economic diversification: explaining the pattern of ... · economic diversification. the model is...
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DESA Working Paper No. 150ST/ESA/2017/DWP/150
August 2017
Economic Diversification: Explaining the pattern of diversification in the global economy and its implications for fostering diversification in poorer countries
Author: Clovis Freire1
1 United Nations, Division for Sustainable Development, 405 E. 42nd Street, New York 10017 NY, USA. [email protected]
D e p a r t m e n t o f E c o n o m i c & S o c i a l A f f a i r s
ABSTRACT
Economic diversification is very relevant for poorer developing countries to create jobs and foster economic development. That need has been recognized in key internationally agreed development goals. The empirical economic literature has identified several stylized facts about the pattern of diversification of economies, but the development of explanations for those patterns in general has been only loosely associated with economic theory on growth, trade, technology change and structural transformation. Making that connection is relevant because it could inform policymakers in developing countries in designing and implementing policies for promoting diversification. This paper presents a model of structural economic dynamics and endogenous technological change that is able to replicate empirical regularities related to economic diversification. The model is used to study strategies to foster diversification in poorer countries, which could help to better target action in the implementation of internationally agreed goals related to the economic diversification of these countries.
Keywords: Diversification, Economic Complexity, Structural Transformation, Productive Capacities, Economic Development.
CONTENTS
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Empirical regularities and theoretical explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Overview of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4. Description of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5. Replication of the stylized facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6. Catch-up strategies of poorer countries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Appendix A. Variables of the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix B. Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix C. Product complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
