3D Container Loading

This dissertation examines three dimensions (3D) container loading problem with the primary objective of maximizing the utilization of 3D container space. Based on the traits of mathematical loading approaches, this dissertation develops an effective solution to 3D container loading problem which will ensure the use of 3D container entirely, ensure the stability of the vessels, maximum loading and timely delivery of the order.

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Abstract
This dissertation examines three dimensions (3D) container loading problem with the
primary objective of maximizing the utilization of 3D container space. Based on the traits of
mathematical loading approaches, this dissertation develops an effective solution to 3D
container loading problem which will ensure the use of 3D container entirely, ensure the
stability of the vessels, maximum loading and timely delivery of the order. Both primary and
secondary data collection approaches were utilized in generating ideas, which were then used
to formulate this solution. Strongly and weakly different loading information was also used
to recommend the most suitable formula. Findings show that this approach will attain a
maximum solution to the problem to slightly above the current 70.64% performance of
procedures captured in the literature review.

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Contents
I. Abstract....................................................................................................................................2
1. CHAPTER ONE: INTRODUCTION......................................................................................4
1.1. Introduction of Container Loading.......................................................................................4
1.2. Container Terminal...............................................................................................................5
1.3. The History of 3D Containers...............................................................................................5
1.4. The Container Loading Problem..........................................................................................6
1.5. Statement of the Problem....................................................................................................10
2. CHAPTER TWO: LITERATURE REVIEW.......................................................................12
2.1. 3D Containers Loading Approaches...................................................................................12
2.2. Summary of Literature Review..........................................................................................21
3. CHAPTER THREE: METHODOLOGY...............................................................................23
4. CHAPTER FOUR: RESULTS..............................................................................................24
5. CHAPTER FIVE: DISCUSSION..........................................................................................24
6. CHAPTER SIX: CONCLUSION AND RECOMMENDATIONS.......................................24
References......................................................................................................................................25

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1. CHAPTER ONE: INTRODUCTION
The problem of three Dimensions container loading has existed for over five decades.
However, modern approaches have failed to offer a permanent solution to the issues.
Surprisingly, the current approaches to mitigation of 3D container problems are advancements of
the previously existing methods (de Azevedo et al., 2012). Also, it is quite absurd to note that
some suitable approaches and opportunities have never been utilized, yet can provide an
appropriate solution to this issue. This description encloses the theme of this Dissertation. Based
on this phenomenon, this dissertation presents an in-depth analysis of the state-of-art in the field
of 3D container loading. The problem of packing three dimension containers is an issue that has
been generated naturally from the ancient containers, namely the one dimension and two
dimension containers (de Azevedo et al., 2012). This issue is mostly associated with the package
of products that can easily fit in tanks or trucks and the products that are first packed on the
pallets.
1.1. Introduction of Container Loading
Transportation at sea all starts with container loading. Container loading is broadly used
to mean arranging or packing goods of various sizes and design in a container such that each
space within the container is counted for both for economic gain and efficient transportation.
Container loading is done based on some specific requirements. The primary person in the
container loading process is the shipper. The shipper is responsible for efficient filling of the
container and does this by selecting the right container. The shipper must check and record the
vessel chosen to ensure that the demands of the order are entirely met. He also examines the
status of the tank to check if there is any leakage, especially around the doors. In this regards, the
entries are efficiently reviewed before loading to avoid wastage of time. Damaged areas and

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repairs are also tested to ensure that the container is in good shape. After selecting the right
container and testing it to ensure that it is the right container for the job, stuffing is then done.
This marks the beginning of the cargo loading process. This process is crucial for the entire
transportation process, and the shipper must ensure that the load is spread evenly within the
container (Tran-Dang, Krommenacker, and Charpentier, 2017). Uneven loading can cause
damage to the cargo. In this regards, all the spaces within the container, ranging from one wall to
the nest, must be utilized entirely. Parking the container tightly is crucial in keeping the cargo
safe by limiting movements that might lead to damages.
1.2. Container Terminal
The use of the container in transporting goods for trading and transportation services has
become crucial in the present days than before. This importance is expected to increase shortly
and beyond due to the rapid growth and development of trade across the world. Based on initial
studies, the number of containers that are shipped internationally is expected to grow to over 500
million by 2022. The increase in container use in the international business was influenced by the
introduction of large vessels, which require not only more but deeper wafts for the temporary
storage of the containers. Also, the use of container gained more essence following the
introduction of three dimension containers, which are advancements from the 1D and 2D bottles.
1.3. The History of 3D Containers
Containers have been taken for granted in the present society because they are common
and can be seen in every port or even along the roads being transported by trucks to various
destinations. However, it is essential to note that containers have come a long way to the
presently used 3Ds. The history of shipping containers is dated back beyond the pre-shipping
period when the man moved across seas taking food and raw materials barely inside a boat.

