Dangerous Goods Container Allocation in Ship Stowage Planning

Hao Lei

and Minjae Ok

†

Department of Industrial Systems Engineering and Management, National University of Singapore,

21 Lower Kent Ridge Rd, Singapore

Keywords: Dangerous Goods, Ship Stowage Problem, Stowage Planning, Bay Assignment, Slot Assignment.

Abstract: Ship stowage problem is difficult to solve due to the complex conditions from real-world business. For

Dangerous Goods (DG) containers, IMDG code mandates the different types of DG must follow the minimum

segregation on vessel and in container yard. In addition, DG containers must meet ship requirements and in-

house rules from port and ship owners. However, there is a lack of research on stowage planning including

DG containers. In this paper, we suggest a novel method to assign DG to integrate the existing stowage

planning model. The proposed method is divided into two parts respectively for bay assignment problem and

slot assignment problem. The bay assignment model separates DG containers into segregation level groups

based on standard IMDG segregation table and assigns different group of containers into bays according to

specific ship structure. The slot assignment model is a search-based heuristic model which able to recommend

possible slot for a new coming DG container according to assigned container distribution and segregation

rules between the new coming DG class and the existed ones. An empirical evaluation on a real-world dataset

obtained from a shipping company demonstrates the effectiveness of our method.

1 INTRODUCTION

1.1 Background

Container shipping has always been an extremely

important resource-intensive industry. Under the

shackles of trade protectionism, the growth rate of

global trade has declined significantly. The global

container shipping trade volume is highly correlated

with the world economy. Because the global

economic and trade situation is not optimistic, the

global container shipping trade has declined slightly

in 2018. However, annual container shipping volume

is 201 million TEUs, and the annual growth rate has

dropped to 4.5% (shashi kallada, 2015).

Ship stowage problem is a well-recognized

difficult problem that involves in terminal side, vessel

side and cargo owner side. The optimization of the

ship stowage problem plays a key role in increasing

the profit of shipping companies. Stowage plans are

used to maximize the economy of shipping and safety

on board as shown in Figure 1 and Figure 2. Since

the ship stowage problem is NP-hard problem, the

complexity will be exponentially growing with the

https://www.isem.nus.edu.sg/research/c4ngp/team/LEI-Hao/

†

https://www.isem.nus.edu.sg/research/c4ngp/team/Ok-Minjae/

increase of container amount under traditional

algorithm, which makes it very hard to implement in

real business condition.

Figure 1: Unsuccessful stowage plan causes severe

accident.

Typically, there are several container types;

general container (GP), dangerous goods (DG),

refrigerated container (REF) and abnormal sized

container (OOG) for a loading list in a specific ship

stowage plan, as shown in Table 1.

Lei, H. and Ok, M.

Dangerous Goods Container Allocation in Ship Stowage Planning.

DOI: 10.5220/0009160602410246

In Proceedings of the 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020), pages 241-246

ISBN: 978-989-758-396-4; ISSN: 2184-4372

241

Figure 2: An example for ship stowage plan.

Table 1: An example of the distribution for container types.

Container Type Distribution

GP-non DG 94.3%

REF 3.3%

GP-DG 1.3%

OOG 1.1%

Except for general container, other types of

container are under different special treatment and

conditions. As for dangerous goods, they are articles

or substances which capable of posing a risk to health,

safety, property, or the environment when transported

by air. To ensure the safe transport of dangerous

goods by air, requirements are set in place for both

shippers, freight forwarders and air operators. These

Classes and divisions have characteristic danger

labels (aka warning diamonds) as shown in Figure 3.

Figure 3: Dangerous Goods Classification.

In a ship stowage plan, dangerous goods are

defined based on UN number, IMO Class, packing

group and flashpoint found in safety data sheet.

Vessels carrying excessive amount of DG may be

restricted to berth locations, which is why ship

owners must be careful when they plan to locate

dangerous goods containers somewhere. Therefore,

despite the small proportion of DG in the loading list,

the constraints on the risk of DG are very strict.

The stowage planning studied so far focused on

optimal slotting of only GP and REF. However, the

planning without considering DG is hard to be

applied in practical business since the insertion of DG

after the planning will affect the performance and

constraints, which will lead an unsuccessful plan. In

this paper, we first suggest an effective framework to

integrate DG model into the existing MIP model. In

the following, we suggest new methods for two DG

module; bay constraints of DG and slot assignment of

DG.

1.2 Related Work

Ship stowage problem is a topic of interest in

industrial engineering recent twenty years.

Researchers usually divide this problem into two

parts: bay assignment problem and slot assignment

problem. Algorithms including mathematical

programming, search-based heuristics and rule-based

heuristics have been applied to solving this problem.

For bay assignment problem, it’s formulated as a

set of integer programs and solved by a heuristic

algorithm that employed a general procedure of the

transportation simplex method by Kang and Kim.

