Forecasting models for cost evolution of network components and - PowerPoint PPT Presentation

Forecasting models for cost evolution of network components and Risk analysis based on uncertainties in demand forecasts and cost predictions Kjell Stordahl Telenor Networks kjell.stordahl@telenor.com 19. okt. 2004 Telenor 1

Forecasting models for cost evolution of network components Kjell Stordahl Telenor Networks kjell.stordahl@telenor.com 19. okt. 2004 Telenor 2

� � � � � Agenda Write and Crawford’s learning curve model The extended learning curve model Discussion of different type of parameters in the models Examples Conclusion on cost prediction models 19. okt. 2004 Telenor 3

Learning curve T. P. Wright proposed the concept of learning curves: T n = n - α α α α ·T 0 where T n is the average production time for n units, and T 0 is the time to complete the first unit. J.R.Crawford applied the same formula, but interpreted T n to be the completing time for the n th unit in a series. Let us assume that the component cost (price) P n is proportional to the production time T n . 19. okt. 2004 Telenor 4

Learning curve coefficient K α P 0 P n = n - α α α P n is the average cost for the n th unit. The learning curve coefficient is defined by: P 2n = K · P n Then K= (2) - α α α α α= − α= α= α= − − − log 2 K 19. okt. 2004 Telenor 5

Relevant K values of different network components LearningCurveClass K_Value CivilWorks 100,00% CopperCable 100,00% Electronics 80,00% SitesAndEnclosures 100,00% FibreCable 90,00% Installation (constant) 100,00% AdvancedOpticalComponents 70,00% Installation (decresing) 85,00% OpticalComponents 80,00% 19. okt. 2004 Telenor 6

Learning curve prediction Κ Κ Κ Κ = 0,8 or α α α α = 0,32 Learning curve predictions as a fuction of number of produced units 1,2 1 0,8 Cost 0,6 0,4 0,2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 19. okt. 2004 Telenor 7

What we need: Cost as a function of time 19. okt. 2004 Telenor 8

The answer To combine the learning curves with volume forecasts of components. α P(0) = − log 2 K P(0) = n(t) − = = P(t) = n(t) − −α − − α α − − 19. okt. 2004 Telenor 9

The answer To combine the learning curves with volume forecasts of components. α P(0) = − log 2 K P(0) = = n(t) − = P(t) = n(t) − − − −α α α − − (Olsen , Stordahl 1993) Extended learning curve model is given by inserting a Logistic model into the learning curve model n(t)= M · [1+ e (a+b·t) ] – γ γ γ γ 19. okt. 2004 Telenor 10

✁ ✁ ✁ ✁ � ✁ Parameters in the model α: Learning curve coefficient K or α: α: α: Production cost, unit no 1 P(0): Saturation M: Parameter in the Logistic model a: b: Parameter in the Logistic model γ : Parameter in the Logistic model γ γ γ 19. okt. 2004 Telenor 11

Reformulation of the parameters The normalized Logistic model is: n r (t) = n(t)/ M The aggregated production volume the reference year, 0: n r (0) The growth period: n r (t 1 ) = 0,1 n r (t 2 ) = 0,9 ∆ ∆ ∆ ∆ T = t 1 - t 2

Interpretation of the parameters 1,2 1,2 1 1 0,8 0,8 0,6 0,6 n r (0) n r (0) 0,4 0,4 0,2 0,2 0 0 0 0 t 1 t 1 t 2 t 2 ∆ T ∆ T ∆ ∆ ∆ ∆ ∆ ∆ 19. okt. 2004 Telenor 13

✠ ✠ ✄ ✄ ☎ ✆ ✝ ✝ ✝ ✝ ✞ ✟ ✔ ✠ ✠ ✠ ✡ ✂ ✎ ✏ ✍ ✌ ✒ ✑ ✏ ✍ ☛ ✌ ☞ ☞ ☞ ☞ ☞ ✄ ✄ ✁ ✘ � � � � ✖ ✚ ✖ ✙ ✑ ✖ ✗ ✖ ✕ The extended learning curve ( γ = 1) log ⋅ K 1 − 2 2 ln 9 ⋅ 1 − − ( ) ln 0 1 − ⋅ nr t ✎✓✎ ✒✓✒ ∆ T 1 − ⋅ ( ) ( ) ( ) = 0 ⋅ 0 1 + P t P nr e P(0): Production cost the reference year (0) n r (0): Relative accumulated production volume the reference year ∆ T: Time for the accumulated volume to grow from 10% to 20% K: Learning curve coefficient 19. okt. 2004 Telenor 14

Cost as a function of Κ n r (0)=0.1, ∆ ∆ T=5 ∆ ∆ Relative cost 1 0.9 0.8 0.7 0.6 Relative 0.5 cost 0.4 0.3 0.2 0.9 0.1 0.5 K 0 0 1 2 3 4 0.1 5 6 7 8 9 Project year 19. okt. 2004 Telenor 15

Cost as a function of n r (0) ∆ ∆ ∆ ∆ T = 5, K = 0.8 Relative cost 1 0.9 0.8 0.7 0.6 Relative 0.5 cost 0.4 0.3 0.2 0.9 0.1 0.5 0 n r (0) 0 1 2 3 4 0.1 5 6 7 8 9 Project year 19. okt. 2004 Telenor 16

