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產品生命週期之型態與預測
任 立 中
國立臺灣大學管理學院國際企業學系暨研究所教授
美國俄亥俄州立大學商學院行銷管理博士
1
The Four Stages of The Product Life Cycle
Introductory
Stage
Growth
Stage
Maturity Stage
Time
Decline
Stage
Marketing Strategies and The Product Life Cycle
Marketing
Mix
Strategy
Introduction
Growth
Maturity
Decline
Product
Strategy
Limited number of
models; frequent
product modifications
Expanded number of
models; frequent
product
modifications
Large number of
models
Elimination of
unprofitable models
and brands
Distribution
Distribution usually
limited, depending on
product; intensive
efforts and high
margins often needed
to attract wholesalers
and retailers
Expanded number of
dealers; intensive
efforts to establish
long-term
relationships with
wholesalers and
retailers
Extensive number of
dealers; margins
declining; intensive
efforts to retain
distributors and shelf
space
Unprofitable outlets
phased out
Promotio
n
strategy
Develop product
awareness; stimulate
primary demand; use
intensive personal
selling to distributors;
use sampling and
couponing for
consumers
Stimulate selective
demand; advertise
brand aggressively
Stimulate selective
demand; advertise
brand aggressively;
promote heavily to
retain dealers and
customers
Phase out all
promotion
Pricing
Strategy
Prices are usually
high to recover
development costs
Prices begin to fall
toward end of
growth stage as
result of competitive
pressure
Prices continue to fall
Prices stabilize at
relatively low level;
small price rises are
possible if
competition is
negligible
Strategy
Product Life-Cycle Stage
Different Product Life Cycles
Style
Time
Fashion
Time
Fad
Time
The Importance of New Products
5
個案研討
1996至
2003年67
款各式熨
斗之月銷
售資料
6
7
8
9
10
11
12
13
1400000
1200000
1000000
800000
600000
400000
200000
0
1
13
25
37
49
61
73
85
Cumulative Monthly Sales Volume
1150000
950000
750000
550000
350000
150000
1996
1997
1998
1999
2000
2001
2002
2003
相乘季節性ARIMA(p,d,q)(P,D,Q)s模型
p (B)P (Bs )d sD Xt  c  q (B)Q (Bs )a t
其中
at~iid N(0, a2 ), c是常數項
p (B) 11B 2 B2  ... p Bp
 P (Bs ) 1  s Bs  2s B2s ...  Ps BPs
q (B) 11B 2 B2  ... q Bq
Q (B) 1s Bs 2s B2s  ... Qs BQs
d  (1 B)d
sD  (1  Bs ) D
17
1600000
ARIMA(1,1,1)(1,1,1)12
1  1B1  12 B12 1  B1  B12  X t  c  1  1B1  12 B12 a t
1400000
1 - 0.2206B 1  0.3696B12  1 - B 1 - B12  X t  1 - 0.7525B 1 - 0.7593B12  a t
1200000
1000000
800000
600000
400000
200000
0
1996
1997
1998
1999
2000
2001
2002
2003
2004
45000
60
Average sales volume per product
40000
The number of product types sold in that month
50
多項式 (The number of product types sold in that
month)
40
35000
30000
25000
30
20000
15000
20
10000
10
5000
0
0
1996
1997
1998
1999
2000
2001
2002
2003
整合型時間數列分析模式之優劣點
優點


考量季節性與長期趨勢之變動
整體預測有助於公司財務之預測與規劃
缺點


缺乏Marketing insights
無助於單一、新產品生命週期之預測
20
Diffusion Model
擴散模型
新產品擴散模型(New Product Diffusion Model)
新技術擴散效應(Diffusion Effect of New Technology)
學習擴散過程(Learning Diffusion Process)
21
Adopters’ Categories Based On Innovativeness
22
Relationship of the Diffusion Process to the
Product Life Cycle
23
Product Life Cycle
S(t)
PLC
Consumer
Heterogeneity
Smaller Consumer
Heterogeneity
產品銷售曲線圖
Time24
Characteristics that explain the rate of acceptance
and diffusion of new product
Complexity
Compatibility
Relative Advantage
Observability
Trialability
25
Western Decision Sciences Institute, Thirtieth Annual Meeting
The Linkage of Cross-National Product Diffusion Patterns: An Application for
Predicting Box-Office Attendance of Motion Pictures
(Best Paper Award)
Lichung Jen
Associate Professor in Marketing
Department of International Business
National Taiwan University
Topic area/track:
Marketing Management and Strategies
Western Decision Sciences Institute
Vancouver, Canada
April 3-7, 2001
26
Research Objective
To forecast the potential box-office
of new motion pictures in Taiwan
where sales data is not available
27
INDUSTRY BACKGROUND
Sales of fashion goods are very
difficult to predict and manage