UN/DESA Working Papers are preliminary documents circulated in a limited number of copies and posted on the DESA website at https://www.un.org/development/desa/publications/working-paper to stimulate discussion and critical comment. The views and opinions expressed here-in are those of the author and do not necessarily reflect those of the United Nations Secretariat. The designations and terminology employed may not conform to United Nations practice and do not imply the expression of any opinion whatsoever on the part of the Organization.
Typesetter: Nancy Settecasi
UNITED NATIONS
Department of Economic and Social Affairs
UN Secretariat, 405 East 42nd Street
New York, N.Y. 10017, USA
e-mail: [email protected]
https://www.un.org/development/desa/publications/working-paper
Acknowledgements: I am grateful to Bart Verspagen and Bart Los for their advice in the development of the model presented in this paper. I thank two anonymous reviewers for their comments on the paper. I am also grate-ful to David Le Blanc for his comments on an earlier version of the paper. All errors are my own.
1
2
3
y = 524.94x0.5005
R² = 0.7766
10
100
1,000
10,000
100,000
0.0 0.1 1.0 10.0 100.0 1,000.0 10,000.0 100,000.0
Nu
mb
er o
f pro
du
cts,
log
arit
hm
sca
le
GDP ($ billion), logarithm scale
USADEU
CHNJPN
FRA
GBR
INDBRA
RUS
NLD
TUV
SAU
VEN
DZA
IRQDMA
SWZ
PLW
30
40
50
60
70
80
90
100
110
120
130
0 5,000 10,000 15,000 20,000 25,000 30,000
kc,1
-C
om
mo
nal
ity o
f p
rod
uct
s ex
po
rted
(nu
mb
er o
f co
un
trie
s ex
po
rtin
g a
sim
ilar
pro
du
ct m
ix)
kc,0 - Diversification (number of products)
Non-diversified countries
producing common products
Diversified countries producing common products
Non-diversified countries
producing uncommon
products
Diversified countries producing uncommon products
Mean=5,488Mean=82.34
USADEU
FRA
GBRITA
JPNCHE
NLD
CHN
IND
BRA
VNM
0
4
5
Household
sector
Production sector 1
Production sector 2
Production sector N
Research and Development sector (R&D)
labour
Products for domestic consumption
Combine existing technologies to create new products
…
Production sectors Exports
Imports
6
𝑁𝑘
𝐿𝑘
𝑙𝑗,𝑘
𝑐𝑗,𝑘
𝑀𝐾𝑗,ℎ,𝑘
𝑤𝑘
𝑤1 = 1
𝑝𝑗,ℎ,𝑘
𝑝𝑗,ℎ,𝑘 = 𝑙𝑗,𝑘𝑤𝑘 𝑀𝐾𝑗,ℎ,𝑘
𝑐𝑗,𝑘
𝑐𝑗,𝑘,ℎ
7
𝑐𝑗,𝑘 = ∑ 𝑐𝑗,𝑘,ℎ𝑅ℎ=1
𝑄𝑗,𝑘 = ∑ 𝑐𝑗,ℎ,𝑘𝑁ℎ𝑅ℎ=1
𝑐𝑗,𝑘
∑ (∑ (∑ 𝑐𝑗,𝑘,ℎ𝑅ℎ=1 𝑁𝑘 𝑝𝑗,𝑘,ℎ)𝑚
𝑗=1 )𝑅𝑘=1
∑ (∑ 𝑐𝑗,𝑘,ℎ𝑁𝑘𝑅𝑘=1 )𝑅
ℎ=1 = ∑ 𝑐𝑗,𝑘𝑁𝑘 𝑅𝑘=1
∑ 𝑄𝑗,𝑘𝑚𝑗=1 𝑙𝑗,𝑘 ≤ 𝐿𝑘
∑ 𝑙𝑗,𝑘(∑ 𝑐𝑗,ℎ,𝑘𝑁ℎ𝑅ℎ=1 ) ≤ 𝐿𝑘
𝑚𝑗=1
∑ 𝑐𝑗,𝑘,ℎ =𝑅ℎ=1 𝑐𝑗,𝑘
𝑐𝑗,𝑘,ℎ ≥ 0
8
𝐸𝑗,𝑘 = 𝑙𝑗,𝑘𝑄𝑗,𝑘
𝐸𝑘 = ∑ 𝐸𝑗,𝑘𝑚𝑗=1
𝑌𝑗,𝑘
𝑌𝑗,𝑘 = ∑ 𝑐𝑗,ℎ,𝑘𝑁ℎ𝑅ℎ=1 𝑝𝑗,ℎ,𝑘
𝑌𝑘 = ∑ 𝑌𝑗,𝑘𝑚𝑗=1
𝑦𝑘 =𝑌𝑘
𝑁𝑘
𝐸𝑥𝑝𝑗,𝑘
𝐸𝑥𝑝𝑗,𝑘 = ∑ 𝑐𝑗,𝑘,ℎ𝑁𝑘𝑅ℎ=1 𝑝𝑗,𝑘,ℎ
𝐸𝑥𝑝𝑘 = ∑ 𝐸𝑥𝑝𝑗,𝑘𝑚𝑗=1
𝑒𝑥𝑝𝑘 =𝐸𝑥𝑝𝑘
𝑁𝑘
𝑤𝑘 = 𝑤1
(∑ 𝑙𝑗,1𝐸𝑗,1
𝑚𝑗=1
𝐸1⁄ )
(∑ 𝑙𝑗,𝑘𝐸𝑗,𝑘
𝑚𝑗=1
𝐸𝑘⁄ )
9
Labour
costs
Markup
A B C A B C
Minimum
price
Step 1 – tentative prices Step 2 – Comparison and determination
A B C
final
prices
10
𝑆𝑃𝑘(𝑡) = ∑ ∑ ((𝑝𝑗,ℎ,𝑘(𝑡) − 𝑙𝑗,𝑘(𝑡)𝑤𝑘(𝑡))𝑄𝑗,𝑘(𝑡)/𝑤𝑘(𝑡))𝑚𝑗=1
𝑅ℎ=1
𝑆𝑃𝑘(𝑡) = ∑ ∑ (𝑙𝑗,𝑘(𝑡)(𝑀𝐾𝑗,ℎ,𝑘(𝑡) − 1)𝑄𝑗,𝑘(𝑡))𝑚𝑗=1
𝑅ℎ=1
𝐿𝐴𝑘(𝑡) = 𝐿𝑘(𝑡) − 𝐸𝑘(𝑡)
𝜖𝑘
𝜖𝑘(𝑡) =𝑚𝑖𝑛 (𝑆𝑃𝑘(𝑡),𝐿𝐴𝑘(𝑡))
𝐿𝑘(𝑡)
𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
(𝑡) + 𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
(𝑡) = 1
0 ≤ 𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
(𝑡) ≤ 1; 0 ≤ 𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠(𝑡) ≤ 1
𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
(𝑡) = 𝐸𝑘(𝑡)/𝐿𝑘(𝑡)𝜕𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡(𝑡) = 1 − 𝐸𝑘(𝑡)/𝐿𝑘(𝑡)
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
(𝑡) + 𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
(𝑡) = 1
0 ≤ 𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
(𝑡) ≤ 1; 0 ≤ 𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑡) ≤ 1
11
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
(𝑡) = 𝑚𝑘(𝑡)/𝑚(𝑡)
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑡) = 1 − 𝑚𝑘(𝑡)/𝑚(𝑡)
𝑚𝑘
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
(𝑡) + 𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
(𝑡) = 1
0 ≤ 𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
(𝑡) ≤ 1; 0 ≤ 𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑡) ≤ 1
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠(𝑡) = 𝑇𝐹𝑘(𝑡)/𝑚𝑘(𝑡)
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑡) = 1 − 𝑇𝐹𝑘(𝑡)/𝑚𝑘(𝑡)
𝑇𝐹𝑘
𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜖𝑘𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝑁𝑘
𝐸𝑗,𝑘/𝐸𝑘
𝑋𝑗,𝑘 ~ 𝑃(𝜖𝑘𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝑁𝑘(𝐸𝑗,𝑘/𝐸𝑘) 𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
)
0 < 𝑟𝑑𝑐𝑗,𝑘 < 1)
𝑙𝑗,𝑘(𝑡) = 𝑟𝑑𝑐𝑗,𝑘 𝑙𝑗,𝑘(𝑡 − 1)
12
𝑟𝑑𝑐𝑗,𝑘
𝑟𝑑𝑐𝑗,𝑘 ~ 𝑈(𝛽1, 1 ) 𝛽1
𝛽1
𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜖𝑘𝜕𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
𝜎𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑁𝑘 𝐸𝑗,𝑘/𝐸𝑘
