The use of sea transport has increased significantly as businesses continue to expand internationally. Containers are commonly used for the transportation of bulky items hence the importance of port terminals in sea transport. The biggest challenge occurs in the allocation of berthing systems especially in continuous terminals, which may result in undesired delays at the port, the dissatisfaction of customers and building a negative reputation for the port authorities (Petering & Murty, 2009).
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Poor berth allocation affects nearly all other functions at the port such as scheduling of the quay and yard cranes as well as jockey truck crew (Lim, Rodrigues, Xiao, & Zhu, 2004). Quay cranes are important at the seaport because they are used when loading and offloading containers from vessels (Van Rensburg, He, & Kleywegt, 2005). Therefore, quay cranes are among the most expensive yet valuable equipment in all port operations. The continuous berth model problem involves the determination of a birthing plan for a given number of incoming vessels with known lengths and predetermined dock or moor days. In this case, the vessel length and processing are positively correlated. Due to a limited number of quay cranes, the loading and offloading should be completed within the shortest time possible (Lee, Chen, & Cao, 2010).
In this case, the planners should assign a given quay crane to a specific set of containers to avoid inconveniences. The total number of cranes in a terminal is limited and, therefore, the assigned numbers should not exceed the number of cranes especially when two or more vessels are being loaded or offloaded (Cheung, Li, & Lin, 2002).
In brief, berth allocation determines the time apportioned to a vessel depending on the number of containers to be loaded and offloaded as well as the length of the vessels to ensure safety when working with quay cranes (Lim, Rodrigues, Xiao, & Zhu, 2004). Quay cranes are usually separated, especially when operating next to each other. It takes about three hours for a quay bay to offload and one minute for the crane to shift from one ship to another (Murty, Liu, Wan, & Linn, 2005).
A survey in China indicates that priority is given to ships that have high processing times (Ak, 2008). Lee and Chen (2009) proposed a model to explain the berth allocation preferences, which was summarized in a first-come-first-served model. However, the model was not efficient at the port terminals and was thus questionable.
Later, Imai, Sun, Nishimura, and Papadimitriou (2005) developed another theory that did not consider the first-come-first-served model but was determined to reduce the total operation times such as waiting and service times as well as lowering the dissatisfaction levels of shippers due to the order of services. They developed a way to curb the problem (static) of quay crane scheduling, which later failed because some ships arrived at the terminal past the scheduled time.
Bierwirth and Meisel (2010) concluded that the berth allocation problem occurred because some ships arrived later than expected. To locate the position of every ship in the berth and to reduce the amount of space occupied in a berth, Lee and Chen developed a model that proposed that the ships should be berthed once they have arrived at the terminal. They used a heuristic algorithm, which performed very well using data obtained from a port in Singapore. Later, this argument failed because it was possible for several ships to arrive at the port terminals before the previous ships had been loaded or offloaded leading to protracted waiting times.
In a different approach, Lee and Chen (2009) assumed that a larger ship took a long time to be cleared than a smaller ship. They presumed that during the processing of a container ship, its position could not be changed and that the berth was only partially available for a non-fixed position. Later on, Liu, Wan, and Wang (2006) researched dynamic quay cranes by considering the minimum distance for safety and non-crossing. They used the heuristic decomposition method but did not consider how to prioritize the handling of each ship at the dock. Therefore, their assumption could not meet the needs of port operations. The method involved the following variables:
- K= the number of quay cranes at the port
- B= number of bays
- Pb= the processing time at bay
- M= constant
- Xbk= 1, if a ship is attended to at bay b by crane k
- Xbb= 1, if ship bay b finishes earlier than ship bay b’
- Cb= completion time of the ship at bay b (Huiqiu, 2008).
The quay cranes and ship bays are arranged in ascending order beginning from the front to the tail of the ship. If quay crane K loads or offloads at bay B and quay crane K’ loads or offloads at bay K’ then K+1≤K’. For instance, if the berthing of ship bays 3 and 8 are performed at the same time such that bay 3 is assigned to crane 4 while bay 8 is assigned to crane 2, the formula 0≥4-2+1 does not hold. This observation is a limitation because it does not satisfy the condition that a given crane schedule will cross over between quay cranes.
In quay crane problems, the cranes are assigned space in a berth and handling times according to the workload and crane capacity in an attempt to ensure safe and efficient use of resources (Liu, Jula, Vukadinovic, & Ioannou, 2004). According to Giallombardo, Moccia, and Salani (2010), the tactical berth allocation algorithm is commonly applied when solving this problem at terminals. Tactical berth allocation deals with container handling and keeps note of the costs that are incurred in the process.
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Giallombardo, G., L. Moccia, M., & Salani, I. V. (2010). Modeling and solving the tactical berth allocation problem. Transportation Research Part B, 44(2), 232-245. Web.
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