supply chain network equilibrium with profit sharing contract responding to emergencies
DESCRIPTION
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. 1. Introduction. 2. Model formulation. 3. Numerical example. - PowerPoint PPT PresentationTRANSCRIPT
ISE-LOGSoutheast University
Supply Chain Network Equilibrium with Profit Sharing Contract Responding to Emergencies
Ating Yang Lindu ZhaoInstitute of Systems Engineering, Southeast University
Nanjing, China
Oct. 23, 2010
LSMS & ICSEE 2010
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1. Introduction
2. Model formulation
3. Numerical example
4. Conclusions
OutlineOutline
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LSMS & ICSEE 2010 1. Introduction1. Introduction
2010 International Conference on Life System Modeling and Simulation & 2010 International Conference on Intelligent Computing for Sustainable Energy and Environment
LSMS&ICSEE2010
Conference program
Achievement
Keynote addressesSpecial sessionsThemed workshops Poster presentations
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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LSMS & ICSEE 2010 1. Introduction1. Introduction
Scenes & Photos
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LSMS & ICSEE 2010 1. Introduction1. Introduction
Background
1995 2000 2005 20101995 2000 2005 2010
Asian financial
crisis1998
London bombings 2005.7.7
Wenchuan earthquake2008.5.12
Sanlu milk powder
incident 2008
Indonesian tsunami
2004.12.26
Haiti earthquake2010.1.12
9-11 terrorist attack
2001.9.11
SARS2003
Iraq war2003.3.20
China’s snowstorm
2008.1 H1N12009.4.13
Sudan red incident2005.3
Yangtze river flood
1998Air France
crash 2000.7.25
North Dakota flood
1997.4.18
Oklahoma City bombing
1995.4.19
Fig. 1 Emergent events in recent years
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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 decision-making, 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.
1. Introduction1. Introduction
Supply chain competition
competitionCompanies Supply chains
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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.
1. Introduction1. Introduction
Emergency environment
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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LSMS & ICSEE 2010 2. Model formulation2. Model formulation
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.
Fig. 2 Network structure of supply chain
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LSMS & ICSEE 2010 2. Model formulation2. Model formulation
Parameters:demand at the retailer j
demand distribution function
demand density function
expectation of demand
transaction quantity between manufacturer i and retailer j
the wholesale price charged by manufacturer i to retailer j
the retail price of retailer j
salvage value
punishment cost of manufacturer i
punishment cost of retailer j
contract parameter(profits holding percentage of retailer j)
jD
jP
jp
ju
ijq
ij
j
jv
ij
ijg
jg
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Expected sales at retailer j:
Expected left over inventory at retailer j:
Lost sales at the retailer j:
The additional transfer payment from retailer j to manufacturer i :
1
(1)n
mi ij
j
q q
1
(2)m
rj ij
i
q q
0( ) min( , ) ( ) (3)
rjqr r r
j j j j j jS q E q D q P x dx
( ) ( ) ( ) (4)r r r rj j j j j j jI q E q D q S q
( ) ( ) ( ) (5)r r rj j j j j j jL q E D q u S q
2. Model formulation2. Model formulation
Without Emergencies:
( , ) (1 ) ( ) (1 ) ( ) (6)ij ijr r rij j ij ij ij ij j j j j ij j j jr r
j j
q qT q q q S q v S q
q q
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The profits of manufacturers :
Manufacturers
if
ijc:production cost function of manufacturer i
:transaction cost between manufacturer i and retailer j
1 1 1
max ( , ) ( ) ( ) ( ) (7)n n n
m ri ij j ij i ij ij ij j j j
j j j
T q f q c q g u S q
2. Model formulation2. Model formulation
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:
1 1
( )( )( )
(1 ) (1 )( ) ( ) 0 (8)
ij rj jrm n
j ij ijr iij ij j ij j j ij j j ij ij
i j ij ij ij
qS q
q c qf qv v g P q q q
q q q
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:handling cost of retailer jjc
1
max ( ) ( ) ( ) ( ) ( , ) (9)m
r r r r rj j j j j j j j j j j j j ij j ij
i
S q v q S q g u S q c Q T q
1 1
( )( )
( ) ( ) (1 )( ) 0 (10)
ij rj jrm n
j jrj j j j j ij ij j ij j j ij ij
i j ij ij
qS q
c Q qv g P q v v q q
q q
Assume the handling cost for each retailer is continuous and convex, then the optimality conditions for all the retailers satisfy the variational inequality:
2. Model formulation2. Model formulation Retailers
The profits of retailers :
Optimality conditions of retailers
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1 1
( ) ( )( )( ) ( ) 0 (11)
m nij ij jr i
j j j ij j j j ij iji j ij ij ij
c q c Qf qv g g P q v q q
q q q
*
( )( )( )
( ) (1 ) (1 )( ) (12)
ij rj jr
ij ij jriij ij j j ij j ij j j
ij ij ij
qS q
c q qf qg P q v v
q q q
2. Model formulation2. Model formulation
Optimality condition of the supply chain network
The optimal condition of wholesale price charged for the product by manufacturer to retailer is:
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Expected sales at retailer j:
Expected left over inventory at retailer j:
Lost sales at the retailer j:
jP jG Demand distribution function:
' '
0( ) min( , ) ( ) (13)
rjqr r r
j j j J j jS q E q D q G x dx
' ' '( ) ( ) ( ) (14)r r r rJ j j J j J jI q E q D q S q
' ' ' '( ) ( ) ( ) (15)r r rj j j j j j jL q E D q u S q
2. Model formulation2. Model formulation
Under Emergencies:
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' '
1 1 1
'
1 1 1 1
max (1 ) ( ) (1 ) ( ) ( )
( ) ( ) (16)
n n nij ijm r r r
i ij ij ij j j j j ij j j j ir rj j jj j
n n n nr
ij ij ij j j j ij ij ij ij ij ijj j j j
q qq q S q v S q f q
q q
c q g u S q q q q q
' ' ' '
1
' '
1 1
max ( ) ( ) ( ) ( )
(1 ) ( ) (1 ) ( ) (17)
mr r r r rj j j j j j j j j j j j j ij ij
i
m mij ijr r r
ij j j j j ij j j jr ri ij j
S q v q S q g u S q c Q q
q qq S q v S q
q q
2. Model formulation2. Model formulation
： extra disposal cost when order quantity declines
ij ： extra production cost when order quantity increases
ij
The optimization problem of manufacturers
The optimization problem of retailers
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LSMS & ICSEE 2010 3. Numerical example3. Numerical example
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.
Two-stage prediction–correction algorithm
Fig. 3 Supply chain network for numerical example
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LSMS & ICSEE 2010 3. Numerical example3. Numerical example
Fig. 4 The convergence of the simulation
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LSMS & ICSEE 2010 3. Numerical example3. Numerical example
Under Emergencies
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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.
4. Conclusions 4. Conclusions
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.