Fashion styles change dramatically
from product to product
Product Life Cycle is very short
Using dynamic pricing strategy to
control the length of life
Need to predict the whole pattern of
PLC, not just a point of sales
28
29
30
Annual Sales Data
200000
150000
100000
50000
0
1995
600000
500000
400000
300000
200000
100000
0
1995
1997
1997
1999
1999
2001
2001
2003
2003
300000
250000
200000
150000
100000
50000
0
1995
20000
2003
0
1995
0
1995
1997
1999
2001
2003
1997
1999
2001
2003
0
1995
1999
2001
2003
1997
1999
2001
2003
1997
1999
2001
2003
1997
1999
2001
2003
100000
50000
1997
1999
2001
2003
0
1995
150000
150000
100000
100000
50000
50000
0
1995
1997
150000
10000
0
1995
0
1995
200000
5000
30000
2001
10000
100000
40000
1999
400000
10000
50000
1997
20000
200000
2003
5000
600000
15000
2001
10000
30000
300000
1999
15000
800000
20000
1997
20000
40000
400000
0
1995
25000
1997
1999
2001
2003
0
1995
31
Annual Sales Data
50000
100000
80000
40000
80000
60000
30000
60000
20000
40000
10000
20000
0
1995
1997
1999
2001
0
1995
2003
40000
20000
1997
1999
2001
2003
0
1995
1999
2001
2003
1997
1999
2001
2003
2003
50000
0
1995
1997
1999
2001
2003
2003
700000
600000
500000
400000
300000
200000
100000
0
1995
1997
1999
2001
2003
500000
50000
250000
400000
40000
200000
300000
30000
150000
200000
20000
100000
100000
10000
50000
0
1995
1997
1999
2001
2003
1999
2001
2003
200000
150000
100000
30000
20000
20000
10000
10000
1997
1997
1999
1999
2001
2001
2003
0
1995
2003
70000
60000
50000
40000
30000
20000
10000
0
1995
0
1995
300000
250000
40000
30000
700000
600000
500000
400000
300000
200000
100000
0
1995
1997
50000
40000
0
1995
0
1995
1997
1997
1997
1999
1999
2001
2001
32
Annual Sales Data
600000
500000
400000
300000
200000
100000
0
1995
1997
1999
2001
2003
400000
800000
300000
600000
200000
400000
100000
200000
0
1995
1997
1999
2001
2003
0
1995
80000
200000
400000
60000
150000
300000
40000
100000
200000
20000
50000
100000
0
1995
300000
250000
200000
150000
100000
50000
0
1995
1997
1999
2001
2003
0
1995
1997
1999
2001
2003
0
1995
1999
2001
2003
1997
1999
2001
2003
1997
1999
2001
2003
2001
2003
1500000
400000
300000
1000000
200000
500000
100000
1997
1999
2001
2003
0
1995
1997
1999
2001
0
1995
2003
80000
1000000
80000
60000
800000
60000
600000
40000
40000
400000
20000
0
1995
1997
20000
200000
1997
1999
2001
2003
0
1995
1997
1999
2001
