Development of a Model for Locating Hubs in a Competitive Environment under Uncertainty: A Robust Optimization Approach

Document Type : Original Article

Authors

1 Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

Abstract

This article explores the development of previous models to determine hubs in a competitive environment. In this paper, by comparing parameters of the ticket price, travel time and the service quality of hub airports, airline hubs are divided into six categories. The degree of importance of travel time and travel cost are determined by a multivariate Lagrange interpolation method, which can play an important role in allocating travelers to follower airline hubs. Then, based on the seasonal demand of travelers, we consider travel demand as uncertain parameters. To determine the robust counterpart of this category of hub location models, a robust optimization method is used. Finally, models are tested in a case study. The central results show that the follower airline's income has a considerable growth and can absorb nearly 2% of travelers of the leader airline due to lower travel costs and travel time compared to that of leader airline.

Keywords


1. Marianov, V. Serra, D. and ReVelle, C., "Location of hubs in a
competitive environment", European Journal of Operational
Research, Vol. 114 , No. 2, (1999), 363-371.  2. Wagner, B., "A note on "location of hubs in a competitive
environment"", European Journal of Operational Research,
Vol. 184, No. 1, (2008), 57-62. 
3. Soyster, A. L., "Convex programming with set-inclusive
constraints and applications to inexact linear programming",
Operations research, Vol. 21, No. 5, (1973), 1154-1157.  
4. Ben-Tal, A. and Nemirovski, A., "Robust solutions of uncertain
linear programs", Operations research letters, Vol. 25, No.1,
(1999), 1-13. 
5. Bertsimas, D. and Sim, M., "The price of robustness", Operations
research, Vol. 52, No.1, (2004), 35-53. 
6. Sasaki, M. and Fukushima, M., "Stackelberg hub location
problem", Journal of the Operations Research Society of Japan,
Vol. 44, No. 4, (2001), 390-402. 
7. Sasaki, M., "Hub network design model in a competitive
environment with flow threshold", Journal of the Operations
Research Society of Japan, Vol. 48, No. 2, (2005), 158-171. 
8. Sasaki, M. Campbell, J. F. Krishnamoorthy, M. and Ernst, A. T.,
"Designing hub and spoke transportation systems for a
competitive environment", in International Conference on
Industrial Engineering and Systems Management, (2009), 13-15. 
9. Eiselt, H. A. and Marianov, V., "A conditional p-hub location
problem with attraction functions", Computers & Operations
Research, Vol. 36, No. 12, (2009), 3128-3135. 
10. Lin, M. H., "Strategic airline alliances and endogenous
Stackelberg equilibria", Transportation Research Part E:
Logistics and Transportation Review, Vol. 40, No. 5, (2004),
357-384. 
11. Zou, L. and Chen, X., "The effect of code-sharing alliances on
airline profitability", Journal of Air Transport Management,
Vol. 58, (2017), 50-57.  
12. Yimga, J. O., "Airline code-sharing and its effects on on-time
performance", Journal of Air Transport Management, Vol. 58,
(2017), 76-90. 
13. Nikoofal, M. E. and Sadjadi, S. J., "A robust optimization model
for p-median problem with uncertain edge lengths", The
International Journal of Advanced Manufacturing Technology,
Vol. 50, No. 1-4, (2010), 391-397. 
14. Ghaffari-Nasab, N. Ghazanfari, M. and Teimoury, E., "Robust
optimization approach to the design of hub-and-spoke networks",
The International Journal of Advanced Manufacturing
Technology, Vol. 76, No. 5-8, (2015), 1091-1110. 
15. Zetina, C. A. Contreras, I.  Cordeau, J. F. and Nikbakhsh, E.,
"Robust uncapacitated hub location", Transportation Research
Part B: Methodological, Vol. 106, (2017), 393-410. 
16. Tavakkoli-Moghaddam, R. Gholipour-Kananib, Y. and
Shahramifarc, M., "A multi-objective imperialist competitive
algorithm for a capacitated single-allocation hub location
problem", International Journal of Engineering-Transactions
C: Aspects, Vol. 26, No. 6, (2013), 605-612. 
17. Ghodratnama, A., Tavakkoli-Moghaddam, R. and Baboli, A.,
"Comparing three proposed meta-heuristics to solve a new p-hub
location-allocation problem", International Journal of
Engineering-Transactions C: Aspects, Vol. 26, No. 9, (2013),
1043-1058. 
18. Bashiri, M. and Rezanezhad, M., "A reliable multi-objective phub
covering location problem considering of hubs capabilities",
International Journal of Engineering-Transactions B:
Applications, Vol. 28, No. 5, (2015), 717-729. 
19. Alizadeh, Y. Tavakkoli-Moghadam, R. and Ebrahimnejad, S., "A
new multi-objective model for a capacitated hub covering
problem solving by two multi-objective evolutionary
algorithms", International Journal of Mathematics in
Operational Research, Vol. 9, No. 1, (2016), 99-124.