158 Supply Chain Management and Logistics
u
ikt
: the binary variable indicating whether vehicle k visits customer
i in period t. If u
ikt
= 1, the customer is visited and 0 otherwise
v
ikt
: the nonnegative variable representing the delivery amounts to
customer i by vehicle k in period t ∈ T
The basic model (BM) can be formulated as follows:
min
,
cx
ij ijkt
ij MkKtT ∈∈∈
(6.1)
st xx iM kK
ijkt jikt
jMjM
.. =0 ,,,−∀∈∀∈∀∈
∈∈
(6.2)
xkKtT
mjkt
jM
o
=∀∈∀∈
∈
, (6.3)
xkKtT
jm kt
jM
o
=∀∈∀∈
∈
, (6.4)
u
ikt
≥ x
ijkt
∀i, j ∈ M, ∀k ∈ K, ∀t ∈ T, (6.5)
uiMtT
ikt
kK∈
≤∀∈∀∈
, (6.6)
v
ikt
≤ min{B
i
, H}u
ikt
∀i ∈ M, ∀k ∈ K, ∀t ∈ T (6.7)
vHkK
ikt
iM
≤∀∈∀∈
∈
(6.8)
yy vd iM
it it iktit
kK
,
1−
∈
+−∀∈ ∀∈
(6.9)
yvBiMkK
it ikti
kK
+≤∀∈ ∀∈
∈
(6.10)
x
ijkt
, u
ikt
∈ {0,1},