# Resource Capacity Requirement for Multi-Terminal Cooperation in Container Ports
## 2 Resource Profiles for Representing Workloads
### Resource Profiles  
Three major resources in a multiterminal container system are the wharf, gate, and yard. Quay cranes (QCs) on the wharf are interfacing resources between vessels and a terminal; the gates are interfacing resources between the terminal and consignees, and the yards are a representative resource for container storage supporting the operations process across the unloading, loading, receiving, and delivering. A resource profile that considers the varying of the capacity requirements for each type of resource over time-shifts is drawn out. This time-phased resource profile provides a means of estimating the workload on a resource throughout the time-shifts, and thus, assess the capacity adequacy of the system in managing the sporadic demands. Figure 1 represents the resource profiles of a yard and QCs graphically for two terminals when a vessel arrives at a terminal. The relevant notations are described as follows:  
\begin{tabular}{l l} \(t_{open}\) & = Time for starting the window for outbound or trans-shipment TEUs to arrive at a terminal. It is typically set to two weeks before the expected vessel arrival. \\ \(t_{close}\) & = Time for ending the window for outbound or trans-shipment TEUs to arrive at the terminal. It is typically set to one day before vessel arrival. \\ \(T_{arrival}\) & = (Random variable) Time that the vessel arrives at the terminal. The ETA of a vessel is nominated when constructing a berth schedule. For purposes of simplicity,this study excludes the berth scheduling, and the vessel arrival is set to follows a probability distribution. \(t_{unload}\) = Time for starting the unloading operations for the vessel. It is typically set to 2 h after vessel arrival. \(T_{switch}\) = (Random variable) Time for switching operation modes. The duration between time when an operation mode is switched and the time when the unloading begins, i.e., \(T_{switch}-t_{unload}\), depends on the QC intensity requested by the vessel and the amount of TEUs for the unloading from the vessel. \(T_{load}\) = (Random variable) Time for TEUs to be loaded onto a vessel, transferred to another terminal (if any) or delivered to mainland. Typically, time window \(T_{load}-T_{switch}=0\). \(T_{end}\) = (Random variable) Time for completing the loading operation for a vessel. \(T_{end}-T_{load}\) also depends on the QC intensity requested by a vessel and the amount of TEUs for the loading operation of the vessel. \(t_{depart}\) = Time for vessel departure. It is typically set to 2 h after the loading completion. \(T_{transfer}\)= (Random variable) Time for TEUs to be loaded onto trucks for transfer to another terminal for trans-shipment on another vessel. Trans-shipment TEUs typically leaves the terminal in 2-3 days after unloading. \(T_{finish}\) = (Random variable) Time that TEUs left the terminal. \(T_{finish}-T_{transfer}\) is dependent on the travel time of a truck between the two terminals and the amount of TEUs scheduled to be transferred. \(C_{a}\) = (Random variable) the amount of TEUs arrived in the terminal before the arrival of the mainline vessel. The actual arrivals of TEU quantity are uncertain but variations are usually minimal. \(C_{b}\) = (Random variable) the amount of inbound and trans-shipment TEUs unloaded from the mainline vessel. There is uncertainty in the amount of TEUs for unloading with a small variance. \(C_{c}\) = (Random variable) the amount of outbound and trans-shipment TEUs loaded to the mainline vessel to be transferred to another terminal or delivered to mainland. It is also uncertain with a small variance. \(C_{d}\) = (Random variable) the amount of TEUs received from transferring operations. It depends on the berth schedule and the TEU information of the corresponding vessel. There is also a small level of uncertainty. \(C_{a}^{f}\) = (Random variable) \(C_{a}\) for a feeder vessel. \(C_{b}^{f}\) = (Random variable) the amount of inbound TEUs unloaded from the feeder vessel. \(C_{c}^{f}\) = (Random variable) the amount of outbound TEUs loaded to the feeder vessel.