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Supply Chainsand the
Environment Fuminori Toyasaki
MKIDS Mini-WorkshopSeptember 10, 2003
The Virtual Center for Supernetworks
Change of environment problem characteristics
Environment problems
Local
Specific industries
Small uncertainty
Present problem
Global
Unspecific industries
Large uncertainty
Future problem
From Supply Chains to Green Logistics
Supply Chain + Environmental = Green Logistics criteria
* Legislation Pressure * Consumer Pressure
My Research Areas
* Supply chain modeling with emission minimization criterion
* Supply chain modeling with E-cycling
* Global supply chain with transboundary pollutions (future)
Supply Chain Supernetworks and Environmental Criteria
Anna Nagurney and
Fuminori Toyasaki
Appears in Transportation Research: Transportation and the Environment
1 i
m
1 nj
1 k i
Manufacturers
Retailers
Demand Markets
Assumptions of this model
• Each manufactures and retailers
1. Maximizes its profit
2. Minimizes its emissions.
• Cournot-Nash oligopoly market.
A manufacturer’s muliticriteria decision-making problem
Maximize
Subject to
))qhh()qh(h(α
)(qc)q(c)Q,(Qf
qρqρ
ikiki
n
1j
2
1l
o
1kijlijlii
o
1k ikikijl
n
1j
2
1l ijl21
i
o
1k ik*1ikijl
n
1j
2
1l
*1ijl
k0,ql;j,0,q ijlijl
The optimality condition of the manufacturers
mo22mn1
*ikik
*1ikijlii
ik
*ikik
ijl
2**1im
1i
o
1k
*ijlijl
*ijlijlii
ijl
*ijlijlm
1i
n
1j
2
1lijl
2**1i
RQ,RQ
0,]q[q]ρ)h(hαq
)(qcq
)Q,(Qf[
]q[q]ρ)h(hαq
)(qc
q)Q,(Qf
[
A retailer’s multicriteria decision-making problem
Maximize
Subject to
))qh(h(β
)(q*ρ)q(c
)(qc)(Qcqρ
m
1i
2
1l ijlijlij
m
1i
2
1l ijl1ijljkl
o
1k
2
1l jkl
m
1i
o
1k ijlijl1
j
o
1k
2
1l jkl*2j
ˆ
landkj,i,0qand0q
jklijl
o
1k
2
1l
m
1i
2
1l ijljkl
The multicriteria equilibrium conditions for demand market k
modes
0,qif,ρ
0,qif,ρhη)Q,(Qcρ
*jkl
*2j
*jkl
*3k
jklk*32*
jkl*2j ˆ
For all retailers n1,...,jj; and :21,ll;
