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

Abstract. In this paper, an integer programming model is offered for capacitated multi-allocation median hub location problems applicable to both cooperative and competitive environments among airlines. We divided the hubs into six independent categories by comparing the parameters of ticket price, travel time, and service quality for both the follower and leader airlines. The degrees of importance for the parameters of time and cost were determined by a multivariate Lagrange interpolation method, which could be of signicant help in allocating travelers to the follower airline hubs. Then, with regard to the seasonal demand of travelers, travel demand was considered as an uncertain parameter. To identify the deterministic equivalent forms for the considered categories of hub location models, the robust optimization method and the chance-constrained programming model were employed. Finally, the developed model was tested for a case study. The results indicated that the coalition of follower airlines could absorb nearly 2% of the leader airline travelers with relatively lower travel cost and time.