Journal of Traffic and Transportation Engineering 4 (2016) 86-93 doi: 10.1726/2328-2142/2016.02.003 D DAVID PUBLISHING Stacking Sequence of Marine Container Minimizing Space in Container Terminals Ning Zhang and Yutaka Watanabe Graduate School of Tokyo University of Marine Science and Technology, Tokyo 13-833, Japan Abstract: Heavier marine containers should be loaded first into ships at container terminals so that ship stability can be maintained during transport. It is helpful for the container terminals if lighter containers arrive earlier than heavier containers, because the latter can be stacked on the former. Therefore, the heavier ones can be loaded into the ships first. Shippers of marine containers do not, however, care for the matters of ships. They follow their own time schedules of supply chains sending marine containers with no relation to container weight. In addition to the conflict explained above, a ship must accommodate numerous containers sent by many shippers. Consequently, marshalling containers at container terminals before loading them into ships is necessary, although it causes inefficiencies of time and cost of cargo handling. This paper presents a proposal of a simple sequence of stacking marine containers at container terminals, adapting to random arrival of the containers irrespective of their weight, but it naturally keeps heavier containers stacked higher together with the stacking space minimized. An algorithm related to this proposal is the following: First, weight-ranked stacking addresses are assigned initially in a block of space at a container terminal; Second, containers are accepted and stacked up in the first block as they arrive at the terminal; Third, a lighter ranked address is sought for the next container if the number of containers on the initially assigned address for the container has already reached the maximum, which depends on the height of cargo handling equipment such as transfer cranes; Fourth, such containers are stacked up on the lighter ranked address. The address is reassigned with the weight rank of the container; Fifth, a heavier ranked address is sought for the next container if no lighter ranked address can be found; Sixth, such containers are stacked up on the heavier ranked address; Seventh, change the block to the next one if either a lighter or heavier ranked address cannot be found; Eighth, repeat the sequence above. This paper demonstrates the algorithm run by a simulation model for which actual arrival records of marine containers to a container terminal of Port of Yokohama are applied. Six ships of different sailing routes are analyzed using the simulation model. All analysis results show that heavier containers are stacked higher with a minimum number of blocks. Therefore, no marshalling of containers is necessary for loading the containers into ships. Key words: Cargo handling, stability of ships, marshalling of containers, port logistics. 1. Introduction A container ship loads thousands marine containers at a time at a container terminal at a port. Heavier marine containers should be loaded first into a ship to maintain ship stability after departure from a port, as generalized in the Container Handbook [1]. Arrival of the containers to the container terminal is, however, random in time series because shippers of the containers have neither relation to nor interest in matters of container terminals, but run their own business cycles, e.g., productions of factories, sales of Corresponding author: Yutaka Watanabe, Dr., professor, research fields: port logistics, intermodal transportation and safety engineering. wholesales and retail. Consequently, the container terminals must manage stacking of marine containers until the container ship berths and starts loading of the containers stacked on the container terminals. Re-handling of the containers wastes time and costs of the container terminals if heavier marine containers are stacked lower under lighter containers. Prevention of re-handling of the containers at the terminals can be done in two ways. One is to have a wider space in the terminals to reduce stacking of the containers, placing them as flat as possible. The other is to stack heavier marine containers as high as possible, although space in the terminals is limited. Because the former is difficult to realize in
Stacking Sequence of Marine Container Minimizing Space in Container Terminals 87 economically developed regions, the latter is the more practical solution, as argued by Sou [2]. 2. Space Limitation versus Marshalling in Container Terminals 2.1 Contradictory Problem of Container Terminals A container terminal at a port must accommodate a huge number of marine containers from an unspecified number of shippers with various weights of the containers. Ships berthing at container terminals must load heavier marine containers at the bottom first, followed by lighter ones stacked on the heavier one, and do so accordingly so that the ships can maintain stability during travel over the oceans, as shown in Fig. 1. Shippers which send their marine containers do not, however, care about such maritime matters because their priorities are centered upon minimizing their own space at their site. For example, a factory of car parts produces many shipments of marine containers daily. All the containers are sent off to container terminals as soon as possible because no space remains at the factory to maintain them. At the terminals, they pay stock costs there, causing congestion at the gates of container terminals because of their arbitrary arrivals, as argued by Watanabe [3]. In contrast, the ability to adapt to any conditions of marine containers flexibly is a necessary service of container terminals for the shippers, as shown in Fig. 2. 2.2 Marshalling Operation in Container Terminals If a container terminal has sufficient space for placing all containers flat, then no matter related to maritime transport occurs because heavier containers can be picked up for loading into the ships at any time. This system was actually introduced by Sea Land Inc., during the early time of containerization, as reported by Muller [4]. Today, most major container terminals are located in the heart of or in close proximity to economically developed hinterlands. Therefore, land prices of the terminals are extraordinarily high, especially in economically developed countries, because marine containers are stacked more than two high at modern container terminals, as shown in Fig. 3. The gap separating maritime matters and shipper situations argued above has engendered a unique operation at container terminals designated as marshalling : equivalent to re-handling for already stacked marine containers. Because such re-handling Fig. 1 Ideal arrival of marine containers to container terminals. Fig. 2 Actual arrival of marine containers to container terminals.
