As a predictive application of data envelopment analysis (DEA), technology forecasting using DEA (TFDEA) measures the rate of frontier shift by which the arrival of future technologies can be estimated. However, it is well known that DEA and therefore TFDEA may suffer from the issue of infeasible super-efficiency especially under the condition of variable returns to scale (VRS). This study develops an extended TFDEA model based on the modified super-efficiency model proposed by Cook, et al. [1] which has the benefit of yielding radial super-efficiency scores equivalent to those obtained from the original super-efficiency model [2] when feasibility is present. The previously published application of liquid crystal displays (LCD) [3] is revisited to illustrate the use of the new model. The results show the proposed approach makes a reasonable forecast for formerly infeasible targets as well as a consistent forecast for feasible targets.

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INFORMS’14
Technology Forecasting using DEA
in the presence of infeasibility
Nov. 9th. 2014
Department of Engineering and Technology Management
Dong-Joon Lim
Portland State University
Maseeh College of Engineering and Computer Science

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2
Introduction
- TFDEA -
 Technology Forecasting using Data Envelopment Analysis (TFDEA)
 First introduced by Anderson and Inman in 2001
 Predictive application of DEA to estimate the future state-of-the-art frontier
 Primary usages
- Product scheduling
: How likely the desired level of product will be operational in a given point in time?
- Development target setting
: What would be the feasible sets of inputs-outputs in a certain point in time?
 Recent applications
- Technological forecasting on supercomputer development (Omega, 2015)
- Technology trajectory mapping of flat panel technologies (R&D Mgt, 2015)
- Measurement of technological change of hybrid electric vehicles (TFSC, 2014)
- Estimation of future specifications of DSLR cameras (AMBF, 2014)

3. Estimated frontier (T+2)
Estimated frontier (T+1)
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3
Introduction
- TFDEA -
Output
Current frontier (T)
Input
Evolution
of
frontiers
 Conceptual framework

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4
Introduction
- TFDEA -
 Local RoC
: Expected progress of adjacent facets
: Value for currently efficient DMUs
 Individualized RoC
: Expected progress of target DMU
: Value for target DMUs

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Motivation
- Why should bother -
?
 Infeasibility
 Occurs occasionally under the condition of VRS
(Also a problem for input-oriented DRS model, output-oriented IRS model,
and CRS model with a zero input value)
 Renders TFDEA unable to estimate the arrival of target
 Alternate measures
- Lovell and Rouse employed a user-defined scaling factor
- Cook et al. used Radial L1 distance
- Lee et al. and Lee and Zhu used Slack based L1 distance
- Chen et al. used L2 distance based on a directional distance function

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6
Extremity
D’ (10,20)
D (5,20) E (20,20)
Extremity
E’ (20,15)
Region I
Infeasible for IO&OO
Region III
Infeasible for OO
I O: Input-oriented model
OO: Output-oriented model
Current frontier
(T)
Input
Region II
Infeasible for IO
Region IV
Feasible for IO&OO
C (25,15)
F (5,5)
5 10 15 20 25
20
15
10
5
2
F’ (10,5)
Output
B (15,10)
Radial
distance
Extremity
Radial
distance
Extremity
Radial
distance
Radial
distance
OO RoC
I O RoC
A (10,2)
D’’ (5,15)
Motivation
- How to approach -

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Formulation
- How to approach -
7
Stage 1. Efficiency measure
< Output-oriented > < Input-oriented >
OO efficiency IO efficiency

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Formulation
- How to approach -
8
Stage 2. Local RoC
< Output-oriented > < Input-oriented >
OO local RoC IO local RoC

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Formulation
- How to approach -
9
Stage 3. Super-efficiency measure
< Output-oriented > < Input-oriented >
OO extremity
OO radial distance
IO extremity
IO radial distance

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Formulation
- How to approach -
10
< Input-oriented > < Output-oriented >
Stage 4.
Forecast
Time period for
the radial distance
Time period for
the extremity
Starting point
of the forecast

