Transcript 幻灯片 1

ISE-LOG
Southeast University
LSMS & ICSEE 2010
Supply Chain Network Equilibrium with Profit
Sharing Contract Responding to Emergencies
Ating Yang Lindu Zhao
Institute of Systems Engineering, Southeast University
Nanjing, China
Oct. 23, 2010
Outline
LSMS & ICSEE 2010
1. Introduction
2. Model formulation
3. Numerical example
4. Conclusions
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1. Introduction
LSMS & ICSEE 2010
LSMS&ICSEE2010
2010 International Conference on Life System Modeling and Simulation & 2010
International Conference on Intelligent Computing for Sustainable Energy and
Environment
Conference program
Keynote addresses
Special sessions
Themed workshops
Poster presentations
Achievement
Received over 800 paper submissions from 23 countries and regions
195 were subsequently selected and recommended for publication by
Springer in two volumes of Lecture Notes in Computer Science (LNCS) and
one volume of Lecture Notes in Bioinformatics (LNBI)
60 high-quality papers are recommended for publication in SCI indexed
international journals
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1. Introduction
LSMS & ICSEE 2010
Scenes & Photos
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1. Introduction
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Background
North Dakota
flood
1997.4.18
Asian
financial
crisis
1998
1995
Oklahoma
City bombing
1995.4.19
9-11 terrorist Iraq war
attack
2003.3.20
2001.9.11
2000
Yangtze
river flood
1998
Wenchuan
earthquake
2008.5.12
Sanlu milk
powder
incident 2008
Sudan red
incident
2005.3
2005
London
bombings
2005.7.7
Indonesian
tsunami
2004.12.26
SARS
2003
Air France
crash
2000.7.25
Haiti
earthquake
2010.1.12
2010
China’s
snowstorm
2008.1
H1N1
2009.4.13
Fig. 1 Emergent events in recent years
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1. Introduction
LSMS & ICSEE 2010
Supply chain competition
Companies
competition
Supply chains
Supply chain network is a network consisted of multiple manufacturers,
multiple suppliers, multiple retailers and multiple customers.
Nagurney et al.(2002) first bring forward this concept.
The steady behaviors of decision-makers can be characterized by a group of
equilibrium conditions.
But, Chee et al.(2004) indicate that the market could hardly be in equilibrium
state, due to the private or imperfect information, decentralized decisionmaking, convert behaviors and so on.
Cachon(2003) describes various contracts in the newsvendor model, and
proves that the buyback contract and profit sharing contract can coordinate a
single supply chain.
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1. Introduction
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Emergency environment
Yu et al.(2005) investigate the supply chain coordination problem under
demand disruptions by using the quantity discount contract.
Sun and Ma(2008) describe a revenue sharing contract model for a two-stage
supply chain that faced stochastic market demands in response to an emergent
event.
Teng et al.(2009) establish a supply chain network equilibrium with stochastic
demands with a quantity discount contract and prove by the numerical
example that the anti-disruption ability of the supply chain network will be
improved with the contract.
In this paper, we introduce profit sharing contract into the supply chain network
equilibrium model and analyze the impacts of emergent events have on this
model. Then prove that manufacturers and retailers need to adjust the contracts
parameters to achieve a new supply chain network equilibrium state.
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2. Model formulation
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Fig. 2 Network structure of supply chain
Assumptions :
Manufacturers must satisfy all of the retailers’ orders;
All information is symmetrical;
Retailers must choose order quantities and manufacturers before the start of a
single selling season.
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2. Model formulation
Parameters:
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Dj
demand at the retailer j
Pj
demand distribution function
pj
demand density function
uj
expectation of demand
qij
transaction quantity between manufacturer i and retailer j
ij
the wholesale price charged by manufacturer i to retailer j
j
the retail price of retailer j
vj
salvage value
gij
punishment cost of manufacturer i
gj
punishment cost of retailer j
ij
contract parameter(profits holding percentage of retailer j)
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2. Model formulation
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Without Emergencies:
n
m
  qij
m
i
q
(1)
j 1
q   qij
r
j
(2)
i 1
Expected sales at retailer j:
qrj
S j (q )  E min(q , D j )   q   Pj ( x)dx
r
j
r
j
r
j
0
(3)
Expected left over inventory at retailer j:
I j (q rj )  E  (q rj  D j )    q rj  S j (q rj )
(4)
Lost sales at the retailer j:
L j (q rj )  E ( D j  q rj )    u j  S j (q rj )
(5)
The additional transfer payment from retailer j to manufacturer i :
Tij (  j , qij )  qij ij 
qij
q
r
j
(1  ij ) q rj  S j (q rj )  v j 
qij
q
r
j
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(1  ij )  j S j (q rj )
(6)
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2. Model formulation
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Manufacturers
f i :production cost function of manufacturer i
cij
:transaction cost between manufacturer i and retailer j
The profits of manufacturers :
n
n
n
max    Tij (  j , qij )  fi (q)   cij (qij )   gij u j  S j (q rj ) 
m
i
j 1
j 1
(7)
j 1
Optimality conditions of manufacturers
Assume that the manufacturers compete in a non-cooperative fashion, and the cost
functions for each manufacturer are continuous and convex, then the optimality conditions
for all the manufacturers satisfy the following variational inequality:
qij


