This paper addresses a problem of ship fleet type decision considering container fleet sizing and empty container repositioning (denoted as empty container allocation). Empirically, the ship fleet type decision is made according to laden container transportation, and does not consider the empty container allocation. This study hence builds a mixed-integer programming model for the problem. Based on the model, it is founded that the empty container allocation has an underlying network flow structure given a fixed ship fleet type and thus can be transferred to a standard minimum cost flow problem. Supposing the empty container allocation is optimized, some properties for the ship fleet type decision are investigated, e.g., given the maximum number of containers that will be carried by ships, the best ship type may not necessarily be the ship type whose capacity is close to the maximum number. Meanwhile, it is shown that if the empty container repositioning is not considered when determining the ship fleet type, the total cost may increase significantly.