Information Technology Reference
In-Depth Information
Although we consider only one seaside / railroad terminal, we introduce a
terminal node for each single container in the system, e.g. if the number of
containers in the system is 5 then nodes 1 to 5 are nodes that belong to the
terminal and node
i
can be used exclusively by container
i
. We use this node-
duplication strategy in order to make the control of the in- and outbound flow
of containers into the terminal easier. We apply the same concept for only the
container depot, e.g. there are
N
CONTAINER
nodes that form the container
depot but each node can be visited or left by exactly one container. Since a
vehicle is allowed to visit the terminal (or the container depot) several times it
is not necessary that we store different arrival times of a vehicle at the depot.
Instead we need to store only one arrival time of a vehicle at a node. We are
going to use the recursive arrival time update [8] for short cycle prevention in
the vehicle flows. Therefore, we need a common outbound node and a common
inbound node for each vehicle depot.
The set of all involved nodes is
N
VDEPOT
is the set of all nodes
N
and
belonging to the truck depot. Set
is the set
of all containers. The set of all requests is
REQS
. It is partitioned into four
subsets, i.e., the set
REQS
EXP
of export requests, the set
REQS
IMP
of import
requests, the set
REQS
STOR
of storage requests, and the set
REQS
PROV
of
provide requests.
The binary parameter
AV AIL
(
k, i
) equals 1 if and only if container
k
is avail-
able at node
i
. Similarly, the binary parameter
REQU I
(
k, i
) equals 1 if and only
if container
k
is allowed to be delivered to node
i
. The length of arc (
i, j
)is
d
(
i, j
).
A route of vehicle
f
starts at node
START
(
f
) and ends in node
STOP
(
f
). If the
pickup (delivery) node of request
r
is specified by the customer then this node
is referred to as
REQST ART
(
r
)(
REQST OP
(
r
)). The current position of con-
tainer
k
is
CONT
_
LOC
(
k
) and the binary parameter
FIXED
(
k, r
)equals1if
and only if request
r
is already matched with container
k
(this is true for all im-
port, export and storage requests). The size of container
k
is given by
C
(
k
). A
20-foot container has size
C
(
k
) = 1 and a 40-foot container has size
C
(
k
)=2.
Finally,
M
is a suciently large integer number.
We construct a complete directed graph from the node set
V
is the set of vehicles and set
C
N
,whichmeans
that the arc set of the graph equals
. The arcs are weighted by their
travel distance
d
(
i, j
). We assume that all vehicles travel at unit speed so that
the absolute value of
d
(
i, j
) equals the absolute value of the time needed to travel
along arc (
i, j
).
N×N
4.2 Constraints and Objective Function
In the following, we present the constraints required to ensure the feasibility of
the generated vehicle routes. The selection of loading and unloading locations for
all containers is controlled by constraints (1)-(16). The assignment of requests to
containers is determined by constraints (17)-(20). Container flows are controlled
by the constraints (21)-(26), and the generation of vehicle routes is subject to
constraints (27)-(47). The matching of container flows and vehicle routes is
achieved by constraints (48)-(54).
