Location Models For Airline Hubs Behaving as M/D/C Queues

1. Location Models For Airline Hubs Behaving as M/D/C Queues By: Shuxing Cheng Yi-Chieh Han Emile White

2. Outline • Heuristic Procedure • HLRA Model • Computational Experience • Examples • CAB data • Solutions and Comparisons • Conclusions

3. M/D/C queue

4. HLRA1 Model k i j m

5. Heuristic Procedure • To solve the model, the procedure has two phases : • Construction phase: • Find the initial set of p (A fixed number of servers) locations by using greedy heuristic model • Randomly chose one of the three best nodes but not the best and add it to the set of locations • Improvement phase: • Use one-opt exchange heuristic and diversification step to find optimum set of locations • Move location of each hub in initial solution to non-hub and compare value before and after trade • Determine new set of locations with tabu search procedure until no improvement is obtained, i.e. no less than minimum solution

6. Computational Experience ( 900 instances ) No. of each hub k i j Assumptions: 1) Traffic between nodes ~uniform[0,5] 2) Hub-to-hub transportation costs save 50% 3) Fixed costs of each hub are set to 10000, 25000 and 50000 4) Right-hand side of the capacity constraint is set to 1200, 1400 and 1600 Result: Fixed Cost of each hub , average cost , number of hubs , 25 s

7. Model • Our model was evaluated on a set of 25 U.S. cities. • Different features of the model were changed to analyze the results: • Savings percentage: α = 0.25, 0.5, 0.75 • Different fixed operating costs: 40,000 vs. 60,000 • Different levels of total flow were analyzed

8. Results • As the savings percentage increased, so did the cost of the operation. • The number and location of hubs varies more for lower levels of α and for lower initial fixed costs. • However, the number and location of hubs tends to stabilize as the level of α increases.

9. Results • We can then choose a specific situation and analyze the statistics of each individual hub airport. • We can then view each different airport hub in the system and determine which airports are near capacity and which ones are relatively underused. • Can view amount of traffic that goes through one hub versus multiple hubs.

10. Different Models • This model differs when compared with previous models without capacity constraints. • Previous work on uncapacitated multiple hub models would focus more traffic through certain hubs. • This may have reduced costs overall, but it can lead to overutilization in some hubs and underutilization of other hubs. • In reality, this would cause overcrowding and delays that the hub. • The new model sets capacity limits that distributes passengers more evenly to different airports. • This means less congestion in certain airports. • To compare the two models, fixed costs were set to zero and a new constraint was added that fixes the number of hubs in the model.

11. Comparison

12. Comparison • This table shows the comparison of our two models. • We can see for the model from this paper (HLRA), the passenger flow is more evenly spread among the different hubs. • The costs are a little higher, but this model potentially alleviates congestion and overcrowding at certain hub airports that could lead to delays that are not accounted for in the models.

17. Figure 2-5 show multiple assignment network with 20-node problem for various values of and 3 hubs using both models. As the value of increases, the number of multiple assignments in both UMAHMP and HLRAI models increases.

18. Conclusions • Compared to the existing models, the congestion at each hub is considered in the new model. • The key feature of this new model is the transformation of the probabilistic constraint stating that the amount of congestion in a hub cannot exceed a given threshold with a given probability, into a deterministic linear constraint. • Hubs are modeled as M/D/c queuing system. • A novel procedure is developed to solve this system.