6. Conclusions and future work
This paper has studied the practical liner shipping network schedule design problem with port time windows. This is a significant tactical planning decision problem because it considers the availability of ports when planning liner shipping services. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear non-convex optimization model. In view of the problem structure, we reformulated the problem as an integer linear optimization model and proposed an iterative optimization approach. The proposed solution method was applied to two networks, consisting of six ports and 21 ports, operated by APL. The results demonstrate that the port time windows, port handling efficiency, and bunker price all affect the total cost, the optimal number of ships to deploy, and the optimal schedule. Higher availability at ports, shorter port time, and lower bunker price result in a lower total cost and a smaller number of ships to deploy. Therefore, port operators can apply the proposed method to quantify whether the benefits to liner shipping companies are worthwhile compared to the cost of expanding the ports’ capacity and improving their effi- ciency. Liner shipping companies may need to charter in more ships if they predict that the future bunker price will increase. In future we will investigate the schedule design problem with port time windows while considering the inventory cost. Moreover, we will also investigate how the schedule design and container routing can be jointly planned.