88 Stacking Sequence of Marine Container Minimizing Space in Container Terminals Fig. 3 Container terminal at the Port of Yokohama. Source: an anonymous Japanese container terminal operator in Port of Yokohama (2000~2010). Arrival records of exporting marine containers at a container terminal in Port of Yokohama (photographed by the author on July 28, 2014). of containers is a costly and time-consuming operation, and because it also presents risks of damage to the cargoes inside the containers, less marshalling is done at better container terminals, as argued by Weilin []. 2.3 Minimization of Space and Marshalling In this regard, this paper presents a proposal of a simple algorithm of stacking marine containers in container terminals, adapting to random arrival of the containers irrespective of their weight but naturally keeping heavier containers stacked higher together with minimization of the stacking space at terminals. Some reports have described topics related to this paper, which were mostly operational studies such as those of Tajima [6] and Yizhong et al. [7]. Unfortunately, such mathematically pure studies do not work well at real container terminals in ports because at a container terminal, there are often more than 10 container ships arriving per week, loaded with thousands of marine containers in which are hundreds of thousands of shippers cargoes. An almost infinite variety of items of commodities are included in the cargoes in the container ships. Moreover, the containers arrive randomly at the container terminal every moment, as referred in Port of Tokyo [8]. All combinations described above cause a so-called explosion of combinations in the field of the operations research, by which the time needed to solve the problem turns out to be unrealistically long, although such a solver might be adopted only theoretically by mathematicians. Actually, a terminal operator described later reported that the allowance of time to produce a stacking allocation for a marine container arriving at the gate of their container terminal was less than one second. No report in the relevant literature describes the solving speed achieved for container terminals at ports. 3. Arrival Record of Marine Containers at a Container Terminal of the Port of Yokohama 3.1 Information on Marine Containers Arriving at a Japanese Major Terminal Operator A major Japanese terminal operator with activities at the Port of Yokohama appreciated the research of the authors and kindly offered arrival records of marine containers at a container terminal at the Port of Yokohama under conditions of non-disclosure of proprietary information. The information offered by
Stacking Sequence of Marine Container Minimizing Space in Container Terminals 89 the operator was presented as follows: identification codes of container ships; sailing routes among ports of call; number of loaded marine containers at the container terminal in Port of Yokohama; weights of respective containers; arrival time (second, minute and hour) and day of each container. This information was observed at the container terminal presented in Fig. 3. 3.2 Arrival Record Details of Marine Containers at a Container Terminal at the Port of Yokohama The information was observed during one month at some time during 2000~2010. The exact year of the observations was not notified to the authors because it is proprietary information of the company, this information was sufficient to achieve the research objectives of the authors. Table 1 presents details of the arrival record of exporting marine containers at the container terminal. 