2003
0
1995
1997
1999
33
Annual Sales Data
200000
400000
150000
300000
100000
200000
50000
100000
0
1995
1997
1999
2001
2003
150000
100000
0
1995
1500000
1000000
500000
1997
1999
2001
800000
100000
600000
80000
0
1995
1997
1999
2001
2003
250000
2003
1200000
1000000
800000
600000
400000
200000
0
1995
2003
600000
500000
400000
300000
200000
100000
0
1995
200000
150000
100000
50000
0
1995
1997
1999
2001
100000
80000
60000
40000
20000
0
1995
1997
1999
2001
1999
2001
2003
1999
2001
2003
40000
200000
0
1995
1997
60000
400000
50000
0
1995
2003
20000
1997
1999
2001
2003
0
1995
1997
20000
15000
10000
5000
1997
1997
1999
1999
2001
2001
2003
0
1995
1997
1999
2001
2003
2003
30000
25000
20000
15000
10000
5000
0
1995
1997
1999
2001
2003
34
Annual Sales Data
20000
1000000
50000
15000
800000
40000
600000
30000
400000
20000
200000
10000
10000
5000
0
1995
1997
1999
2001
2003
0
1995
80000
400000
60000
300000
40000
200000
20000
100000
0
1995
120000
100000
80000
60000
40000
20000
0
1995
1997
1999
2001
2003
0
1995
1997
1999
1999
2001
2001
2003
0
1995
1997
1999
2001
2003
2003
30000
25000
20000
15000
10000
5000
0
1995
1997
1999
2001
2003
2003
300000
250000
200000
150000
100000
50000
0
1995
1997
1999
2001
2003
1997
1999
2001
2003
100000
80000
60000
40000
20000
1997
1999
2001
2003
0
1995
2000000
200000
1500000
150000
1000000
100000
500000
50000
0
1995
1997
1997
1999
2001
2003
0
1995
1997
1999
2001
500000
400000
300000
200000
100000
1997
1999
2001
2003
0
1995
35
Annual Sales Data
600000
500000
400000
300000
200000
100000
0
1995
1997
1999
2001
2003
300000
250000
200000
150000
100000
50000
0
1995
500000
40000
400000
30000
300000
2001
2003
10000
100000
1997
1999
2001
2003
0
1995
1997
1999
2001
2003
60000
50000
40000
30000
20000
10000
0
1995
1997
1999
2001
2003
150000
100000
50000
0
1995
1999
20000
200000
0
1995
1997
1997
1999
2001
2003
1997
1999
2001
2003
500000
400000
300000
200000
100000
0
1995
36
Forecasting Models
From Statistical point of view
37
Forecasting Models
Model 1: Linear Regression Model
X
Y  e 
ln Y  ln   X  ln 
38
Forecasting Models
Model 2: Poisson Regression Model
（Grogger and Carson 1991）
Pr (Yi i ) 
Yi  i
i e
Yi !
E Yi   i  X i 
39
Forecasting Models
Model 3: Negative Binomial Distribution Model
（Ehrenberg 1988；Morrison and Schmittlein 1988）
Pr (Yi  i )  (i )Yi exp( i ) / Yi !
g ( i  ,  i ) 
Yi  0,1,2......