11. 276 LK601R3LA19 2010 0.6737 1.4558 1.1609 1.4553 2007.00 2010.27
277 LTA550HJ06 2010 0.8159 1.7228 1.1738 1.1940 2006.77 2011.09
282 P546HW02 V0 2010 0.9151 2.3603 1.1415 1.1986 2006.70 2012.11
283 P645HW03 V0 2010 0.9674 1.8781 1.1413 1.2088 2006.56 2010.13
284 P650HVN02.2 2010 0.9674 1.7607 1.1603 1.2088 2006.56 2009.75
293 R300M1-L01 2010 0.7910 2.7735 1.1156 1.6838 2007.00 2009.52
298 LTF320HF01 2010 0.9590 1.1092 1.2043 1.1817 2006.95 2007.79
305 V315H3-L01 2010 0.9590 1.3354 1.2039 1.1817 2006.95 2008.91
321 T400HW03 V3 2010 0.9018 1.2863 1.1955 1.1866 2006.88 2008.92
325 V420H2-LE1 2010 0.8893 1.9215 1.1832 1.1877 2006.86 2011.35
330 V370H4-L01 2010 0.9211 1.3982 1.1982 1.1849 2006.90 2009.33
331 V400H1-L10 2010 0.9018 1.4399 1.1952 1.1866 2006.88 2009.58
336 LTA460HN01-W 2011 0.9778 1.9895 1.1825 1.1941 2006.77 2010.78
341 V500HK1-LS5 2011 0.9489 2.5756 1.1354 1.1962 2006.74 2012.43
344 BR650D15 2011 0.8571 1.3431 1.1650 1.2028 2006.64 2009.24
349 LK600D3LB14 2011 0.6012 1.5420 1.1686 1.1866 2006.88 2012.67
350 LK695D3LA08 2011 0.8268 1.8865 1.1446 1.2050 2006.61 2011.42
353 LTI700HA01 2011 0.9289 1.6223 1.1510 1.2110 2006.52 2009.56
355 T706DB01 V0 2011 0.9060 2.8878 1.1286 1.2345 2006.56 2012.41
357 V546H1-LS1 2011 0.8159 2.0305 1.1688 1.1940 2006.77 2012.06
ETM
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Demonstration
- Proof of concept -
11
 LCD
 Input-oriented / VRS / 31 (out of 95) infeasible targets in 2007
DMU
(k)
LCD
panel name
Actual
year of release
(푡푘 )
Extremity
(1 − 휌훰 푘
)
Radial distance
훰 )
(1 + 휏푘
Individualized
output-oriented RoC
퐶푂 푛
푗=1 ∙ 훿푗
휆푗 ,푘
퐶
퐶푂 푛
휆푗 ,푘
푗=1
Individualized
input-oriented RoC
퐶푂 푛
푗=1 ∙ 휁푗
휇푗 ,푘
퐶
퐶푂 푛
휇푗 ,푘
푗=1
Effective date
퐶푂 푛
푗=1 ∙ 푡푗
휇푗 ,푘
퐶푂 푛
휇푗 ,푘
푗=1
Forecasted
year of release
