Methodology - Model Testing
3. A check is performed from the Ω matrix to determine if the “nominated flight” has been assigned to another aircraft in the chromosome
6.5 Fleet assignment and aircraft rotation: An exampleexample
A test was conducted to determine solution time, flight assignment cost and routing differences for each aircraft between the MCNF FAM which was pre-sented using equations (3.1) to (3.6) and the NLIP FAM which was defined by equations (4.6) to (4.9). This test is done for a subset of 168 flights which are taken from data set 9 which has 2 599 flights. A minimum ground time and turn-around time of 30 minutes was used in the test. The MCNF FAM solution is obtained using the mixed integer programming solver from CPLEX and the NLIP FAM is executed using the GA solver presented earlier. The following steps for this test are undertaken:
(a) The MCNF FAM is executed for the subset of data.
(b) The results of the MCNF FAM are converted to an approximate aircraft-time representation using the process in Figure 6.15 in order to determine aircraft routing.
(c) The NLIP FAM is executed for the subset of data.
(d) The flight assignment costs, solution time and flight routing are compared.
A decision to use five aircraft was taken because any lower number of aircraft would not provide a solution which assigns all 168 flights to aircraft.
Two tests were conducted for each model. The first test uses the fleet types and aircraft shown in Table 6.8. The second test uses five aircraft from the Airbus 319 family. These two tests are done in order to determine the uniqueness of the aircraft routing found for each group of aircraft. Below is the aircraft allocation for the first test:
Fleet type # Seats # Aircraft Costs for each hour of flight
Airbus A319 120 1 $10, 000
Airbus A320 148 1 $12, 000
Airbus A332 222 1 $15, 000
Airbus A343 253 1 $18, 000
Airbus A336 317 1 $20, 000
Table 6.8: Aircraft allocation for each fleet type
After the result is obtained for the MCNF FAM, it is converted to an aircraft-time representation as indicated in step (b) using the process shown in Figure 6.15 which is coded in Java (main class in Appendix I). The conver-sion of the MCNF FAM to aircraft-time representation creates aircraft routing which is similar to results obtained from the NLIP FAM. The steps for the conversion process which are shown in the flow chart in 6.15 are below:
1. The MCNF FAM solution file, the data set file (file with departure air-port, arrival airair-port, departure time and arrival time for each flight) and a file with information on each fleet type with the number of aircraft are read in.
2. Sort flights by departure time from the earlist to the latest flight.
3. Add the assigned fleet type from the solution file to each flight. Thus each flight will have departure airport, arrival airport, departure time, arrival time and assigned fleet type.
4. Iterate through all flights. In each instance, the fleet type to which the flight is assigned is determined. This is followed by the allocation of the flight to a random aircraft of that fleet type so that minimum ground time and conservation of aircraft flow are observed.
Start
Read data set information, fleet information and timespace solution
Sort all flights by departure time
Match assigned fleet type to each flight
Iterate through flights and assign each flight to aircraft of fleet type complying to constraints
Stop
Figure 6.15: Process flow for converting results from the time-space model to an aircraft-time line
Table 6.9 shows that the flight assignment cost for the MCNF FAM is the same as that obtained for the NLIP FAM for the aircraft data in Table 6.8 for the 168 flights being tested. It is observed that the non-linear integer programming fleet assignment model is significantly slower. An analysis of the difference in aircraft routing showed that there were no differences in aircraft routing from both models.
Table 6.9: MCNF FAM and NLIP FAM results for the aircraft data in Table 6.8
The above test was repeated for both the GA solver and the mixed integer programming solver in CPLEX. The same data set of 168 flights was used, the only difference being that instead of using a single aircraft for each fleet type as in Table 6.8, 5 aircraft of the same fleet type (Airbus A319) were utilised.
Results obtained are shown in Table 6.10. The flight assignment cost for the
MCNF FAM is the same as that obtained for the NLIP FAM. It is observed that the NLIP FAM solver is slower.
MCNF FAM:
Table 6.10: MCNF FAM and NLIP FAM results when using 5 Airbus A319 aircraft
An analysis of the difference in aircraft routing showed that the same air-craft from each model had different flight routing. This result is shown in Table 6.11 which shows the number of common flights between the two models for each aircraft. In total, only 29 out of the 168 flights were assigned the same aircraft between the two models. This is an indicator of multiple optimal so-lutions. From this result, it can be deduced that if there is more than a single aircraft for each fleet type, the NLIP FAM could have multiple solutions.
Aircraft Fleet type # Common flights
1 Airbus A319 1
2 Airbus A319 4
3 Airbus A319 11
4 Airbus A319 12
5 Airbus A319 1
Table 6.11: Common flights found for each aircraft in solutions for the MCNF FAM and NLIP FAM
The fleet assignment results which include aircraft routing from the second test for the MCNF FAM and NLIP FAM are shown for the first aircraft in Figure 6.16 and Figure 6.17. There were 42 airports used in the data set which are shown vertically. The flights assigned to the first aircraft are shown with the departure and arrival time for each flight. Dissimilar to the aircraft-time representation shown in Figure 4.1, the flight lines in Figure 6.16 and Figure 6.17 are shown vertically in order to show all flights flown by the first aircraft from both models. The length of each flight line does not show the duration of the flight as only the departure airport and arrival airport are
shown. These also determine where each flight line starts and where it ends.
The descriptors for each flight, departure time and arrival are aligned to each flight line. These descriptors are also put one below the other to ensure all flights flown are shown. Two observation are made from both figures, the first is that only flight 137 is common for this aircraft in both models. The second is that airport 1 is a hub in the data set because of the number of arrivals and departures. Because of the number of common flights for each aircraft, it can be deduced that no aircraft from the results of the MCNF FAM is the same as that of the NLIP FAM.
1
Figure 6.16: Flight representation for aircraft 1 using the NLIP FAM
1
Figure 6.17: Flight representation for aircraft 1 using the MCNF FAM