Wilson and Roach mentioned that the container

stowage problem concerns a multi-port journey

container placement problem. Anna Sciomachen et

al. tried to minimize the total loading time and allow

an efficient use of the quay equipment by using a rule-

based heuristics model considering size, weight of the

containers and operational and security constraints

which are related to the weight distribution on the

ship. Pasino et al. added stack weight and height

limits and other stacking rules to minimize over-

stowage and free as many stacks as possible. Daniela

Ambrosino et al. provided a 0/1 linear programming

model by using exchange algorithm and

decomposition approach.

However, due to its high complexity and variable

rules for different ships and shipping companies, not

much research work has been done in this area for

dangerous goods container allocation problem. In this

paper, we suggest a framework with 3 modules

including the existing MIP model and the methods to

assign DG into bays and slots satisfying IMDG

segregation rules and ship requirement.

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2 PROPOSED METHOD

2.1 Problem Definition

As dangerous goods can cause tremendous danger to

people, property and the environment, it is crucial

handling them in a safe and compliant manner to

minimize the risks that they may have upon in the

field.

The requirements for the storage and handling of

dangerous goods can be found in the Australian

Standards. The Australian Standards are documents

that outline the best practices for the storage and

handling of dangerous goods in the workplace. Each

dangerous goods class poses different risks upon the

workplace and therefore Standards Australia have

developed a different standard for each dangerous

goods class. Incompatible dangerous goods should

not be transported or stored together to avoid possible

reactions between the dangerous goods or reduce the

hazards of any accidental leakage or spillage. For

incompatible materials, shared transportation or

storage may still be allowed if the materials are

separated from each other by a minimum distance.

Figure 4 represents the dangerous goods segregation

table which shows the segregation levels among all

the DG classes.

Figure 4: Segregation table.

Another requirement we need to consider is ship

requirement which indicates which DG class can be

located underdeck or on deck according to the

property of a certain ship that is applied in addition to

the general segregation rule. Table 2 shows an

example of DG requirement for a ship where x means

‘NOT PERMITTED’ and P means ‘PACKED

GOODS PERMITTED’.

Table 2: An example of ship requirement for DG.

Bay

Class

Underdeck On deck

1,3-5 2 6 1-6 8

1.1 x P x P P

1.4 P P P P P

2.3 x x x P P

2.2 Model Framework

Our proposed framework includes mainly two part;

(1) Bay constraints generation and (2) Available slot

generation. As mentioned in Section 1, our goal is

providing DG information to the existing model.

Therefore, DG constraints reflecting bay-related

regulation is conveyed to the any MIP model, and

then any slotting model will obtain the feasible slots

for a given DG container. Figure 5 describes the

relationship between two frameworks and the flows

between modules. In Figure 5(a), we apply the ship

requirement into each bay structure, which is

explained in section 2.3. Based on the total available

slots per each class of DG, we generate constraints for

the MIP model from segregation table in section 2.4.

Final module calculates all the possible slots out of

available slots for a given DG container from the

slotting algorithm.

Figure 5: Model Framework.

2.3 Bay Capacity for DG

For a certain ship, each bay has its own structure that

indicates the number of slots available. Due to the

special requirement of ship in Table 2, we need to

limit the number of available slots per each bay and

each DG class. Since DG class is given by a container

list, this module only calculates available slots for the

given DG. The result of this module is used to define

Dangerous Goods Container Allocation in Ship Stowage Planning

243

a DG feasible region for the next step, generating DG

constraints.

2.4 DG Constraints for MIP

Following Section 2.3, we suggest an algorithm to

determine how many DG containers can be located at

each DG feasible region per bay for a given DG list. In

addition, we decide the minimum bay interval when

the distance should be longer than the size of feasible

region. From the loading list provided by shipping

company, it is easy to find dangerous goods class of

each container converted by UN number. What needs

to be emphasized is, there could be several UN

numbers in one DG container due to the mixture of

different types of hazardous cargo. So that when we

think about the allocation of DG containers, it is

necessary to concern all DG classes packages in one

container. Here is an example about how to search

segregation level from the segregation table and DG

container data.

Example 1

UN 1263, Class 3

UN 1944, Class 4.1

1. Column 16b of above both UN Numbers does not

contain any segregation codes

2. Intersecting column between classes 3 and 4.1 in

segregation table shows “x”

Conclusion = Both may be packed in same container

or stowed together.

In pre-processing, we will create segregation level 3,4

matrix A:



0⋯1

⋮⋱⋮

2⋯1



For every element 



(for ∀∈,∀∈) of matrix A,

we have







0,1,2

4

3

Then we can use two functions to separate

segregation level class pairs. After filtering and

separating all DG groups, we will come up with

mathematical constraints generated automatically for

each segregation level group. Together with general

container allocating constraints and stability

validation constraints, we’re able to generate a table

with container type, container DG class, bay number

and number of this containers which can assigned into

this bay.

2.5 Slot Assignment of DG

For slot assignment model, it works like a black box

in which an automated calculating program inside.

When the main program of general slot assignment

model finds that next coming container is DG

container, it will call the DG slot assignment model

with input data of the coming container and exist DG

containers in same bay and adjacent bays. Detailed

input and output have been showed below.

