Weekly container delivery patterns in liner shipping planning models

This paper addresses a fundamental question related to nearly all container liner shipping planning models: whether the implicit assumption of identical container delivery pattern every week is valid in a situation of identical shipping services and identical cargo demand every week. We prove that when the number of containers transported from one port to the next is formulated as a continuous variable, the resulting mathematical model with an identical container delivery pattern is equivalent to the model with general container delivery patterns which can be different in different weeks. When the number of containers transported is formulated as an integer variable, the model with an identical container delivery pattern is not equivalent to the model with general container delivery patterns. However, the difference between the optimal objective values of the two models is negligible for practical applications. In sum, little, if not nothing, is lost by assuming an identical container delivery pattern in liner shipping planning models.