Journal of Cleaner Production xxx (2014) 1e13 Contents lists available at ScienceDirect

X_jkt: amount of ELV shipped from collection center j to dis-mantler k in period t

Y_klt: amount of hulk shipped from dismantler k to shredder l in period t
Z_lut: amount of ASR shipped from shredder l to landfill u in period t
V_kpt: amount of non-reusable fluid shipped from dismantler k to recycling facility p in period t
W_krt: amount of non-reusable tyre shipped from dismantler k to recycling facility r in period t
U_kst: amount of non-reusable battery shipped from dismantler k to recycling facility s in period t
P_1lnt: amount of ferrous material shipped from shredder l to recycling facility n in period t
P_2lnt: amount of non-ferrous material shipped from shredder l to recycling facility n in period t
Q_1kmt: amount of ferrous material shipped from dismantler k to secondary market m in period t
Q_2kmt: amount of non-ferrous material shipped from dismantler k to secondary market m in period t
Q_3kmt: amount of fluid shipped from dismantler k to secondary market m in period t
Q_4kmt: amount of battery shipped from dismantler k to sec-ondary market m in period t
Q_5kmt: amount of other material (i.e. plastics, glass, textile, rub-ber) shipped from dismantler k to secondary market m in period t
e_kt: if dismantler k is opened in period t, 1; otherwise, 0

e_lt: if shredder l is opened in period t, 1; otherwise, 0

3.4. Formulation

3.4.1. Minimize

X X fkt $ekt þ X X flt $elt þ											(1)
k	t	l	t
X X X tijt Aijt $dij þ X X X tikt: Bikt: $dik þ X X
i	j	t	i		k		t			jk
	X	tjkt $Xjkt $djk þ X X X tklt $Yklt $dklþ
	t		k		l		t
X X X tkpt $Vkpt $dkp þ						X X X tkrt $Wkrt $dkr þ X X
k	p	t			k		r		t	ks
	X	tkst $Ukst $dks þ X X X tlut $Zlut $dluþ
	t		l		u		t
										(2)
X X X Bikt $dckt þ X X X Xjkt $dckt þ										(3)
i	k	t	j		k		t
X X X sclt $Yklt þ											(4)
k	l	t
X X X rcpt $Vkpt þ X X X rcrt $Wkrt þ X X
k	p	t	k		r		t		k	s

X X X lcut $Zlut

(6)

l

u

t

X X X

s1t $Q1kmt

þ

s2t $Q2kmt

þ

s3t $Q3kmt

þ

s4t $Q4kmt

m

ð

k

t

þ s5t $Q5kmt Þ

(7)

X X X

z1t $P1 ln t

þ

z2t $P2 ln t

Þ

(8)

n

ð

l

t

3.4.2. Constraints

X Aijt þ X Bikt

¼ Rit

ci; t

(9)

j

k

X Aijt ¼

X Xjkt

cj; t

(10)

i

k

• 
  1
  

X

Yklt

¼

a$

X Xjkt

X

Bikt

A

ck; t

(11)

l

@ j

þ

i

0

1

X Q1kmt

¼

m1

$

X Xjkt

þ

X Bikt

A

ck; t

(12)

m

@ j

i

0

1

X Q2kmt

¼

m2

$

X Xjkt

þ

X Bikt

A

ck; t

(13)

m

@ j

i

0

1

X Q3kmt

¼

m3

$

X Xjkt

þ

X Bikt

A

ck; t

(14)

m

@ j

i

0

1

X Q4kmt

¼

m4

$

X Xjkt

þ

X Bikt

A

ck; t

(15)

m

@ j

i

0

1

X Q5kmt

¼

m5

$

X Xjkt

þ

X Bikt

A

ck; t

(16)

m

@ j

i

0

1

X Vkpt

¼

l1

$

X Xjkt

þ

X Bikt

A

ck; t

(17)

p

@ j

i

0

1

X Wkrt

¼

l2$

X Xjkt

X Bikt

A

ck; t

(18)

r

@ j

þ

i

X Ukst

0

X Xjkt

X Bikt

1

ck; t

(19)

¼

l3

$

þ

A

s

@

j

i

X rcst $Ukst þ	(5)	X Zlut ¼ b$	X :Yklt cl; t	(20)
t		u	k

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