Technology forecasting using dea in the presence of infeasibility
- 1. ETM Extreme Technology Analytics Research Group –– tfdea.com 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
- 2. ETM Extreme Technology Analytics Research Group – tfdea.com 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) ETM Extreme Technology Analytics Research Group – tfdea.com 3 Introduction - TFDEA - Output Current frontier (T) Input Evolution of frontiers Conceptual framework
- 4. ETM Extreme Technology Analytics Research Group – tfdea.com 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
- 5. ETM Extreme Technology Analytics Research Group – tfdea.com 5 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
- 6. ETM Extreme Technology Analytics Research Group – tfdea.com 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 -
- 7. ETM Extreme Technology Analytics Research Group – tfdea.com Formulation - How to approach - 7 Stage 1. Efficiency measure < Output-oriented > < Input-oriented > OO efficiency IO efficiency
- 8. ETM Extreme Technology Analytics Research Group – tfdea.com Formulation - How to approach - 8 Stage 2. Local RoC < Output-oriented > < Input-oriented > OO local RoC IO local RoC
- 9. ETM Extreme Technology Analytics Research Group – tfdea.com Formulation - How to approach - 9 Stage 3. Super-efficiency measure < Output-oriented > < Input-oriented > OO extremity OO radial distance IO extremity IO radial distance
- 10. ETM Extreme Technology Analytics Research Group – tfdea.com 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 Extreme Technology Analytics Research Group – tfdea.com 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 Extreme Technology Analytics Research Group – tfdea.com 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
- 13. ETM Extreme Technology Analytics Research Group – tfdea.com Demonstration - Proof of concept - 13 Deviation statistics (actual vs forecast)
- 14. ETM Extreme Technology Analytics Research Group – tfdea.com 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
- 15. ETM Extreme Technology Analytics Research Group – tfdea.com 15 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
- 16. ETM Extreme Technology Analytics Research Group – tfdea.com Backup 16
Editor's Notes
- #16: Limitation: RoC would not be captured depending on the model: constant 1 for IO