How Many Routes Can Be Removed in Airline Network?

Since the pioneering work of O’Kelly[5], designing an airline network has been an alluring topic in operations research studies, and seemingly hub location problems are main concerns in the literature, see [1] for recent survey. In this paper a different approach is taken to the design problem in an attempt to find a compact and efficient sub-network of the original airline network. In Fig. 1 Japanese domestic airline network in 2006 is shown over the map of Japan. Total number of regular airlines was 211 and they covers almost all the area. Recently two big Japanese airline companies announced that they started to reduce the airlines which were not profitable. Our interest in this paper is in how many links can be removed from the network with satisfying all the passengers demand by using alternative one-stop or two-stop routes. This approach is close to Jaillet et al. [2] (see also [4]), although they did not aim to reduce the number of airlines but to find the minimum cost rearrangement of airline network. This paper is organized as follows. In Sec. 2 we give a mixed integer programming formulation for our model and some comments on similar models are followed. In Sec. 3, we apply our model to Japanese airline network and make investigations on the obtained solutions. Sec. 4 summarizes the result and gives some remarks.