4. Algorithm of Weight Prioritized Stacking of Marine Container for Random Arrivals to Container Terminal 4.1 Weight Ranks for Marine Containers The maximum number of marine containers stacked at container terminals is generally five because of the yard crane height. This is, however, merely a physical limitation. Usually, the stacks should be limited to four in actual container handling operations at most container terminals to prevent inefficiency of marshaling. In this regard, the maximum number of stacking marine containers is set as four in the algorithm proposed by the authors below. There are generally six rows between the legs of the left and right side of yard cranes. Consequently, the algorithm accommodates 24 marine containers stacked in a block in which there are six rows and four marine containers stacked on each row. It was reported during an interview by the authors to the Japanese terminal operator described above in Table 1 Ship code Information on arrival record of exporting marine containers at a container terminal at the Port of Yokohama. Seaway Number of containers loaded into ships in Port of Yokohama 42 Yokohama China (Dalian) China (Qingdao) Yokohama 14 221 Yokohama China (Hong Kong) Italy Holland Germany Singapore Nagoya Yokohama 68 1. Yokohama Nagoya Kobe Hong Kong Kaohsiung; 243 2. Yokohama New Zealand California Mexico America 370 Germany Holland Canada America 1. Yokohama America New Zealand South Korea Taiwan Yokohama; 44 2. Taiwan Hong Kong Singapore Malaysia Sri Lanka 373 Malaysia; 3. A man Italy Spanish Canada American Spanish 1. Yokohama Kobe Taiwan Hong Kong America; 608 2. Hong Kong Shenzhen Singapore Malaysia Spain United Kingdom Holland Sweden Germany Holland 390 Spain 926 Shanghai South Korea America New Zealand American Yokohama Nagoya Shanghai 80 98 N/A 80 21 N/A 89 Source: an anonymous Japanese container terminal operator in Port of Yokohama (2000~2010). Weight of containers Gross weight of containers (a box of containers with cargoes inside) recorded by the kilogram Arrival date and time of containers to Port of Yokohama Arrival sequence of containers recorded by date, time, minutes and seconds
90 Stacking Sequence of Marine Container Minimizing Space in Container Terminals Section 3.1 that the weights of marine containers were ranked by units of or 10 t because it was sufficient for calculating ship stability and it is also better to reduce unnecessary computational loads on server computers at container terminals. Consequently, in the algorithm, the weight unit was set as t. Consequently, six weight groups were composed as follows: less than t; to less than 10 t; 10 to less than 1 t; 1 to less than 20 t; 20 to less than 2 t; equal to or greater than 2 t. The legal gross weight limit of a marine container with cargoes loaded inside under the International Safe Container Convention is about ~3 t, which depends on the kind of structure of marine containers. Therefore, the six ranks above are practical and suitable for the six rows between the legs of the yard cranes. 4.2 Pair of Mutually Conflicting Extreme Concepts Stacking space, i.e., the number of blocks, can be minimized when marine containers are stacked solely according to the order of arrival at the container terminals. However, it would drastically worsen marshaling. No marshaling occurs when marine containers are stacked solely according to the weight ranks presented above. However, it would cause the worst number of blocks there because the total number of containers in each weight rank differed, as shown in Fig. 4. Consequently, it is readily apparent that both concepts of stacking the containers are useless. Therefore, an algorithm able to incorporate both must be created. 4.3 Algorithm of Stacking Containers Enabling Minimization of both the Number of Blocks and Marshalling To enable minimization of both the number of blocks and marshalling at container terminals, the authors proposed the following algorithm: (1) start the algorithm; (2) set a block in the container terminal for stacking marine containers that have arrived; (3) categorize rows in a block according to the weight rank as described above; (4) accept an arriving marine container; () identify the weight rank of the container and set it as the indicator for searching a targeted row; (6) search a row by the indicator with less than four marine containers stacked from the first block to the end one, i.e., at the beginning of the algorithm, the first block is the same as the end one; Fig. 4 Consequence of stacking marine containers according only to the weight ranks.
