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Sādhanā

, 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
Article
  • 42 Downloads

Abstract

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.

Keywords

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

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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

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

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