Cost as a function of ∆ T n r (0) = 0.1, K = 0.8 Relative cost 1 0.9 0.8 0.7 0.6 Relative 0.5 cost 0.4 0.3 0.2 18 0.1 10 0 ∆ ∆ ∆ ∆ T 0 1 2 3 2 4 5 6 7 8 Project year 19. okt. 2004 Telenor 17

Historical diffusions of selected goods in Canada. 100 90 fixed telephone 80 70 Cable 60 50 VCR PC 40 Television 30 Mobile 20 Internet 10 0 3 6 2 6 5 2 5 7 9 1 3 5 7 9 5 5 6 6 7 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19. okt. 2004 Telenor 18

Historical diffusions of selected goods in Finland. 100 Color TV 90 Freezer 80 Microwave 70 60 PC Mobile 50 Video recorder Dishwasher 40 Internet 30 20 CD player 10 0 6 0 0 8 0 2 7 8 9 9 0 0 9 9 9 9 0 0 1 1 1 1 2 2 19. okt. 2004 Telenor 19

Recommended values on the parameters when cost time series are not available ∆ T VolumeClass n r (0) Emerging_Fast 0,001 5,00 Emerging_Medium 0,001 10,00 LearningCurveClass K_Value Emerging_Slow 0,001 20,00 CivilWorks 100,00% Emerging_VerySlow 0,001 40,00 CopperCable 100,00% Mature_Fast 0,1 5,00 Electronics 80,00% Mature_Medium 0,1 10,00 SitesAndEnclosures 100,00% Mature_Slow 0,1 20,00 Mature_VerySlow 0,1 40,00 FibreCable 90,00% New_Fast 0,01 5,00 Installation (constant) 100,00% New_Medium 0,01 10,00 AdvancedOpticalComponents 70,00% New_Slow 0,01 20,00 Installation (decresing) 85,00% New_VerySlow 0,01 40,00 OpticalComponents 80,00% Old_Fast 0,5 5,00 Old_Medium 0,5 10,00 Old_Slow 0,5 20,00 Old_VerySlow 0,5 40,00 Straight Line 0,1 1000,00 19. okt. 2004 Telenor 20

Forecasts for ADSL line costs. Estimation: P(2000)= 212 Euro, ∆ ∆ ∆ ∆ T=8, n(2000)=0,1%,K=0,736 Forecast model for ADSL line costs Forecast model for ADSL line costs 250 250 Model Model Data Data 200 200 150 150 Euro Euro 100 100 50 50 0 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 19. okt. 2004 Telenor 21

Forecasts for STM equipment costs. Estimation: P(2000)=1188 Euro, ∆ ∆ ∆ T=8, n(2000)=7,4%, K=0,756 ∆ Forecast model for STM equipment costs Forecast model for STM equipment costs 1400 1400 Model Model 1200 1200 Data Data 1000 1000 800 800 Euro Euro 600 600 400 400 200 200 0 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 19. okt. 2004 Telenor 22

Logistic model with different γ values 1,2 1,2 1 1 0,3 0,3 0,8 0,8 0,5 0,5 0,6 0,6 1 1 2 2 0,4 0,4 4 4 0,2 0,2 10 10 0 0 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -0,2 -0,2 19. okt. 2004 Telenor 23

✝ ✝ ✟ ✞ ✝ ✝ ✑ ✝ ✝ ✝ ✝ ✠ ✝ ✆ ☎ ✄ ✄ ✄ ✄ ✄ ✠ ✠ ✄ ☞ ✌ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ✠ ☞ ☛ ✡ ✠ ✠ ✠ ✠ ✠ ✠ ✄ ✄ ✄ ✑ � � � � � ✢ ✜ ✛ ✙ ✕ ✒ ✔ ✍ ✍ ✂ ✁ ✌ ✒ The extended learning curve (diff γ ) log ⋅ K − γ 2 1 − ✖✏✖✗✖✘✖ ✖✏✖✗✖✘✖ ✎✏✎✏✎✏✎✏✎✏✎✏✎ ✓✏✓✏✓✏✓✏✓✏✓✏✓ ln δ y ln ( ) 0 − 1 + ✎✏✎✏✎ ✓✏✓✏✓ ⋅ nr t ∆ T ✖✏✖✗✖✚✖ ✖✏✖✗✖✚✖ 1 − ( ) ( ) 0 ( ) 0 1 = ⋅ ⋅ + P t P nr e P(0): Production cost the reference year (0) n r (0): Relative accumulated production volume the reference year ∆ T: Time for the accumulated volume to grow from 10% to 20% K: Learning curve coefficient γ: Parameter asymmetry γ γ γ 19. okt. 2004 Telenor 24

� � � � � � � Use of the the Extended learning curve model RACE 2087/TITAN 1992-1996 AC 226/OPTIMUM1996-1998 AC364/TERA1998-2000 IST-2000-25172 TONIC2000-2002 ECOSYS / CELTIC 2004- Many Eurescom projects – P306, P413, P614, P901 etc Within Telenor and other project partners organizations 19. okt. 2004 Telenor 25

� � � � Advantages with the extended learning curve model The model makes forecasts of component costs (predictions as a function of time The model has the possibility to include both a priori knowledge and statistical information at the same time The model can be used to forecast component costs evolution even if no cost observations are known The model can be used to forecast component costs based on estimation of the parameters when historical costs are available 19. okt. 2004 Telenor 26

Risk analysis based on uncertainties in demand forecasts and cost predictions Kjell Stordahl Telenor Networks kjell.stordahl@telenor.com 19. okt. 2004 Telenor 27