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Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry

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  • Mehdi Toloo
  • Atefeh Masoumzadeh
  • Mona Barat

Abstract

Nowadays, algorithms and computer programs, which are going to speed up, short time to run and less memory to occupy have special importance. Toward these ends, researchers have always regarded suitable strategies and algorithms with the least computations. Since linear programming (LP) has been introduced, interest in it spreads rapidly among scientists. To solve an LP, the simplex method has been developed and since then many researchers have contributed to the extension and progression of LP and obviously simplex method. A vast literature has been grown out of this original method in mathematical theory, new algorithms, and applied nature. Solving an LP via simplex method needs an initial basic feasible solution (IBFS), but in many situations such a solution is not readily available so artificial variables will be resorted. These artificial variables must be dropped to zero, if possible. There are two main methods that can be used to eliminate the artificial variables: two-phase method and Big-M method. Data envelopment analysis (DEA) applies individual LP for evaluating performance of decision making units, consequently, to solve these LPs an IBFS must be on hand. The main contribution of this paper is to introduce a closed form of IBFS for conventional DEA models, which helps us not to deal with artificial variables directly. We apply the proposed form to a real-data set to illustrate the applicability of the new approach. The results of this study indicate that using the closed form of IBFS can reduce at least 50 % of the whole computations. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Mehdi Toloo & Atefeh Masoumzadeh & Mona Barat, 2015. "Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 323-336, February.
    • Handle: RePEc:kap:compec:v:45:y:2015:i:2:p:323-336
    DOI: 10.1007/s10614-014-9423-1
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    References listed on IDEAS

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    1. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    2. Saeid Mehrabian & Gholam R. Jahanshahloo & Mohammad R. Alirezaee & Gholam R. Amin, 2000. "An Assurance Interval for the Non-Archimedean Epsilon in DEA Models," Operations Research, INFORMS, vol. 48(2), pages 344-347, April.
    3. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    4. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, September.
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    Cited by:

    1. Toloo, Mehdi & Babaee, Seddigheh, 2015. "On variable reductions in data envelopment analysis with an illustrative application to a gas company," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 527-533.
    2. Ai-bing Ji & Ye Ji & Yanhua Qiao, 2018. "DEA-Based Piecewise Linear Discriminant Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 809-820, April.
    3. Mahdiloo, Mahdi & Toloo, Mehdi & Duong, Thach-Thao & Farzipoor Saen, Reza & Tatham, Peter, 2018. "Integrated data envelopment analysis: Linear vs. nonlinear model," European Journal of Operational Research, Elsevier, vol. 268(1), pages 255-267.
    4. Mehdi Toloo & Rahele Jalili, 2016. "LU Decomposition in DEA with an Application to Hospitals," Computational Economics, Springer;Society for Computational Economics, vol. 47(3), pages 473-488, March.
    5. Mehdi Toloo & Soroosh Nalchigar & Babak Sohrabi, 2018. "Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 1027-1051, December.

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