Stacking Sequence of Marine Container Minimizing Space in Container Terminals 91 Stack by the algorithm proposed proposed by the author by the author 1 10 10 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 1 1 1 2 20 20 2 2 2 2 2 2 2 2 2 2 2 2 2 Space reduced ~ ~ t t t~10t t~10 t 10t10 ~1t t~1 t 1t1 ~20t t~20 t 20t ~2t t~2 t 2t t~ ~t t or heavier Fig. Mechanism of minimizing both the number of blocks and marshaling. (7) stack the container on the row of the block if the row is found by the last block, and replace the category of the row of the block to the weight rank of the container stacked: no replacement of the category occurs as long as the row is found by the initial indicator, then go to x; (8) set a lighter weight rank than the present indicator as the new indicator if the category of the row searching for the stack is not less than t, and go back to vi; (9) forward a new block and reset the new indicator as the weight rank of the container again and go back to vi; (10) end the algorithm if the container was the final one to be accepted, and else go back to iv. Fig. shows how the algorithm works. No problem arises when heavier containers are stacked on lighter containers at a row in a block, although the initial weight category of the row differs from that of stacked containers. The indicator in the algorithm allows each row to change its weight category to adopt heavier marine containers to the greatest degree possible. This algorithm might be designated as an algorithm of weight prioritized stacking of marine container for random arrivals to container terminal, which could be abbreviated to AWPSMC.. Reproduction Simulation of Stacking Marine Container by AWPSMC with Real Arrival Record of Exporting Marine Containers.1 Simulation Overview A computer simulation model was programmed based on AWPSMC. The real arrival record of marine containers at a container terminal at the Port of Yokohama, as shown in Table 1, was used for the simulation model. Computations related to stacking of marine containers were done not only by AWPSMC, but also according to the order of arrival and weight ranking only. Results of the computations were compared with the number of blocks needed and according to whether marshalling is needed or not. The computations were also done separately by each group of containers loaded to the six ships, as shown in Table 1..2 Verification of Simulation Results Table 2 presents results of the computations by the simulation model.
92 Stacking Sequence of Marine Container Minimizing Space in Container Terminals Table 2 Simulation results for the algorithm of AWPSMC and for the order of arrival and weight ranks. Ship code Stack method Block numbers Marshalling 221 926 21 42 44 243 608 98 Order of arrival 29 Yes Weight rank only 44 No AWPSMC algorithm 29 No Order of arrival 4 Yes Weight rank only 7 No AWPSMC algorithm 4 No Order of arrival 4 Yes Weight rank only 6 No AWPSMC algorithm 4 No Order of arrival 7 Yes Weight rank only 17 No AWPSMC algorithm 7 No Order of arrival 16 Yes Weight rank only 29 No AWPSMC algorithm 16 No Order of arrival 16 Yes Weight rank only No AWPSMC algorithm 16 No Order of arrival 17 Yes Weight rank only 22 No AWPSMC algorithm 17 No Order of arrival 4 Yes Weight rank only 11 No AWPSMC algorithm 4 No AWPSMC was able to achieve the minimum number of blocks with no marshalling necessary, whereas the algorithm according only to the order of arrival needed marshalling to achieve the minimum number of blocks. The algorithm using only the weight ranks achieved no marshalling but needed almost two times greater number of blocks compared to the result obtained by AWPSMC. These conditions of results did not differ from the ships loading the containers, although the number of containers, the sailing routes and the ports of call were substantially different from each other, as shown in Table 1. 6. Conclusions This paper introduced the algorithm of weight prioritized stacking of marine containers for random arrivals to container terminals and simulation using the algorithm to reproduce stacking of marine containers recorded at a container terminal in Port of Yokohama. The algorithm achieved the minimum number of blocks with no marshalling. The algorithm is independent of any complex mathematics such as operations research, but it follows the simple sequence as shown in Section 4.3. This algorithm is better for container terminals in that it does not force a computational load onto server computers of the container terminals unnecessarily. Such computers are invariably busy processing huge amounts of information related to shipping and logistics with their customers, such as shipping lines of ships and shippers of containers. The algorithm might be applied for prioritizing not only by weight but also by other characteristics of marine containers, such as sequence of ports of call, dangerous cargoes included or not, and the degree of vulnerability of cargoes inside. In this respect, the authors intend to aim their research at combining more than two priorities into the algorithm.
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