푡푓표푟푒푐푎푠푡 _퐼푂
(푘
)
165 T520HW01 V0 2008 0.9351 1.6236 1.1778 1.1972 2006.72 2009.82
166 V562D1-L04 2008 0.9632 1.0035 1.1876 1.6580 2007.00 2007.16
212 V460H1-LH7 2009 0.8183 1.3059 1.1932 1.1879 2006.86 2009.53
218 LTA550HF02 2009 0.9151 2.0317 1.1708 1.1986 2006.70 2011.16
248 V400H1-L08 2009 0.8508 1.2724 1.1984 1.1849 2006.90 2009.21
265 LK460D3LA63 2010 0.9778 2.2312 1.1752 1.1941 2006.77 2011.43
266 LTA460HM03 2010 0.9778 1.7685 1.1826 1.1941 2006.77 2010.11
268 LTA460HQ05 2010 0.9778 2.0760 1.1824 1.1941 2006.77 2011.02
271 P460HW03 V0 2010 0.9778 2.0760 1.1824 1.1941 2006.77 2011.02
273 V460H1-L11 2010 0.8183 1.2929 1.1932 1.1879 2006.86 2009.48
274 V460H1-LH9 2010 0.8653 1.4340 1.1900 1.1898 2006.83 2009.73
276 LK601R3LA19 2010 0.6737 1.4558 1.1609 1.4553 2007.00 2010.27
277 LTA550HJ06 2010 0.8159 1.7228 1.1738 1.1940 2006.77 2011.09
282 P546HW02 V0 2010 0.9151 2.3603 1.1415 1.1986 2006.70 2012.11
283 P645HW03 V0 2010 0.9674 1.8781 1.1413 1.2088 2006.56 2010.13
284 P650HVN02.2 2010 0.9674 1.7607 1.1603 1.2088 2006.56 2009.75
293 R300M1-L01 2010 0.7910 2.7735 1.1156 1.6838 2007.00 2009.52
298 LTF320HF01 2010 0.9590 1.1092 1.2043 1.1817 2006.95 2007.79
305 V315H3-L01 2010 0.9590 1.3354 1.2039 1.1817 2006.95 2008.91
321 T400HW03 V3 2010 0.9018 1.2863 1.1955 1.1866 2006.88 2008.92
325 V420H2-LE1 2010 0.8893 1.9215 1.1832 1.1877 2006.86 2011.35
330 V370H4-L01 2010 0.9211 1.3982 1.1982 1.1849 2006.90 2009.33
331 V400H1-L10 2010 0.9018 1.4399 1.1952 1.1866 2006.88 2009.58
336 LTA460HN01-W 2011 0.9778 1.9895 1.1825 1.1941 2006.77 2010.78
341 V500HK1-LS5 2011 0.9489 2.5756 1.1354 1.1962 2006.74 2012.43
344 BR650D15 2011 0.8571 1.3431 1.1650 1.2028 2006.64 2009.24
349 LK600D3LB14 2011 0.6012 1.5420 1.1686 1.1866 2006.88 2012.67
…
…
…
…
…
…
…
…
…

