Multi-period Efficiency Measurement with Fuzzy Data and Weight Restrictions

Shiang-Tai Liu ()
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Shiang-Tai Liu: Graduate School of Business and Management, Vanung University

Chapter Chapter 4 in Handbook of Operations Analytics Using Data Envelopment Analysis, 2016, pp 89-111 from Springer

Abstract: 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.

Keywords: Data envelopment analysis; Fuzzy sets; Network system; Weight restriction (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-1-4899-7705-2_4

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