Information Technology Reference
In-Depth Information
-
τ
i,
1
: move from position P
2
to P
1
to pick up container
i
;
-
τ
i,
2
: transport container
i
from position P
1
to P
2
;
-
τ
i,
3
: transport container
i
from position P
2
to P
3
;
-
τ
i,
4
: transport container
i
from position P
3
to P
4
;
-
τ
i,
5
: move from position P
4
to P
3
in preparation for picking up container
i
+1;
-
τ
i,
6
: move from position P
3
to P
2
in preparation for picking up container
i
+1;
Each task is carried out using a specific piece of equipment. Task
τ
i,
1
and
τ
i,
2
are carried out by the QC. Task
τ
i,
3
and
τ
i,
6
are carried out by the AGV. Task
τ
i,
4
and
τ
i,
5
are carried out by the ASC. An event refers to either the beginning
or the completion of a task. For the six types of tasks defined above, whether
or not task
τ
i,
1
and task
τ
i,
3
can begin depends on both the completion of task
τ
i,
2
and task
τ
i,
6
; the beginning of task
τ
i,
4
and task
τ
i,
6
depends on both the
completion of task
τ
i,
3
and task
τ
i,
5
.Let
x
i,j
denote the time at which task
τ
i,j
ends. The time at which both two various types of equipment are available for
the shift of one container is called the meeting time. The time at which the
different tasks end can be computed as follows:
x
i,
1
=max(
x
i−
1
,
2
,x
i−
1
,
6
)+
s
i,
1
(1)
x
i,
2
=
x
i,
1
+
s
i,
2
(2)
x
i,
3
=max(
x
i−
1
,
6
,x
i,
2
)+
s
i,
3
(3)
x
i,
4
=max(
x
i−
1
,
5
,x
i,
3
)+
s
i,
4
(4)
x
i,
5
=
x
i,
4
+
s
i,
5
(5)
x
i,
6
=max(
x
i−
1
,
5
,x
i,
3
)+
s
i,
6
,
(6)
where
s
i,j
describes the time required for doing task
τ
i,j
.
Task
τ
Task
τ
Task
τ
i,2
i,3
i,4
QC
ASC
AGV
P
P
P
P
Vessel
Stacking pile
Task
τ
Task
τ
Task
τ
i,1
i,6
i,5
Fig. 3.
The sequence of transporting containers by three pieces of equipment
2.3 Lower-level Continuous-time Dynamics
At the lower level the continuous-time dynamics of individual pieces of equip-
ment are considered. In this paper, we assume that the dynamics of the pieces
of equipment are identical. Let the continuous-time dynamics of one piece of
equipment be described as follows:
