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A New MIP Approach on the Least Distance Problem in DEA

Author

Listed:
  • Xu Wang

    (Department of Industrial and Management Systems Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan)

  • Kuan Lu

    (Department of Industrial Engineering and Economics, School of Engineering, Tokyo Institute of Technology, 2-12-1 Ohokayama Meguro-ku, Tokyo 152-8552, Japan)

  • Jianming Shi

    (School of Management, Tokyo University of Science, 1-11-2 Fujimi, Chiyoda-ku, Tokyo 102-0071, Japan)

  • Takashi Hasuike

    (School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan)

Abstract

In this paper, we deal with the least distance problem (LDP) in Data Envelopment Analysis (DEA), which is to find a closest efficient target over the whole efficient frontier. To this end, we define the efficient frontier by a linear complementarity system and propose a mixed integer programming (MIP) approach to solve the LDP. Our proposed MIP approach: (1) can solve the LDP based on ℓp-norm (p ≥ 1) by using a state-of-the-art solver and obtain the closest efficient target over the whole efficient frontier instead of a subset of it; (2) can be applied for computing the least distance DEA models satisfying the monotonicity; (3) is more user-friendly, because it allows a decision maker to improve the efficiency of a decision making unit (DMU) by setting the affordable input/output level under his/her circumstance. Thus, the efficient target provided by our approach may be more appropriate from the perspective of the decision makers of DMUs.

Suggested Citation

  • Xu Wang & Kuan Lu & Jianming Shi & Takashi Hasuike, 2020. "A New MIP Approach on the Least Distance Problem in DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(06), pages 1-18, December.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:06:n:s021759592050027x
    DOI: 10.1142/S021759592050027X
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    Cited by:

    1. Fangqing Wei & Yanan Fu & Feng Yang & Chun Sun & Sheng Ang, 2023. "Closest target setting with minimum improvement costs considering demand and resource mismatches," Operational Research, Springer, vol. 23(3), pages 1-29, September.

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