Information Technology Reference
In-Depth Information
where
gap
f
1
,f
2
=
e
f
2
−
l
f
2
if
e
f
1
>e
f
2
.The
shape of
p
f
1
,f
2
is appropriate for the problem since the smaller gaps are penalised
much more heavily than the larger gaps. Moreover
p
f
1
,f
2
saturates, which means
that the penalty for really large gaps is fixed (equal to 1). It is reasonable to
argue that only the gap from the immediately preceding flight on the gate should
matter, and that gaps from earlier flights should be irrelevant.
The second component refers to effective usage of the gate space. The size
of a flight that is allocated to a gate should correspond to the size of a gate,
possibly being equal to the maximal size (
maxSize
) that gate
g
can absorb. It
cannot be larger, which is guaranteed by the first constraint (Equation 1). When
it is smaller, then such allocation is penalised, to keep the larger gates clear in
case they are needed later if flights have to be reallocated. The gate-flight size
function
r
f,g
that is used to penalise the allocation is given by Equation 10,
where
biggestGateSize
refers to the size of the biggest gate at a terminal.
l
f
1
if
e
f
2
>e
f
1
or
gap
f
1
,f
2
=
e
f
1
−
r
f,g
=
maxSize
(
g
)
size
(
f
)
biggestGateSize
−
,
(10)
The third component of the objective function refers to the airline preferences.
The preferences are established based upon statistical data analysis, by checking
how often particular gates have been used by particular airlines. The airline pref-
erence factor
a
f,g
which is used in the objective function to weight the allocation
of flight
f
to gate
g
is calculated according to Equation 11, where
maxFreq
is
the maximal value of all frequencies and refers to the most frequently used gate
by the most popular airline at the terminal.
a
f,g
=
1
freq
f,g
−
maxFreq
if freq
f,g
>
0
(11)
1
if freq
f,g
=0
,
The last component refers to the 'dummy gate' allocations. 'Dummy gate' sym-
bolises remote stands or holding places at an airport representing aircraft which
cannot be allocated to gates so usage of it is strongly penalised.
5 Experimental Settings
The data which is currently used in the experiments has been provided by
Manchester Airport and contains a record of five days of airport allocations:
both the planned allocation and the final actual allocation, and includes infor-
mation about gate usage (which gates have been used by which aircraft types
and airlines), size group information for aircraft (that divides aircraft into groups
according to their sizes) and sizes of gates. It is for Terminal 1 which is the bus-
iest terminal at the airport. The numerical results shown in Section 6 have been
obtained by solving five days of airport operations one after another.
Information about occupied gates for flights that arrive one day and depart
the next day has been passed from day to day. Information about the airlines
and airport preferences is hard to capture because it often relies on human