𝑋𝑗,𝑘 ~ {𝑃(𝜖𝑘𝜕𝑘
𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝜎𝑘
𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑁𝑘(𝐸𝑗,𝑘/𝐸𝑘) 𝜆𝑘
𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛)
0,
𝑙𝑗,𝑘(𝑡) = 𝑙𝑗,ℎ(𝑡)
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜖𝑘𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑁𝑘𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑋𝑘 ~ 𝑃(𝜖𝑘 𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜎𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑁𝑘𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
)
𝑙𝑛𝑒𝑤
𝑙𝑛𝑒𝑤,𝑘(𝑡) =∑ 𝑙𝑗,𝑘(𝑡−1)
𝑚𝑘𝑗=1
𝑚𝑘(𝑡−1)
13
𝜆𝑘𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
φ
𝜖𝑘𝜕𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜎𝑘𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑁𝑘)
φ
φ
φ𝑗,𝑐(𝑡) = ∑ 𝑌𝑗,𝑘(𝑡−1)𝑅
𝑘=1 −∑ 𝑌𝑗,𝑘(𝑡−2)𝑅𝑘=1
∑ ∑ 𝑌𝑅𝑘≠𝑐 𝑖,𝑘
𝑚𝑖=1 (𝑡−1)−∑ ∑ 𝑌𝑅
𝑘≠𝑐 𝑖,𝑘𝑚𝑖=1 (𝑡−2)
∑ 𝑌𝑗,𝑘𝑅𝑘=1
∑ ∑ 𝑌𝑅𝑘≠𝑐 𝑖,𝑘
𝑚𝑖=1
𝑋𝑗,𝑘(𝑡)~ {𝑃(𝜖𝑘𝜕𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝜎𝑘
𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑁𝑘φ𝑗,𝑐𝜆𝑘𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛)
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒,
𝑡′′ 𝑡′
𝑙𝑗,𝑘(𝑡′′) = 𝑙𝑗,ℎ(𝑡′)
𝑐𝑗,𝑘(𝑡) = 𝑐𝑗,𝑘(𝑡 − 1)𝑒𝑟𝑗,𝑘
𝑟𝑗,𝑘(𝑡)
14
𝑟𝑗,𝑘
𝑟1,𝑘 ≥ 𝑟2,𝑘 ≥ ⋯ ≥ 𝑟𝑚𝑘,𝑘
𝑚𝑎𝑥𝑐𝑗
𝑐𝑗,𝑘 𝑚𝑎𝑥𝑐𝑗
∀𝑗 ∃ 𝑚𝑎𝑥𝑐𝑗, 𝑐𝑗,𝑘(𝑡) = min (𝑐𝑗,𝑘(𝑡 − 1)𝑒𝑟𝑗,𝑘 , 𝑚𝑎𝑥𝑐𝑗)
𝑚𝑎𝑥𝑐𝑗
𝑀𝐴𝑋𝑗
𝑚𝑎𝑥𝑐𝑗 > 𝑀𝐴𝑋𝑗 = max (𝑐𝑗,1(1), 𝑐𝑗,2(1), . . . , 𝑐𝑗,𝑚𝑘(1))
𝑚𝑎𝑥𝑐𝑗
𝑚𝑎𝑥𝑐𝑗 ~ 𝑈(𝑀𝐴𝑋𝑗 , β 𝑀𝐴𝑋𝑗 )
β
𝑀𝐴𝑋𝑗 = 10 β𝑚𝑎𝑥𝑐𝑗
15
𝑟
{𝑟𝑗,𝑘(𝑡) > 0, 𝑖𝑓𝑒𝑥𝑝𝑘(𝑡 − 1) < 𝑦𝑘(𝑡 − 1)
𝑟𝑗,𝑘(𝑡) < 0, 𝑖𝑓𝑒𝑥𝑝𝑘(𝑡 − 1) > 𝑦𝑘(𝑡 − 1)
𝑟
{
𝑟𝑗,𝑘 ~ 𝑈(0, max(𝑟)), 𝑖𝑓𝑒𝑥𝑝𝑘(𝑡 − 1) < 𝑦𝑘(𝑡 − 1)
𝑟𝑗,𝑘 ~ 𝑈(− max(𝑟), 0), 𝑖𝑓𝑒𝑥𝑝𝑘(𝑡 − 1) > 𝑦𝑘(𝑡 − 1)
𝑟𝑗,𝑘 = 0, 𝑖𝑓𝑒𝑥𝑝𝑘(𝑡 − 1) = 𝑦𝑘(𝑡 − 1)
max(𝑟) 𝑟
𝛼
𝑡′′)𝑡′
𝑐𝑗,𝑘(𝑡′′) { > 0, 𝑖𝑓 𝑦𝑘(𝑡′′ − 1) ≥ 𝛼
= 0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑠𝑖,𝑗
𝑠𝑖,𝑗
κ
𝑠𝑖,𝑗 ~ 𝑈(1 − κ, 1 + κ)
𝑐𝑗,𝑘(𝑡) = min (𝑠𝑖,𝑗 𝑐𝑗,𝑘(𝑡 − 1)𝑒𝑟𝑗,𝑘 , 𝑚𝑎𝑥𝑐𝑗)
𝑚𝑎𝑥𝑐𝑗(𝑡) = 𝑠𝑖,𝑗 𝑚𝑎𝑥𝑐𝑗(𝑡 − 1)
16
• 𝑙1 = 𝑙2 = ⋯ = 𝑙30 = {0.5, 0.5,0.5,0.5,0.5, 0.5,0.5,0.5,0.5,0.5}
• 𝑐1 = 𝑐2 = ⋯ = 𝑐30 =
{0.01, 0.01,0.01, 0.01,0.01, 0.01,0.01, 0.01,0.01, 0.01}
• 𝑤1 = $ 1
• β = 2
• 𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
= 𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
= 1/200
• 𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
= 𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
= 1/100
•
17
10 12 14 16 18 20 22 24 2610
0
101
102
103
Diversification (kc0 - number of products)
GD
P
10 12 14 16 18 20 22 24 2612
14
16
18
20
22
24
26
28
30
Diversification (kc0 - number of products)
Avera
ge u
biq
uity (
kc1)
10 12 14 16 18 20 22 24 260
5
10
15
20
25
30
35
40
45
Diversification (kc0 - number of products)
Em
plo
ym
ent
(perc
enta
ge o
f popula
tion)
10 12 14 16 18 20 22 24 260.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Diversification (kc0 - number of products)
Consum
ption p
er
capita
10 12 14 16 18 20 22 24 260.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
Diversification (kc0 - number of products)
Avera
ge labour
coeff
icie
nt
18
19
20
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
=1
100; 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =1
10
21
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
=1
200; 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =1
20
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
=1
100; 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =1
50
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
=1
200; 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =1
100
22
23
-0.2 0
0
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
0.8
1
11.2
1.21.4
1.6
1.6
1
1
1.2
0.2
0.4
Configura
tion
Strategy
1 2 3 4 5 6 7 8A
B
C
D
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0
10
0
100
100
100
10
0
20
0
200
300
300
100
10
0
400
500
Configura
tion
Strategy
1 2 3 4 5 6 7 8A
B
C
D
0
100
200
300
400
500
600
50
50
50
50
10
0
100
100
100
15
0
150
200
200
250
300
350
100
Configura
tion
Strategy
1 2 3 4 5 6 7 8A
B
C
D
50
100
150
200
250
300
350
24
25
26
27
28
𝑁𝑘
𝐿𝑘
𝑙𝑗,𝑘
𝑐𝑗,𝑘
𝑀𝐾𝑗,ℎ,𝑘
𝑤𝑘
𝑝𝑗,ℎ,𝑘
𝑐𝑗,ℎ,𝑘
𝑄𝑗,𝑘
𝐸𝑗,𝑘
𝐸𝑘
𝑌𝑗,𝑘
𝑌𝑘
𝑦𝑘
𝐸𝑥𝑝𝑗,𝑘
𝐸𝑥𝑝𝑘
𝑒𝑥𝑝𝑘
• 𝑙1 = 𝑙2 = ⋯ = 𝑙10 = {0.5, 0.5,0.5,0.5,0.5, 0.5}
• 𝑐1 = 𝑐2 = ⋯ = 𝑐10 =
{0.01, 0.01,0.01, 0.01,0.01, 0.01}
29
•
• 𝑤1 = $ 1
• β = 2
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = 𝜆𝑘
𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡 = 1/100
𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
= 1/500
• 𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠
= 𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡
• 𝜆𝑘𝑝𝑟𝑜𝑐𝑒𝑠𝑠_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
= 𝜆𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡_𝑒𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
30
𝑘𝑐,𝑁 =1
𝐾𝑐,0∑ 𝑀𝑐𝑝𝑘𝑝,𝑁−1𝑝
𝑘𝑝,𝑁 =1
𝐾𝑝,0∑ 𝑀𝑐𝑝𝑘𝑐,𝑁−1𝑐
𝑃𝐶𝑂𝑀𝑃 =𝑘𝑝,5−𝑘𝑝,5̅̅ ̅̅ ̅̅
𝜎
𝑘𝑝,5̅̅ ̅̅ ̅ 𝜎