0,qif,ρ
0,qif,ρ)h(hη)Q,(Qcρ
*ik
*2j
*ik
*3k
ikik*32*
ik*1ik ˆ
0ρif,qq
0ρif,qq)(ρd
*3k
n
1j
2
1l
m
1i
*ik
*jkl
*3k
n
1j
2
1l
m
1i
*ik
*jkl
*3k
m1,...,ii; •For all manufactures
Variational Inequality Formulation
on2nomo2mn3
321*3k3k
*3k
m
1i
*ik
o
1k
n
1j
2
1l
*jkl
*jj
o
1k
2
1l
*ijl
n
1j
m
1i
2
1l
*ijl
*jkljkl
m
1j
*3kjklk
*j
*32*jkl
o
1k
2
1l jkl
*jkljkl
*ikik
*3kikiki
*3m
1i
o
1k
2*ik
ijl
2**1ijl
ijl
2**1i
*ijlijl
*jijliji
m
1i
n
1j
2
1l ijl
*ijlj
ijl
*ijlj
*ijl
*ijlijl
ijl
2**1i
R)ργ,,Q,Q,(Q0,]ρ[ρ)](ρdqq[
]γ[γ]qq[
]q[q]ρhηγ)Q,(Qcq
)(qc[
]q[q
]ρ)h)(hη(α)Q,(Qcq
)Q,(Qc
q)Q,(Qf
[
]q[q
]γ)h)(hβ(αq
)(qc
q
)(qc
q
)(qc
q)Q,(Qf
[
ˆ
ˆ
ˆ
The Dynamics
1. Describe the manufactures’, retailers’ and consumers’ product and price adjustment.
2. Formulate the dynamic adjust process as a projected dynamical system.
Demand market price dynamics
n
1j
2
1l
m
1i3kikjkl3k
n
1j
2
1l
m
1i3kikjkl3k
3k
0,ρif},qq)(ρd,max{0
0,ρif,qq)(ρd
ρ
Dynamics between the retailers and the demand markets
0qif},γhη
q
)(qc)Q,(Qcρ,max{0
0qif,γhηq
)(qc)Q,(Qcρ
q
jkljjklkjkl
jkljkl32jkl3k
jkljjklkjkl
jkljkl32jkl3k
jkl
ˆ
ˆ
The projected dynamical system
The dynamic model of the supply chain supernetwrok and environmental criteria can be formulated as follows:
onto
0K XX(0)F(X)),(X,X
K is the projection operator of F(x)
)ρ,γ,Q,Q,(QX 03
03210
000
is the initial point
.
Stationary equilibrium points
Theorem
The set of stationary points coincides with the set of equilibrium points.
Proof.
See Dupuis and Nagurney (1993).
1
1
1
2
2
2
Manufactures
Retailers
Demand Markets
Numerical Examples
Change of environment criteria
3.4611
2.3907
3.3214
2.4309
3.1136
2.4250
3.1270
2.4347
13.033 13.3127 13.4861 13.396
5.8513 5.7509 5.5362 5.5603
263.908 264.047 264.309 263.623
274.701 274.820 274.843 274.881
Total
Emission
114.089 112.918 111.381 111.213
1Q
2Q
3Q
0
0
0
0
0
1
0
1
1
1
1
1
Increase in weights on environment criteria
Total
Emission 111.2138 110.5442 105.8604 99.7104
1
1
1
5
1
1
5
1
5
5
5
5
Summary
• First rigorous mathematical supernetwork model which deals with multicriteria decision makers, include environmental one.
• Developed both a static and a dynamic model.
• Evaluated the equilibrium solutions as we changed the weight of the environmental criteria.
Electronic Waste Management and Recycling: A Multitiered Network Equilibrium Framework for E
-Cycling
Anna Nagunrey and Fuminori Toyasaki
Movement of E-Cycling
• 63 million PC will be obsolete in 2003 in the U.S.
• About 10 million waste electric products are dumped per year in Japan.
* Electronic wastes contain not only hazardous materials, but also precious ones.
• The Home Appliances Recycling Law in Japan (2001)
• Waste from Electrical and Electronic Equipment Directive (WEEE) in EU (2008)
1 h
1 i
j
1
1
k
r
m
n
m+1
n+1
O+1o
Recyclers
Processors
Source of Electronic Waste
Demand Markets
Landfill
Landfill
Landfill
Assumptions of the model
• The sources minimize their costs
• The recyclers and the processors maximize their profits, respectively.
• Cournot-Nash oligopoly market.