r

S
(
q
)
j
j

m n 
q rj
fi (q ) cij (qij ) 
r

 ij  (1  ij )v j  (1  ij )(v j   j )
 gij Pj (q j ) 

  qij  qij   0

qij
qij
qij 
i 1 j 1 




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2. Model formulation
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Retailers
c j :handling cost of retailer j
The profits of retailers :
m
max    j S j (q )  v j q  S j (q )   g j u j  S j (q )   c j (Q)  Tij (  j , qij )
r
j
r
j
r
j
r
j
r
j
(9)
i 1
Optimality conditions of retailers
Assume the handling cost for each retailer is continuous and convex, then the optimality
conditions for all the retailers satisfy the variational inequality:
qij



S j (q rj ) 

r
m n
(v    g ) P (q r )  c j (Q)     v  (1   )(   v ) q j
  q  q   0

j
j
j
j
j
ij
ij j
ij
j
j
ij 
  ij
qij
qij
i 1 j 1 




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2. Model formulation
LSMS & ICSEE 2010
Optimality condition of the supply chain network

c j (Q) 
fi (q) cij (qij )
r

(
v



g

g
)
P
(
q
)



v

 j
   qij  qij   0

j
j
ij
j
j
j
qij
qij
qij 
i 1 j 1 

m
n
(11)
The optimal condition of wholesale price charged for the product by manufacturer to
retailer is:
ij* 
fi (q) cij (qij )

 gij Pj (q rj )  (1  ij )v j  (1  ij )(v j   j )
qij
qij
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
qij
q
r
j
S j (q rj )
qij
(12)
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2. Model formulation
LSMS & ICSEE 2010
Under Emergencies:
Demand distribution function:
Pj
Gj
Expected sales at retailer j:
qrj
S (q )  E min(q , D )   q   G j ( x)dx
0
'
j
r
j
r
j
'
J
r
j
(13)
Expected left over inventory at retailer j:
I J' ( q rj )  E (q rj  DJ' )    q rj  S J' (q rj )
(14)
Lost sales at the retailer j:
L' j ( q rj )  E ( D 'j  q rj )    u 'j  S 'j ( q rj )
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2. Model formulation
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The optimization problem of manufacturers
qij


max    qij ij   r (1  ij )  q  S (q )  v j   r (1  ij )  j S 'j (q rj )  fi (q)
j 1
j 1 q j
j 1 q j
n
qij
n
m
i
n
n
r
j
'
j
n
r
j
n
 cij (qij )   gij u  S j (q )    
j 1
ij
ij
j 1
'
j
r
j
j 1

ij
q
ij


ij
q
    q
n
j 1

ij

ij
 qij 

(16)
：extra production cost when order quantity increases
：extra disposal cost when order quantity declines
The optimization problem of retailers
m
max    j S (q )  v j  q  S (q )   g j u  S (q )   c j (Q)   qij ij
r
j
'
j
m

i 1
qij
r
j
r
j
'
j
r
j
'
j
'
j
r
j
qij


(1


)
q

S
(
q
)
v

(1  ij )  j S 'j ( q rj )

ij 
j
r
r

qj
i 1 q j
i 1
m
r
j
'
j
r
j
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3. Numerical example
LSMS & ICSEE 2010
Two-stage prediction–correction algorithm
The algorithm generates two predictors which satisfy two acceptance criteria.
That projection-based algorithm merely requires dynamic regulation of step length,
avoiding excessive iterations.
It is a light-weight approach, which can be easily applied in practice.
Comparing to the common Euler algorithm is proved having a better global convergence.
Fig. 3 Supply chain network for numerical example
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3. Numerical example
LSMS & ICSEE 2010
Fig. 4 The convergence of the simulation
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3. Numerical example
LSMS & ICSEE 2010
Under Emergencies
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4. Conclusions
LSMS & ICSEE 2010
Conclusions:
Propose a SCN equilibrium model under emergencies;
profit sharing contract can coordinate the model;
manufacturers and retailers can adjust the contracts parameters together
to achieve a new supply chain network equilibrium state through
bargaining when facing emergent events.
Future work:
Other contracts: quantity discount, buy back, option contract etc.
Compare and identify the application situation of different contracts;
Find a optimal range of contract parameters.
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ISE-LOG
Southeast University
http://log.seu.edu.cn
[email protected]
2010-10-23