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knowledge. In this research it has been estimated using statistical analysis of the
data. For example, how often each airline uses each gate was measured and used
as an estimation of airline preferences.
As mentioned in the previous sections the model contains several settings,
which have been determined based upon our observations in relation to Terminal
1 at Manchester Airport and these are summarised in Table 1.
Tabl e 1.
Model settings
Name
Symbol Value
Average number of flights per day
n
110
Number of gates
m
25
Time at which flights are split for towing
240 min
Size of the gap for which
p
saturates
90 min
Penalty for remote allocation
d
90
Minimal allowed size of the gap between flights
10 min
Shortest time margin for conflicts within group of gates
3 min
Longest time margin for conflicts within group of gates
10 min
Maximal number of conflicting flights per GR
M
2
There was only one shadowing constraint in the data, for the large gate 12,
which can be divided into two smaller gates, left 13 and right 14. Figure 1 shows
the groups of gates for Terminal 1. The gate-group adherence is as follows: GR1:
22, 24, 26, 28, 29, 32, 31; GR2: 21, 23, 25, 27; GR3: 2, 4, 6, 8; GR4: 10, 12, 13,
14; GR5: 1, 5, 7, 9, 11, 15.
6 Results and Discussion
The first part of this section shows how the new conflict constraint influences the
final allocation. Results for one chosen day are displayed and allocations obtained
for the model with and without the conflict constraint are briefly compared with
the actual recorded allocation. The second part of the section shows numerical
results obtained using five days of data. For these calculations the full config-
uration (with the conflict constraint) of the model has been used. The results
are compared against the actual allocations recorded during the day of airport
operation. All results have been obtained using CPLEX (version 12.2) executed
on a reasonable powerful desktop PC (24GB RAM, 500GB disk space, 3.06 GHz
Intel i7-950). An optimal solution was reached for each of the calculated days.
More detailed results are also shown for an illustrative day having 111 flights.
Figure 4 compares three allocations for the day: Figure 4a shows the real al-
location, Figure 4b the allocation obtained for the model without the conflict
constraint and Figure 4c the allocation for the model with the conflict constraint.
The horizontal axis of each of the charts shows time and the vertical axis the
names of the gates, flights are symbolised by chains of markers. The gates are
