Information Technology Reference
In-Depth Information
-
X
g,f
- a decision variable that takes the value 1 if flight
f
is allocated to
gate
g
or 0 if not
-
U
g,f
1
,f
2
- an indicator variable that is 1 if the two flights
f
1
and
f
2
are both
allocated to gate
g
-
p
f
1
,f
2
- the constant penalty function for each flight pair which indicates the
penalty to apply if flights
f
1
and
f
2
are both allocated to the same gate
-
r
f,g
- the constant penalty for each gate-flight pair which indicates the
penalty to apply if flight
f
is smaller than the maximal size of flight that
can be allocated to gate
g
-
a
f,g
- the constant penalty for each gate flight pair which indicates how
strongly gate
g
is preferred by an airline that is operating flight
f
-
freq
f,g
- the constant which indicates how often an airline which is operating
flight
f
has used gate
g
, based upon statistic data analysis
-
d
- the constant penalty for usage of 'dummy gate'
-
C
d
(
f
),
C
a
(
f
) - a set of flights which can be in conflict with the departure
time (
C
d
(
f
)) or arrival time (
C
a
(
f
)) of flight
f
if the flights are allocated to
the same group of gates.
4.2 Constraints
X
g,f
=0
,
∀
f/
∈
F
(
g
)
,
∀
g
∈
G.
(1)
G.
(2)
Each flight has to be allocated to a gate. A 'dummy gate' (gate
m
+1) is also
included in this constraint to which ungated flights will be allocated:
m
+1
U
g,f
1
,f
2
=0
,
∀
(
f
1
∨
f
2
)
/
∈
F
(
g
)
,
∀
g
∈
X
g,f
=1
,
∀
f
∈{
1
, ..., n
}
,
(3)
g
=1
No two flights can be allocated to the same gate at the same time. If two
flights overlap or are within a minimum time gap of each other then they must
be assigned to different gates, Inequality 4. This gap is set to 10 minutes, since
some time is needed to clear the gate. However, the precise value is not important
for these experiments, since there is an objective to increase these gaps.
1
,
∀
f
1
,f
2
∈
F
(
g
)
,
∀
g
∈
G, f
1
=
f
2
,
X
f
1
,g
+
X
f
2
,g
≤
(4)
(
e
f
2
≥
e
f
1
)
∧
(
e
f
2
−
l
f
1
≤
10)
.
The mathematical formulation of the time gap constraint is given below, it
introduces a new variable which is set if two flights are allocated to the same
gate. The constraint is introduced only for gaps smaller than 1
.
5 hour, which are
more than sucient. The gaps which are smaller than 1
.
5 hour are maximised
in the objective function using the new variable so that potential, minor delays
on the day of operation can be absorbed.
1
,
∀
f
1
,f
2
∈
F
(
g
)
,
∀
g
∈
G, f
1
=
f
2
,
U
g,f
1
,f
2
≥
X
f
1
,g
+
X
f
2
,g
−
(5)
(
e
f
2
≥
e
f
1
)
∧
(10
<e
f
2
−
l
f
1
<
90)
.