1
( i )  1 exp(  i )
( )  i
i
Pr (Yi  , i )   p(Yi i ) g (i  , i )di  C
Yi  1
Yi
E (Yi |  , i )   
i
1 1
)  i
i  1 i  1
(
  0,  0,  0
Yi
 i 




1
 i


 1 




1
 i

V (Yi |  , i )   
i
1 2
)  i ( i  1)
i  1 i  1
(
NBD Regression Model：
E (Yi |  , i )  i  exp( xi )
40
Forecasting Models
Model 4(a): Exponential Decay Model
（Krider & Weinberg 1998）
Yt   0 e
1( t 1)  2 ( t 1)2  t
t  1,2,......　0  0,   0
0: The sales volume at first time period (week)
Decay Rate = 1  e  2t 
1
2
2
Forecast Model: Regress 's on X
 0  X    
0
0
1  X    
1
1
 2  X    
2
2
41
Forecasting Models
Model 4(b):Exponential Decay Model with
Hierarchical Bayes Estimation Approach
Yn  X nn  n n ~ Multivariate Normal (0, n )　n  2n I
12 0 


n  Z n  un un ~ Multivariate　Normal(0, )     
0　 2 
k

The posterior distribution of
 n | Yn , X n , Z n , ,  n ,  ~ Multi var iate　Normal{[( X n'  n1 X n  1 ) 1 ( X n'  n1Yn  1n Z n )], ( X n'  n1 X n  1 )}
T
1
 n2 | Yn , X n ,  n , v, M ~ Inverse　Gamma{v  , [ M 1  (Yn  X n  n ) ' (Yn  X n  n )]}
2
2
N
N
N
1
1
1
k | 1k ,...,  Nk , Z1,..., Z N , k ,  0 , V 0 ~ Multi var iateNormal　[(k 2  Z n Z n'  V01 )1 (k 2  nk Z n  V01 0 ), (k 2  Z n Z n'  V01 )1 ]
42
Forecasting Models
From Marketing Perspective
43
The Driving Forces of PLC
Innovation Rate (創新使用者) -- p
Imitation Rate (模仿採用者) -- q
Product Diffusion Model
44
Product Diffusion Model
d N t 
q
n t  
 p m  N t   N t m  N t 
dt
m
式中的第一項， p[m - N(t)]，代表不受之前採
用人數影響的創新採用者，稱p為“創新係數”
式中的第二項， (q/m) N(t)[m - N(t)]，代表受
之前採用人數影響的模仿採用者，稱q為"模仿
係數"。
45
Product Diffusion Model
p<q
p>q
Time
Time
產品銷售曲線圖
46
Forecasting Models
Model 5(a): Bass Diffusion Model by OLS
Estimation Method (Bass,1967）
q
(CumYt  i ) 2
m
q
a  pm　b  q  p　c  
m
Yt  pm  (q  p )CumYt 1 
Let
Yt  a  bCumYt 1  c(CumYt  i ) 2
Yt: the total purchasers at time t CumYt-1: the cumulative purchasers at time t-1
m : market potential
p : innovation coefficient q : imitation coefficient
Forecast Model: Regress p,q,m on X
P  X p   p
Q  X q   q
M  X m   m
47
Forecasting Models
Model 5(b): Bass Diffusion Model with Hierarchical
Bayes Estimation Approach
Yn  X nn  n n ~ Multivariate Normal (0, n )　n  2n I
12 0 


n  Z n  un un ~ Multivariate　Normal(0, )     
0　 2 
k

The posterior distribution of
 n | Yn , X n , Z n , ,  n ,  ~ Multi var iate　Normal{[( X n'  n1 X n  1 ) 1 ( X n'  n1Yn  1n Z n )], ( X n'  n1 X n  1 )}
T
1
 n2 | Yn , X n ,  n , v, M ~ Inverse　Gamma{v  , [ M 1  (Yn  X n  n ) ' (Yn  X n  n )]}
2
2
N
N
N
1
1
1
k | 1k ,...,  Nk , Z1,..., Z N , k ,  0 , V 0 ~ Multi var iateNormal　[(k 2  Z n Z n'  V01 )1 (k 2  nk Z n  V01 0 ), (k 2  Z n Z n'  V01 )1 ]
48
Forecasting Models
Model 6: Bass Diffusion Model by Nonlinear Least
Square Estimation Method（Jain and Rao,1990）
 F (t )  F (t  1) 
Yt  (m  CumYt 1 )  
  where

 1  F (t  1) 
1  e  ( p  q )t
F (t ) 
q
1  e ( p  q )t
p
,
Yt: the total purchasers at time t CumYt-1: the cumulative purchasers at time t-1
m : market potential
p : innovation coefficient q : imitation coefficient
F(t) = the purchase ratio at time tI
 = error term
Forecast Model: Regress p,q,m on X
P  X p   p
Q  X q   q
M  X m   m
49
美國影片在美國擴散型態參數估計值彙總表
序 電影中文片名
號
估計值 p
(標準誤)
估計值 q
(標準誤)
估計值 m
(標準誤)
R2
1 是誰搞的鬼 !?
0.30976
(0.006885)
0.74542
(0.027719)
0.11939
(0.04188)
0.742063
(0.045056)
0.372951
(0.0453)
0.154092
(0.019631)
0.001
(0.06828)
0.538471
(0.18287)
0.001
(0.114089)
0.001
(0.11381)
14280004
(35434)
10915541
(38053)
11350362
(298555)
7568655
(54185)
16463913
(340125)
0.99720
2 星艦戰將
3 真假公主娜塔西亞
4 異形 4 - 浴火重生
5 飛天法寶
0.99802
0.66192
0.99574
0.92560
50
美國影片在臺灣擴散型態參數估計值彙總表
序 電影中文片名
號
估計值 p
(標準誤)
估計值 q
(標準誤)
1 是誰搞的鬼 !?
0.541747
(0.003797)
0.833319
(0.052935)
0.450419
(0.020324)
0.966199
(0.15361)
0.724229
(0.072626)
0.770295
(0.014844)
0.181367
(0.156826)
0.554239
(0.079099)
0.009833
(0.456453)
0.805581
(0.238448)
2 星艦戰將
3 真假公主娜塔西亞
4 異形 4 - 浴火重生
5 飛天法寶
估計值 m
2
R
標準誤
(
)
106903
(122)
129853
(1314)
60788
(569)
147952
(4790)
94758
(916)
0.99998
0.99885
0.99829
0.99507
0.99902
51
美國影片在臺銷售預測模型：
TWp =αp+β1USp+β2USq+β3HR+β4SF+β5 DR+β6 STR+β7 RNK +β8 HDYp +εp
TWq =αq+γ1HR+γ2SF+γ3 DR+γ4 STR+γ5 RNK +γ6 HDYq +εq
TWm =αm+η1USm+η2HR+η3SF+η4 DR+η5 STR+η6 RNK +η7 HDYm +εm
52
截距項
美國之創新係數
美國之模仿係數
美國之市場潛量
恐怖片
科幻片
非文藝劇情片
票房明星
明星票房價值
假日檔期
臺灣市場擴散預測模型
創新係數 模仿係數
市場潛量
p
q
m
0.11452
0.566785
5.42551
(1.157)
(5.463)***
(1.754)*
0.780212
(4.239)***
0.378401
(1.895)*
0.8852
(6.634)***
0.216599
0.35278
3.293445
(1.981)*
(1.721)*
(0.675)
0.003265
0.43695
10.48246
(0.037)
(2.912)*** (2.819)***
0.0403
0.08145
5.184564
(0.609)
(0.675)
(1.772)*
0.00301
0.465978
12.2084
(0.014)
(1.185)
(1.284)
0.000379
0.00752
0.204109
(0.144)
(1.551)
(1.722)*
0.02728
0.131548
5.834916
(0.529)
(1.329)
(2.248)**
The Measurements of Predictability (1)
1. Mean Absolute Deviation for Total Sales
1
N
N
Tn
 Y
n 1
nt
t 1
Tn
  Yˆnt
t 1
2. Mean Absolute Deviation of Weekly Sales
1
N
1


n 1  Tn
N

ˆ
Ynt  Ynt 

t 1

Tn
3. RMSE（Root Mean Square Error）of Weekly Sales
1
N
N

n 1
1
Tn
Tn
 (Y
t 1
nt
 Yˆnt ) 2
54
The Measurements of Predictability (2)
4. MAPE（Mean Absolute Percentage Error）of Weekly Sales
1
N

1


n 1 Tn

N
 Ynt  Yˆnt




100
%

 Y

t 1 
nt


Tn
5. Mean Absolute Deviation for First Week Sales
1
N
N
Y
n 1
n1
 Yˆn1
6. MAPE（Mean Absolute Percentage Error）for First Week Sales
1
N
 | Yn1  Yˆn1 |

