Decision Making and Performance Evaluation Using Data Envelopment Analysis by Dariush Khezrimotlagh & Yao Chen

Author:Dariush Khezrimotlagh & Yao Chen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.16)

As illustrated in Sect. 5.​6, the best benchmarking for H by the fractional programming in Eq. 6.16 might not be found by Forms 1, 2 and 3. Indeed, the strengths or the weaknesses of both input and output factors are not simultaneously measured by Forms 1 and 2. Form 3 is also the same as Form 1 (Form 2), while the same constraints of Form 1 (Form 2) are selected for Form 3. Of course, Form 3 can simultaneously measure the strengths and the weaknesses of both input and output factors. Nonetheless, different restrictions for the weights in Form 3 may yield different outcomes. Form 3 also does not measure the magnitude of the linear combination of the input factors in comparison with the linear combination of the output factors, which is necessary for measuring the relative scores of the airports. Even if Forms 1, 2 and 3 did not have these shortcomings, and Eqs. 5.​21 and 6.​16 could easily be solved, only the maximum values of the relative scores of the airports are measured which neither represent the desired relative scores for the airports nor provide a measure to examine the differences between the proposed scores for an airport and its delta neighborhood .

In addition, the coefficient, (1 − δ)/(1 + δ), is the only difference between Eqs. 5.​21 and 6.​16, and does not affect the optimal weights in the both equations. In other words, the optimal weights to measure the maximum value of the relative scores of a δ-neighborhood of H suggest the maximum value of the relative scores for H as well. This phenomenon is due to the way of introducing a delta neighborhood, which has the same proportionate increasing of the values of input factors and decreasing of the values of output factors. From such an approach, we try to find a new measure (different with Eq. 5.​21 and Forms 1–3) which lets us calculate Types 1–4 is Sect. 1.​2 and Types 5 and 6 in Sect. 4.​4.

In contrast, while the delta value is changed, the objective in Form 3 is not equivalent for δ-neighborhoods of H (l = 8), as Eq. 6.17 displays. This important difference can lead us to introduce a new measure to bridge between the concepts of doing the job right and doing the job well.

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