Information Technology Reference
In-Depth Information
that stores a container becomes the start node of a provision request. No node
receives more containers than requested (14) and no node provides more con-
tainers than available at this node (15). The starting and the terminating node
assigned to a container are unequal (16).
Request to Container Assignment
y
rk
=1
∀
r
∈
REQS
(17)
k
∈C
y
rk
≤
1
∀
k
∈C
(18)
r
∈
REQS
∀
r
∈
REQ
EXP
,k
∈C
y
rk
=
FIXED
(
k, r
)
(19)
∀
r
∈
REQ
IMP
,k
∈C
y
rk
=
FIXED
(
k, r
)
(20)
Each request is assigned to exactly one container (17) and each container receives
at most one request (18). The two constraints (19) and (20) ensure consistency of
fully known import and export requests with the corresponding used containers.
Container Flows
x
CON
iik
=0
∀
i
∈N
,k
∈C
(21)
x
CON
ijk
≥
z
+
ik
∀
i
∈N
,k
∈C
(22)
j
∈N |
j
=
i
x
CON
jik
≥
z
ik
∀
i
∈N
,k
∈C
(23)
j
∈N |
j
=
i
+
iin
N
+
i
∈N
z
+
jk
=
z
jk
x
CON
ijk
x
CON
jik
∀
j
∈N
,k
∈C
(24)
Self-referencing flows of containers are not allowed (21). If node
i
has been se-
lected as starting node of the flow of container
k
then container
k
leaves node
i
(22). In case that
i
has been selected to be the terminal node of the flow of
container
k
then constraint (23) ensures that
k
travels to
i
. Constraint (24) pre-
serves the balance of inbound and outbound flow of container
k
at node
i
.If
i
is
the selected start node of the flow of container
k
then there is no inbound flow
of
k
into
i
. Similarly, if
i
is selected to be the terminus node of container
k
then
there is no outbound flow of
k
from
i
.
t
CON
ik
≥
0
∀
i
∈N
,k
∈C
(25)
t
CON
ik
·
x
CON
ijk
≤
t
CON
jk
−
x
CON
ijk
+
d
(
i, j
)
+(1
)
·
M
∀
i, j
∈N
,k
∈C
(26)
Vehicle Routing.
In order to avoid short cycles of the flowing containers,
we recursively calculate the arrival times of container
k
at the nodes along the
determined flow path (25)-(26) as proposed by [8].
