chance-constrained programming and robust optimization approaches for uncertain hub location problems in a cooperative competitive environment

In this paper, we propose an integer programming model for capacitated multi-allocation median hub location problem, which is applied in a both cooperative and competitive environment among airlines. we divide the hubs into six independent categories by comparing the parameters of the ticket price, travel time, and the service quality of hub airports are controlled by follower and leader airlines. in this paper, the degree of importance of time and cost parameters determine 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 deterministic equivalent forms of this category of hub location models, robust optimization method and chance-constrained programming model are used. finally, the proposed model test in a case study. based on the results, a coalition of follower airlines can absorb nearly 2% of travelers of leader airline due to lower travel cost and travel time compared to that of leader airline.