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

qq

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 !!