## 3 Methods
### Simulation Modeling
#### 3.1.2 Simulation Logic for Large-Vessel-First-Use Policy  
Our preliminary analysis estimated the unit fuel cost of a vessel for one round-trip voyage between the origin and destination ports using the average fuel cost per round trip divided by the vessel capacity. Due to the confidentiality of the information, we can only mention that a large vessel has a lower unit fuel cost than a small vessel, indicating that using a large vessel first would reduce the operating cost as proposed by [29]. On the other hand, a small vessel takes less loading and unloading time than a large vessel. Thus, using a small vessel first would more often improve the operational agility of the whole shipping system. Therefore, it would be worthwhile to investigate the impact of using a large vessel first on both operating costs and overall system performance.  
The proposed large-vessel-first-use (LVFU) policy requires selecting a large vessel first among all the available vessels in the waiting area. We can implement this relatively easily by assigning a higher ranking to large vessels than small vessels in the list of vessels. In addition, under the LVFU policy, when large and small vessels are loading products simultaneously at the origin port, large vessels should be filled first whenever possible. Because implementing such loading priority control is not trivial, we demonstrate our implementation logic as depicted in Figure 3.  
We added six virtual docks to simulate the three physical docks with the LVFU policy. Three docks (S1, S2, and S3) are used only for small vessels, and the other three (L1, L2, and L3) are only used for large vessels. Because the \"Dock capacity\" resource restricts the number of vessels that can be berthed to be three, only up to three of six virtual docks can be used, making the terminal capacity the same as the three physical docks. Then, by controlling the flow priority on the paths connecting the Yard tank to each dock, three docks for large vessels will prioritize loading products over the other three docks for small vessels. The three paths connected to the same group of docks have equal priority.  
We explain the presented logic further using an example. Suppose that two large vessels are berthed at Docks L1 and L2, and one small vessel is berthed at Dock S1. Then, no other vessels can enter the terminal area, and all must wait at the waiting area. When the inventory in the Yard tank is sufficient, large and small vessels can be loaded simultaneously.  
Figure 3: Simulation logic for LVFU policy.  
If the inventory in the Yard tank is not sufficient, products will be supplied from the Yard tank to Dock L1 and L2 first until two large vessels are fully loaded. Then, products will be provided to Dock S1 to load the small vessel. If any one of three vessels finishes loading and departs via a tugging path, then another vessel (large vessel first) at the waiting area can be berthed and begin to load products. The maximum number of vessels berthed is three, and a large vessel will always have a higher priority for loading products. This pattern will be retained continuously throughout the simulation run.