12. ETM
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DMU
(k)
LCD
panel name
Actual
year of release
(푡푘 )
Demonstration
- Proof of concept -
Extremity
(1 − 휌훰 푘
)
Radial distance
훰 )
(1 + 휏푘
Individualized
output-oriented RoC
퐶푂 =1 휆푗 ,푘
∙ 푗
푛훿푗
퐶
퐶푂 =1
휆푗 ,푘
푗
푛Individualized
input-oriented RoC
퐶푂 =1 휇푗 ,푘
∙ 푗
푛휁푗
퐶
퐶푂 푛푗
=1
휇푗 ,푘
Effective date
퐶푂 =1 휇푗 ,푘
∙ 푗
푛푡푗
퐶푂 푛푗
=1
휇푗 ,푘
Forecasted
year of release
푡푓표푟푒푐푎푠푡 _퐼푂
(푘
)
165 T520HW01 V0 2008 0.9351 1.6236 1.1778 1.1972 2006.72 2009.82
166 V562D1-L04 2008 0.9632 1.0035 1.1876 1.6580 2007.00 2007.16
212 V460H1-LH7 2009 0.8183 1.3059 1.1932 1.1879 2006.86 2009.53
218 LTA550HF02 2009 0.9151 2.0317 1.1708 1.1986 2006.70 2011.16
248 V400H1-L08 2009 0.8508 1.2724 1.1984 1.1849 2006.90 2009.21
265 LK460D3LA63 2010 0.9778 2.2312 1.1752 1.1941 2006.77 2011.43
266 LTA460HM03 2010 0.9778 1.7685 1.1826 1.1941 2006.77 2010.11
268 LTA460HQ05 2010 0.9778 2.0760 1.1824 1.1941 2006.77 2011.02
271 P460HW03 V0 2010 0.9778 2.0760 1.1824 1.1941 2006.77 2011.02
273 V460H1-L11 2010 0.8183 1.2929 1.1932 1.1879 2006.86 2009.48
274 V460H1-LH9 2010 0.8653 1.4340 1.1900 1.1898 2006.83 2009.73
276 LK601R3LA19 2010 0.6737 1.4558 1.1609 1.4553 2007.00 2010.27
277 LTA550HJ06 2010 0.8159 1.7228 1.1738 1.1940 2006.77 2011.09
282 P546HW02 V0 2010 0.9151 2.3603 1.1415 1.1986 2006.70 2012.11
283 P645HW03 V0 2010 0.9674 1.8781 1.1413 1.2088 2006.56 2010.13
284 P650HVN02.2 2010 0.9674 1.7607 1.1603 1.2088 2006.56 2009.75
293 R300M1-L01 2010 0.7910 2.7735 1.1156 1.6838 2007.00 2009.52
298 LTF320HF01 2010 0.9590 1.1092 1.2043 1.1817 2006.95 2007.79
305 V315H3-L01 2010 0.9590 1.3354 1.2039 1.1817 2006.95 2008.91
321 T400HW03 V3 2010 0.9018 1.2863 1.1955 1.1866 2006.88 2008.92
325 V420H2-LE1 2010 0.8893 1.9215 1.1832 1.1877 2006.86 2011.35
330 V370H4-L01 2010 0.9211 1.3982 1.1982 1.1849 2006.90 2009.33
331 V400H1-L10 2010 0.9018 1.4399 1.1952 1.1866 2006.88 2009.58
336 LTA460HN01-W 2011 0.9778 1.9895 1.1825 1.1941 2006.77 2010.78
341 V500HK1-LS5 2011 0.9489 2.5756 1.1354 1.1962 2006.74 2012.43
344 BR650D15 2011 0.8571 1.3431 1.1650 1.2028 2006.64 2009.24
349 LK600D3LB14 2011 0.6012 1.5420 1.1686 1.1866 2006.88 2012.67
350 LK695D3LA08 2011 0.8268 1.8865 1.1446 1.2050 2006.61 2011.42
353 LTI700HA01 2011 0.9289 1.6223 1.1510 1.2110 2006.52 2009.56
355 T706DB01 V0 2011 0.9060 2.8878 1.1286 1.2345 2006.56 2012.41
357 V546H1-LS1 2011 0.8159 2.0305 1.1688 1.1940 2006.77 2012.06
12

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Demonstration
- Proof of concept -
13
 Deviation statistics (actual vs forecast)

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14
 TFDEA extension
Conclusion
- Summary of Talk -
 Developed based on Cook et al.’s modified super-efficiency model
 Bi-directional distances are estimated from RoCs from corresponding orientations
 Always yields a feasible and a finite forecast
 Returns results equivalent to the original TFDEA model when feasibility is present
(Feasible target has an extremity value of zero, which reduces presented model to
the original TFDEA model)
 Applied to the LCD dataset
- Formerly infeasible 31 targets could be forecasted
- Results showed not only consistent forecasts for feasible targets
but also reasonable forecasts for infeasible targets

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Future Works
- Matters for Speculation -
 Comprehensive benchmark tests
 Apply current model to more/bigger datasets
 Comparison with alternate super-efficiency measures
 Practical interpretation of ‘Extremity’
 Extremity indicates occurrences of unprecedented levels of inputs/outputs
 Degree/Ratio of infeasible targets to feasible targets over time might imply
the direction of technological innovation
 Comparison between IO extremities and OO extremities
 Weighted distance for extremity

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Backup
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