Information Technology Reference
In-Depth Information
We set, by constraints (42) and (43), the payload variation
δ
if
of vehicle
f
at
node
i
to
C
(
k
)ifcontainer
k
has been assigned to vehicle
f
(
w
kf
=1)andif
i
is
the starting (pickup) node associated with container
k
(
z
+
ik
= 1). Similarly, we
set, by constraints (44) and (45), the payload variation
δ
if
of vehicle
f
at node
i
to
−
C
(
k
)ifcontainer
k
has been assigned to vehicle
f
(
w
kf
=1)andif
i
is
the terminus (delivery) node associated with container
k
(
z
ik
=1).
−
x
VEH
ijf
l
if
+
δ
jf
≤
l
jf
+(1
)
·
M
∀
i, j
∈N
,f
∈V
(46)
x
VEH
jif
l
jf
≤
2+(1
−
)
·
M
∀
j
∈N
,f
∈V
(47)
i
∈N
The payload variation along the route of vehicle
f
is updated by
δ
if
recursively
(46) so that the payload is increased by at least 1 (TEU) if
f
visits a node with
a container pickup but the payload is reduced by at least 1 (TEU) if
f
visits
a container delivery node. It is not allowed that a vehicle carries a payload of
more than 2 TEU at any position of its route (47).
Matching of Container Flows and Vehicle Routes
w
cf
≤
1
∀
c
∈C
(48)
f
∈V
w
cf
≥
y
rc
∀
c
∈C
(49)
f
∈V
r
∈
REQS
Each container is assigned to at most one vehicle for being moved (48). If con-
tainer
k
is assigned to a request
r
then it is necessary that
k
is assigned to
exactly one vehicle
f
(49).
x
CON
ijc
≤
x
VEH
ijf
+(1
−
w
cf
)
·
M
∀
i, j
∈N
,c
∈C
,f
∈V
(50)
In the situation where container
k
moves along arc (
i, j
) and if container
k
has
been assigned to vehicle
f
it is necessary that vehicle f also travels along arc
(
i, j
)(50).
1+
i,j
∈N
x
VEH
ijf
2
·
w
kf
≥−
∀
f
∈V
(51)
k
∈C
With the goal to avoid the insertion of dummy nodes into the route of vehicle
f
with the goal to artificially reduce the payload of
v
, we restrict the number of
visited nodes to the least possible number (51), e.g. if
m
requests are assigned
to
f
then the least necessary number of visited nodes is 2
m
+ 1 (the starting
node is not visited but only left by
f
).
y
rk
=
f
∈V
w
kf
∀
k
∈C
(52)
r
∈
REQS
