Information Technology Reference
In-Depth Information
All in all, the CPDP presented here distinguishes itself from previous models
by explicitly taking into account 20-foot and 40-foot containers simultaneously
and supporting store and provide requests with unknown pickup or delivery
locations. However, in contrast to many models from the literature time windows
are not yet considered.
4 Mixed-integer Linear Program
The parameters of CPDP and the decision variables are introduced in Section 4.1.
Section 4.2 presents the constraints and the objective function.
4.1 Parameters and Decision Variables
The basic idea of our decision model is to integrate the three decision tasks
request completion, container flow determination and vehicle routes into one
mixed-integer linear program. We deploy a first set of decision variables which
represents the request completion decision problem. Another set of decision vari-
ables controls the container flow and a third decision variable set is dedicated
to the compilation of executable vehicle routes. Two additional decision variable
families are introduced in order to control the assignment of completed requests
to containers and for conducting the matching of the flows of containers and the
vehicle routes. All five decision variable collections are declared in Tab. 2.
Table 2.
Decision Variables
completion of requests
z
+
ik
∈{
0; 1
}
equals 1 if and only if node
i
is the pickup node of container
k
z
ik
∈{
0; 1
}
equals 1 if and only if node
i
is the delivery node of container
k
assignment of requests to containers
y
rk
∈{
equals 1 if and only if request
r
is assigned to container
k
determination of the container flow
x
CON
ijk
0; 1
}
∈{
0; 1
}
equals 1 if and only if container
k
flows along arc (
i, j
)
t
CON
ik
∈
R
≥
0
visiting time of container
k
at node
i
assignment of containers to vehicles
w
kf
∈{
0; 1
}
equals 1 if and only if container
k
is assigned to vehicle
f
determination of the vehicle routes
x
VEH
ijf
∈{
0; 1
}
equals 1 if and only if vehicle
f
flows along arc (
i, j
)
t
VEH
if
∈
R
≥
0
visiting time of vehicle
f
at node
i
l
if
∈
N
outbound payload of vehicle
f
leaving node
i
δ
if
∈
Z
payload variation of vehicle
f
at node
i