For DG slot assignment model, the input is:

1. block/bay structure: discrete integer points group

in coordinate (r, t)





= {(



, 



), (



, 



), …, (



, 



)}

2. vessel structure 



,



,



,…

3. exist DG container slot location (



, 



), with

DG category 





(p: POD, d: dangerous good

class)

4. new DG container with category 





(p: POD, d:

dangerous good class)

Output is:

Possible slot for this new coming DG container

(



,



) ∈,

After DG slot assignment model return the possible

slots for this new coming DG container, the main

slot assignment model will find overlapping parts of

the feasible domain and assign this DG container in

the domain randomly.

3 EXPERIMENTAL RESULT

To validate the performance of our algorithms, we

used a real-world container list from a shipping

company in Singapore and ship information for a ship

with 13686 TEUs. Table 3 shows the DG feasible

region on each bay.

Table 3: DG feasible region.

Number Rows Tiers

01 8 8

02 9 9

03 7 8

04 6 9

05 8 10

The loading list can be summarized as Table 4

using a mapping table from IMDG code to numeric

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244

class code; 1 to 17 according to the same distance

group.

Table 4: Loading List.

class

Number of Containers POD

1 5 Sin

apore

2 4 Sin

apore

5 8 Singapore

8 2 Sin

apore

16 6 Sin

apore

1. Get all DG classes with POD: Singapore from

loading list:

[1, 2, 5, 8, 16]

2. Find all distance level pairs from DG class:

{[1, 5, 0], [1, 8, 1], [1, 16, 1], [2, 1, 0],

[2, 2, 0], …}

3. Filter segregation level 3 pairs:

[2, 8, 1]

4. Find segregation level 4 pairs:

{[1, 8, 1], [1, 16, 1]}

5. Get constraints for all segregation pairs. Final

output of constraints showed in table 5:

Table 5: Bay Assignment Output.

class 1

class 2

Bay

number

Inside Constraint

2 8 Bay 01 















48

1 5 Bay 01 















56

1 2 Bay 01 















56

2 2 Bay 02 







5

For DG slot assignment model, we interpreted a

small part of bay assignment data as an input.

Table 6: Slot Assignment Input.

DG Class Assigned Bay

Number of

Containers

1 Ba

01 5

2 Bay 01 4

5 Ba

01 8

8 Ba

02 2

By calling the DG assignment model for DG

containers one by one, the output is showed below:

Table 7: Slot Assignment Output.

DG Class Assi

ned Ba

 Possible Slot

1 Bay 01

(1,2), (1,3),

(2,2), …

2 Bay 01

(1,2), (2,3),

(4,2), …

5 Bay 01

(3,1), (3,2),

(3,3), …

8 Bay 02

(1,1), (1,3),

(2,1), …

Using the result of Table 7, any slot assignment

model will find overlapping parts of the feasible

domain and assign DG containers one by one with

other types of containers according to stacking rules.

In summary, From the result of Table 5, we can

add the constraints into any MIP model to determine

the number of containers in each position. After

determining the number of containers, sequential

allocation module for stacking containers finally fix

the slot of containers out of the result of Table 7.

4 CONCLUSIONS

In this paper, we proposed a method to find feasible

solutions for dangerous goods allocating problem in

ship stowage planning. We used real-world data to do

experiments and get in-house rules from ship

companies. We successfully built a bay assignment

model to separate DG containers into segregation

level groups based on standard IMDG segregation

table and completed an MIP model with constraints

about hazardous containers to assign different groups

of containers into bays according to specific ship

structure. We made the slot assignment model as a

function which can be called to recommend feasible

slots for a given DG container according to assigned

container distribution and segregation rules between

the new coming DG class and the existing ones.

As a future work, we need to consider any in-

house rule that applies only a specific port as user-

defined input. In addition, unlike the standardized

DGs discussed so far, there exist OOG-DG type of

containers, which is difficult to handle since they

have the property of both OOG and DG. We can use

data mining technology to find patterns of special

types of slotting inside the data based on the historical

data from shipping companies.

Dangerous Goods Container Allocation in Ship Stowage Planning

245

REFERENCES

shashi kallada. June 3, 2015. Stowage and Segregation of

Dangerous Goods on General Cargo Ships. IMDG

Code Compliance Centre

J. G. Kang, Y. D. Kim. Stowage planning in maritime

container transportation. Journal of the Operational

Research Society (2002) 53, 415¨C426.

ID. Wilson and PA. Roach. Container stowage planning: a

methodology for generating computerised solutions.

Journal of the Operational Research Society (2000).

Anna Sciomachen, Elena Tanfani. A 3D-BPP approach for

optimizing stowage plans and terminal productivity.

European Journal of Operational Research (2005).

Pacino, Dario, Jensen, Rune Møller. Fast Generation of

Container Vessel Stowage Plans. PhD Thesis (IT

University of Copenhagen)

Daniela Ambrosino, Anna Sciomachen, Elena Tanfani. A

decomposition heuristic for the container ship stowage

problem. Journal of Heuristics (2013).

APPENDIX

Appendix 1: part of Matrix A.

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