered from undesirable outputs. Eur. J. Oper. Res. 251: 182–197MathSciNetCrossRefGoogle Scholar
  24. 24.
    Mogale D G, Kumar S K and Tiwari K M 2016 Two-stage Indian food grain supply chain network transportation-allocation model. In: Proceedings of the Manufacturing IFAC Conference, pp. 1767–1772Google Scholar
  25. 25.
    Mogale D G, Kumar S K and Tiwari M K 2018 An MINLP model to support the movement and storage decisions of the Indian food grain supply chain. Control Eng. Pract. 70: 98–113CrossRefGoogle Scholar
  26. 26.
    Mogale D G, Dolgui A, Kandhway R, Kumar S K and Tiwari M K 2017 A multi-period inventory transportation model for tactical planning of food grain supply chain. Comput. Ind. Eng. 110: 379–394CrossRefGoogle Scholar
  27. 27.
    Imanirad R, Cook W D and Zhu J 2013 Partial input to output impacts in DEA: production considerations and resource sharing among business subunits. Nav. Res. Logist. 60: 190–207MathSciNetCrossRefGoogle Scholar
  28. 28.
    Yang H and Pollitt M 2010 The necessity of distinguishing weak and strong disposability among undesirable outputs in DEA: environmental performance of Chinese coal-fired power plants. Energy Policy 38: 4440–4444CrossRefGoogle Scholar
  29. 29.
    Kuosmanen T and Podinovski V 2009 Weak disposability in nonparametric production analysis: reply to Färe and Grosskopf. Am. J. Agric. Econ. 91: 539–545CrossRefGoogle Scholar
  30. 30.
    Kuosmanen T and Kazemi Matin R 2011 Duality of weakly disposable technology. Omega 39: 504–512CrossRefGoogle Scholar
  31. 31.
    Charnes A and Cooper W W 1962 Programming with linear fractional functional. Nav. Res. Logist. 9: 181–185MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Karaj BranchIslamic Azad UniversityKarajIran

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