“…Most studies on liner shipping services require fixed port rotations as input of the models (Dong and Song, 2009;Bell et al, 2011;Qi and Song, 2012;Song and Dong, 2012;Wang and Meng, 2012b;Brouer et al, 2013;Wang et al, 2013b). One line of literature relevant to the optimization of port rotation directions is port rotation design, which is usually referred to as liner ship route design or liner shipping network design; for example, Shintani et al (2007), Agarwal and Ergun (2008), Alvarez (2009), Meng et al (2012, Reinhardt and Pisinger (2012). Nevertheless, none of these studies explicitly investigate the impact of the directions of port rotations.…”