 100%


Y
n 1 

n1

N
55
The Measurements of Predictability (3)
7. Weighted RMSE
1
N
N

n 1



Tn 
Ynt
2
ˆ ) 
 T

(
Y

Y

nt
nt
n

t 1 
Y
  nt

 t 1

8. Weighted MAPE
 



ˆ
N  Tn
Y

Y
nt
nt
1
 Ynt 



100
%


T

N n 1  t 1  n
Ynt

   Ynt

  t 1
56
The Performance of Out Samples Forecasting
st
MAD(1 week)
MAPE(1st week)
MAD(Weekly)
MAD(Total Sales)
RMSE
Weighted RMSE
MAPE
Weighted MAPE
Model 1:
Model 2:
Model 3:
Model 4(a):
Model 4(b):
Model 5(a):
Model 5(b):
Model 6:
Model 1 Model 2 Model 3 Model 4(a) Model 4(b) Model 5(a) Model 5(b) Model 6
38598 30695 33360
23799
17660
9947
9006 6044
47%
52%
39%
40%
33%
14%
16%
12%
14114
101625
20060
30537
115%
51%
11306
76400
15730
23308
120%
54%
14344
100476
18772
26567
218%
55%
9831
70506
13879
20798
46%
39%
8296
58737
12051
18376
40%
36%
5056
36054
7239
11047
61%
21%
5958
41766
8221
11844
79%
26%
4431
31517
5890
7850
32%
19%
Linear Regression Model
Poisson Regression Model
Negative Binomial Distribution Model
Exponential Decay Model
Exponential Decay Model with Hierarchical Bayes Estimation Approach
Bass Diffusion Model by OLS Estimation Method
Bass Diffusion Model with Hierarchical Bayes Estimation Approach
Bass Diffusion Model by Nonlinear Least Square Estimation Method
Forecasting Results: Weekly Box-Office Attendance
60,000
55,000
50,000
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
Soldier
Actual
第1週
第2週
第3週
第4週
第5週
第6週
Prediction
第7週
Forecasting Results: Weekly Box-Office Attendance
110,000
The Siege
100,000
90,000
80,000
70,000
Actual
Prediction
60,000
50,000
40,000
30,000
20,000
10,000
0
第1週
第2週
第3週
第4週
第5週
第6週
第7週
Forecasting Results: Weekly Box-Office Attendance
90,000
Meet Joe Black
80,000
70,000
60,000
Actual
50,000
Prediction
40,000
30,000
20,000
10,000
0
第1週
第2週
第3週
第4週
第5週
第6週
Forecasting Results: Weekly Box-Office Attendance
I Still Know What You Did Last Summer
30,000
25,000
20,000
Actual
Prediction
15,000
10,000
5,000
0
第1週
第2週
第3週
第4週
Forecasting Results: Weekly Box-Office Attendance
A Bug's Life
120,000
110,000
100,000
90,000
80,000
Actual
70,000
Prediction
60,000
50,000
40,000
30,000
20,000
10,000
0
第1週
第2週
第3週
第4週
第5週
第6週
第7週
第8週
Forecasting Results: Weekly Box-Office Attendance
110,000
Soldier
100,000
The Siege
Meet Joe Black
90,000
I Still Know What You Did Last Summer
80,000
A Bug’s Life
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
第1週
第2週
第3週
第4週
第5週
第6週
第7週
第8週
Concluding Remarks
Individual (two-stage) models outperform aggregate models.
The information from leading market is crucial.
Hierarchical Bayes model is better (but no so significant).
The Lesson:

A forecasting model based on the theory has superior predictability
The Key:

Finding appropriate product attributes as predictive variables
The Inspiration:

Codified Knowledge Management
64
臺灣市場擴散預測模型
創新係數- 模仿係數- 市場潛量p
q
m
截距項
0.11452
0.566785
(1.157)
(5.463)***
美國之創新係數 0.780212
(4.239)***
美國之模仿係數 0.378401
(1.895)*
美國之市場潛量
恐怖片
Coding
科幻片
非文藝劇情片
票房明星
明星票房價值
假日檔期
-5.42551
(-1.754)*
0.8852
(6.634)***
0.216599
-0.35278
3.293445
(1.981)*
(-1.721)*
(0.675)
0.003265
-0.43695
10.48246
(0.037)
(-2.912)*** (2.819)***
0.0403
-0.08145
5.184564
(0.609)
(-0.675)
(1.772)*
-0.00301
0.465978
-12.2084
(-0.014)
(1.185)
(-1.284)
0.000379
-0.00752
0.204109
(0.144)
(-1.551)
(1.722)*
0.02728
0.131548
5.834916
(0.529)
(1.329)
(2.248)**
這
些
係
數
隨
著
時
間
新
資
料
的
加
入
而
不
斷
的
更
新
天底下沒有白吃的午餐
簡易的公式只能說明簡單的世界，複雜
的現象則需藉助深層的模式才得以彰顯。
你們覺得行銷世界是
「簡單」還是「複雜」？
66
指導與建議
67