There usually exist a few big customers at ports of near-sea container shipping routes who have preferences on the weekly ship arrival times due to their own production and sale schedules. Therefore, in practice, when designing ship schedules, carriers must consider such customers’ time preferences, regarded as weekly soft-time windows, to improve customer retention, thereby achieving sustainable development during a depression in the shipping industry. In this regard, this study explores how to balance the tradeoff between the ship total operating costs and penalty costs from the violation of the weekly soft-time windows. A mixed-integer nonlinear nonconvex model is proposed and is further transformed into a mixed-integer linear optimization model that can be efficiently solved by extant solvers to provide a global optimal solution. The proposed model is applied to a near-sea service route from China to Southeast Asia. The results demonstrate that the time preferences of big customers affect the total cost, optimal sailing speeds, and optimal ship arrival times. Moreover, the voyage along a near-sea route is generally short, leaving carriers little room for adjusting the fleet size.