Stacking Sequence of Marine Container Minimizing Space in … · 2016-05-10 · Journal of Traffic...

Journal of Traffic and Transportation Engineering 4 (2016) 86-93 doi: 10.17265/2328-2142/2016.02.003

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 135-8533, 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

D DAVID PUBLISHING

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

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 [5].

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


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 Information on arrival record of exporting marine containers at a container terminal at the Port of Yokohama.

Ship code Seaway Number of containers loaded into ships in Port of Yokohama

Weight of containers

Arrival date and time of containers to Port of Yokohama

42 Yokohama→China (Dalian)→China (Qingdao)→Yokohama 154

Gross weight of containers (a box of containers with cargoes inside) recorded by the kilogram

Arrival sequence of containers recorded by date, time, minutes and seconds

221 Yokohama→China (Hong Kong)→Italy→Holland→ Germany→Singapore→Nagoya→Yokohama

685

243 1. Yokohama Nagoya Kobe Hong Kong Kaohsiung; 2. Yokohama New Zealand California Mexico America →Germany→Holland→Canada→America

370

44

1. Yokohama→America→New Zealand→South Korea→ Taiwan→Yokohama; 2. Taiwan Hong Kong Singapore→Malaysia→Sri Lanka →Malaysia; 3. A man Italy Spanish→Canada→American→Spanish

373

608

1. Yokohama→Kobe→Taiwan→Hong Kong→America; 2. Hong Kong Shenzhen Singapore Malaysia Spain→ United Kingdom→Holland→Sweden→Germany→Holland →Spain

390

926 Shanghai→South Korea→America→New Zealand→ American→Yokohama→Nagoya→Shanghai

80

958 N/A 80

21 N/A 89

Source: an anonymous Japanese container terminal operator in Port of Yokohama (2000~2010).


90

Section 3.1 that the weights of marine containers were

ranked by units of 5 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 5 t. Consequently, six

weight groups were composed as follows:

less than 5 t;

5 to less than 10 t;




equal to or greater than 25 t.

The legal gross weight limit of a marine container

with cargoes loaded inside under the International

Safe Container Convention is about 30~35 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;

(5) 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.


91

30303030

25252525

15151515

10101010

5555

10101010

～ 5t 5t～10t 10t～15t 15t～20t 20t～25t 25t～30t or heavier

Stack by the algorithm proposed by the authorSpace re

duced

20202530

30×

×

25

×

15

×

×

55515

10101010

15151515

15151515

25252525

25252525

30303030

30303030

Fig. 5 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 5 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. 5 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.

5. Reproduction Simulation of Stacking Marine Container by AWPSMC with Real Arrival Record of Exporting Marine Containers

5.1 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.

5.2 Verification of Simulation Results

Table 2 presents results of the computations by the

simulation model.

Stack by the algorithm proposed by the author

~5 t 5 t~10 t 10 t~15 t 15 t~20 t 20 t~25 t 25 t~30 t

Space reduced


92

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

Order of arrival 29 Yes

Weight rank only 44 No

AWPSMC algorithm 29 No

926




21




42




44




243




608




958




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.


93

References

[1] GDV (Gesamtverband der Deutschen Versicherungswirtschaft e.V.). 2016. “Shipping Stresses—General Information.” GDV. Accessed April 4, 2016. https://www.containerhandbuch.de/chb_e/stra/inde x.html?/chb_e/stra/stra_02_03_03.html.

[2] Sou, E. 2015. “An Algorithm of Stacking Marine Containers for Prioritizing Orders of Loading into Ships.” Master thesis, Graduate School of Tokyo University of Marine Science and Technology.

[3] Watanabe, Y., and Oikawa, T. 2003. “Environmental Impact of Intermodal Transportation by Trucks on Ports.” In Proceedings of the 2003 International Association of Maritime Economists Conference, 864-73.

[4] Muller, G. 1999. Intermodal Freight Transportation.

Illinois: Intermodal Association of North America. [5] Weilin, L., and Watanabe, Y. 2001. “Statistical

Guidelines for Developing Container Terminal.” In Proceedings of the 2003 International Association of Maritime Economists Conference, 995-1004.

[6] Tajima, H. 2001. “An Innovative Management System of Database for Intermodal Container Transportation.” Logistics System 10 (2): 21-5.

[7] Yizhong, D., and Xiaolong, H. 2006. “A Practical Optimal Model of Berth Planning at a Container Terminal.” Journal of the Marine Engineering Society in Japan 41 (9): 176-82.

[8] Port of Tokyo. 2016. “Oceangoing Container Liners to/from Port of Tokyo.” Port of Tokyo. Accessed April 5, 2016. http://www.kouwan.metro.tokyo.jp/en/business/lin ers.pdf.

Stacking Sequence of Marine Container Minimizing Space in … · 2016-05-10 · Journal of Traffic...

Documents

Transcript of Stacking Sequence of Marine Container Minimizing Space in … · 2016-05-10 · Journal of Traffic...