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Multi-period Efficiency Measurement with Fuzzy Data and Weight Restrictions

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Handbook of Operations Analytics Using Data Envelopment Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 239))

Abstract

In measuring the overall efficiency of a set of decision making units (DMUs) in a time span covering multiple periods, the conventional approach is to use the aggregate data of the multiple periods via a data envelopment analysis (DEA) technique, ignoring the specific situation of each period. In the real word, there are situations that the observations are inexact and imprecise in nature and they have to be estimated. This study proposes using a relational network model to take the operations of individual periods into account in measuring efficiencies, and the input and output data are treated as fuzzy numbers. Moreover, the assurance region approach is utilized in the model to reduce the weight flexibility for the prevention of overly optimistic, even unrealistic, measures of efficiency. The overall and period efficiencies of a DMU can be calculated at the same time, and since the observations are fuzzy, the derived overall and period efficiencies are fuzzy as well. A pair of two-level mathematical programs is developed to calculate the lower and upper bounds of the α-cut of the fuzzy efficiencies. It is shown that the fuzzy overall efficiency is still a weighted average of the fuzzy period efficiencies. Fuzzy measures obtained from fuzzy observations are more informative than crisp measures obtained from fuzzy observations to be precise.

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Acknowledgment

This research was supported by the Ministry of Science and Technology of the Republic of China (Taiwan), under grant MOST 103-2410-H-238-005.

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Authors and Affiliations

  1. Graduate School of Business and Management, Vanung University, Chung-Li, Tao-Yuan, 320, Taiwan, ROC

    Shiang-Tai Liu

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  1. Shiang-Tai Liu
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Correspondence to Shiang-Tai Liu .

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Editors and Affiliations

  1. Dept of Business Administration, Ming Chuan University, Taipei, Taiwan

    Shiuh-Nan Hwang

  2. College of Maritime Science & Mgmt, National Taiwan Ocean University, Keelung, Taiwan

    Hsuan-Shih Lee

  3. School of Business, Worcester Polytechnic Institute, Worcester, Massachusetts, USA

    Joe Zhu

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Liu, ST. (2016). Multi-period Efficiency Measurement with Fuzzy Data and Weight Restrictions. In: Hwang, SN., Lee, HS., Zhu, J. (eds) Handbook of Operations Analytics Using Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 239. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7705-2_4

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