## 3 Application to the Resource Allocation Problem in the Mobile Harbor System
### Simulation for the Port of Surabaya  
The goal here is to use detailed simulation to obtain a more accurate minimal cost for the architecture for which the estimated performance satisfies our target.  
We employed the following assumptions in our simulation model:  
1. The inter-arrival times (IAT) to the port for container ships with 1000-3999 TEU and 4000-5999 TEU capacities are exponentially and uniformly distributed, respectively. Larger capacity ships have more tightly controlled schedules and thus, we give the associated inter-arrival times a distribution with a smaller standard deviation. Several container ships can arrive at the same time since we use probability distribution for ship inter-arrival times.
2. The number of mooring points on a 1000-2499 TEU capacity container ship for mobile harbors with capacity 250, 600, and 1200 TEU is 2, 1, and 1, respectively. For the small size container vessel, only 250 TEU MH is able to process both sides unloading due to the crane interference and safety issue which was determined when MH was conceptually designed by considering its physical and operational issues in 2011 (MH report 2010).
3. The number of mooring points on a 2500-5999 TEU capacity containership for mobile harbors with capacity 250, 600, and 1200 TEU is 3, 2, and 2, respectively.
4. Mooring time of MH at container ship is 30 min.
5. The mean inter-arrival time obtained is 365 * 24/# of visiting ships per year for the scenario.
6. The mean call size per ship is calculated as the yearly throughput/# of ships yearly.
7. There are six offshore service locations that can be used at one time by container ships.
8. The ratio of import cargo volume to export cargo volume is 1:1 based on the MH report 2011. These ratios each require a potentially different sequence of service events.
9. The service level metric is the average W/S ratio (waiting time/service time) and we require it to be less than 0.1 (as recommended by UNCTAD [28]);  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Design \#**} & \multirow{2}{*}{\begin{tabular}{c} **Capacity** \\ **(TEU)** \\ \end{tabular} } & \multicolumn{2}{c}{**Loading or Unloading Speed (TEU/h)**} & \multirow{2}{*}{\begin{tabular}{c} **Travel Time** \\ **(h)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cost of MH** \\ **(M US5/year)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Cost of Berth** \\ **(M US5/year)** \\ \end{tabular} } \\ \cline{3-6}  & & & & & & \\ \hline
1 & 250 & 37.5 & 250 & 2.70 & 4.30 & 1.63 \\
2 & 250 & 37.5 & 125 & 2.70 & 3.90 & 1.62 \\
3 & 1200 & 75 & 500 & 3.07 & 11.30 & 2.40 \\
4 & 1200 & 75 & 250 & 3.07 & 10.60 & 2.10 \\ \hline \end{tabular}
\end{table}
Table 2: Operation speed and cost of the MH.  
The resulting input data of ships for the simulations is provided in Table 3.  
The value of call size decrease as the ship size increases since the (un)loading rates of 1000-2499 TEU capacity container ship, 2500-3999 TEU capacity container ship and 4000-5999 TEU capacity container ship are anticipated as 0.8, 0.2 and 0.1 [34]. For example, 5000 TEU container ship, only 500 TEU cargo will unload/load at Surabaya port since it is a port of call for large size vessels. Small size container ships are a feeder vessel. Therefore, they have small number of port to visit.  
We acquired results for the optimal system design by utilizing the simulation model and the simulation optimization process. The result of the simulation model is given in Table 4. The operation speed at land is a prime determinant of the number of berths. However, it does not affect the number of MHs as much as it does on berths. The yearly cost of building berths on land to handle 2 M TEU/year, enlarge and dredge the 40 km entrance channel was calculated in the MH report 2010 as 186.1 M USD/year by assuming 20 year projects life. MH is able to reduce 20.8-26.4 M USD per year.