The behavior of the sources
Minimize
m
1i
1m
1ihihi1)h(m1)1h(mhi
*1hi )(qcqρqρ
Subject to :
1m,1,i0,q
Sq
hi
h1m
1ihi
Variational Inequality Formulation of the sources
1m
1ihi
hhi
11
r
1h
*1)h(m1)h(m1)1h(m
1)h(m
*1)h(m1)h(m
r
1h
m
1i
*hihi
*1hi
hi
*hihi
0}qandSqthatsuch{QKK,Q
0,]q[q]ρq
)(qc[
]q[q]ρq
)(qc[
Recyclers’ behavior
Maximize
r
1h
2ihihi
1n
1jijij1)i(n1)2i(n
n
1j
r
1hhi
*1hiij
*2ij )(Qc)(qc)(qcqρqρqρ ˆ
Subject to
1n,1,j0,qr;,1,h0,q
qqα
ijhi
1n
1j
r
1hhiijij
Processors’ behavior
Maximize
m
1iijij
m
1i
1o
1kjkjkij
*2ij
1)j(o1)3j(o3
jjk
o
1k
*3jk
)(qc)(qcqρ
qρ)(Qcqρ
ˆ
Subject to
m
1iij
1o
1kjkjk qqβ
The demand markets
0ρif,q
0ρif,q
)(ρd
,0qif,ρ
0qif,ρ)(qcρ
*4k
n
1j
*jk
*4k
n
1j
*jk
*4k
*jk
*4k
*jk
*4k*
jkjk*3jk ˆ
Variational Inequality Formulation
K)ρ,η,Q,γ,Q,(Q
0,]ρ[ρ)](ρdq[]η[η]qβq[
]q[q]ρηβ)(qcq
)(qc
q
)(Qc[
]γ[γ]qαq[
]q[q]ηγαq
)(qc
q
)(qc
q)(Qc
[
]q[q]ηγαq
)(qc
q
)(qc
q)(Qc
[
]q[q]ρq
)(qc[]q[q]γ
q)(qc
q)(qc
[
*4
**3*2**1
*4k4k
*4k
o
1k
n
1j
*jk
n
1j
*jj
m
1i
1o
1k
*jkjk
*ij
*jkjk
*4k
*jjk
*jkjk
jk
*ijjkn
1j
o
1kjk
*3j
m
1i
*ii
1n
1j
*ijij
r
1h
*hi
*1)i(n1)i(n
*j
*iij
ij
*ijij
ij
*ijijm
1iij
2*i
*ijij
*j
*iij
ij
*ijij
ij
*ijijm
1i
n
1jij
2*i
*1)h(m
r
1h 1)1h(m1)h(m
*1)h(m1)h(mr
1h
*hihi
*i
m
1ihi
*hihi
hi
*hihi
ˆ
ˆ
ˆ
ˆ
Numerical Examples
1 2
1 2 3
1 2 3
31 2
Sources
rRecyclers
Processors
DemandMarkets
Landfill
Landfill
Landfill
10.00 10.00 9.53
0.00 0.00 0.95
10.00 20.00 19.06
0.00 0.00 0.00
10.00 20.00 76.26
0.00 0.00 0.00
231.79 372.47 40.67
247.97 212.24 45.40
279.99 274.28 242.14
hiq
h3q
ijq
i3q
jkq
j3qγη
4kρ
1β
1α
1β
0.5α
0.25β
0.5α
Change of conversion rates
High demand and low demand
10.00 3.50
0.00 13.00
10.00 3.50
0.00 0.00
10.00 3.50
0.00 0.00
231.79 4.52
247.97 14.03
279.99 26.56
hiq
h3q
ijq
i3q
jkq
γj3q
η4kρ
10001.5ρ2ρd
10001.5ρ2ρd
41422
42411
1001.5ρ2ρd
1001.5ρ2ρd
41422
42411
1β
1,α
Summary
• Proposed a rigorous E-cycling mathematical model * the endogenous equilibrium prices and material ship
ments between tiers.
• Decision makers’ behavior in a bottom tier influences those in a upper tier.
* influence of a bottom tier’s conversion rate. * influence of low demand.
Sustainable E-cycling system
Global Supply Chain Networksand
Transboundary Emisssion Risk
Economic Globalization and Transboundary Pollution
Economics globalization may exacerbate transboundary pollutions (Coperand (1995), Benarroch (2001) )
* Increase in volume of traffic * Relaxation of environment standards for helping domestic firms
Transboundary pollution (pollution across boundaries)
Carbon dioxides, methane, Chlorofluorocarbons (CFCs), Sulphur dioxide, Nitrogen oxides and so on
Risks of transboundary pollution
* No clear relationship between how much a country emits and how much is deposited there.
* Hard to predict how much pollution travels from a country according to the natural conditions.
Thank You !!
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