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However, boats were also few and could be hardly present in goods collection points. In this
regards, products were collected in a port warehouse as the shipper waits for a boat to come. In
those days, goods were loaded into the vessel typically through the use of crates, bales, and
sacks. This ancient mechanism was referred to as break bulk cargo as one ship would carry about
200,000 loads. This situation depicted the utmost level of lack of standardization as it took a lot
of time for products to be transported from the ships to a cargo. This inefficiency induced the
urge to standardize the shipping process. As a result, McLean created the first type of containers
at around 1995. However, the journey remained procedural. For instance, he first introduced one
dimension containers, which the latter advanced having been convinced by his ideas. Later on,
he developed the 2D vessels to 3D, which are widely used today for shipping activities, and are
present at virtually every sea and airports. However, his development did not mean that the
advancement of the containers stopped. Beyond 1956 to date, containers have been standardized
and also expanded considerably to make the shipping process more efficient.
1.4. The Container Loading Problem
The emergence of 3D containers enhances the shipping process. However, it does not mean that
it guaranteed success because, in some instances, the shipping process turns up to be a massacre
or unsatisfactory. This notion implies that it takes a specialist to load a container for safe and
secure shipment efficiently. There are fundamental problems that must be handled efficiently for
the shipping process to be a success (de Azevedo et al., 2012). This concept forms the base of
this Dissertation.
3D container loading problems primarily trigger issues about shipment planning and
loading of the order in a suitable position to ensure specific constraints. According to Tran-Dang,
Krommenacker, and Charpentier (2017), this Dissertation stretches significantly to engineering

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background and the present day management of containers along the shipment line, which is
marked by the two main terminals. Generally, the issue of container loading in Nondeterministic
Polynomial (ND) complex issue targeting at creating a mathematical approach and establishing
efficient formula based on the various shipping environments. The three dimension container
loading problem is grouped into 14 categories based on cargoes. However, only two of the 14
types formed the basis of this Dissertation since they are the most general and capture virtually
all concepts of the problem (de Azevedo et al., 2012). The relatively complex NP problem has
been solved partially over the past years through the use of mathematical approaches captured in
existing scholarly publications. These approaches are enclosed under the broad umbrella of
intelligent optimized method, which includes the tabu, simulated annealing, and genetic
calculation
The above approaches are typically used to solve practical container loading issues.
These models are also grouped into two main categories, namely improved heuristic and
placements heuristic. The latter is sometimes referred to as the basis heuristic, which entails
searching for the solutions and applying them typically based on the loading rules. The basic
heuristic is commonly used to solve the container packing issue. Although this approach is not
fully efficient as captured on some early studies, it can offer a reliable solution to 3D container
loading problem (Tran-Dang, Krommenacker, and Charpentier, 2017). On the other hand, just as
the name suggests, an improved heuristic approach is a hybrid formula formed by combining the
basic historic model with different search methods from the neighborhood.
Robinson and George proposed a representation of theheuristic placement through their
first introduction of the concept of layers in the trading field. Based on their method, 14
heuristics were created by Marriott and Bischoff by mixing three approaches and six following

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rules that initially existed. After that, Nee and Loh surveyed a weakly different theistic problem
by taking and using the charge density as an objective function. They recommended building a
horizontal layer during loading of the container then loading from the bottom going upwards.
They also designed 15 test data sets, which were commonly used large form formula as standard
data sets. Progressively, Ngoi et al. recommended that the most suitable way of loading the
container is horizontally and rotationally. By abandoning the layers concept, they formulated a
unique approach of representation of matrix to simplify the loading steps. Then came Radcliff
and Bischoff, who proposed a heuristic approach with several destinations contracts based on the
place where the cargo was ordered and how they arrived. Instead of building layers as had been
proposed earlier, this technique makes columns to ease loading of similar cargoes in a particular
space.
Matric spacing, similar to Ngoi et al.’s was also used in their approach. A tabu search
method was proposed by Gehring and Bortfeldt to solve the 3D container loading since they
believed that it ensures maximum stability of the containers (Tran-Dang, Krommenacker, and
Charpentier, 2017). Flowing continuous advancements, they created two composite approaches
for loading the containers. They include a block composing os similar cargoes and another block
containing two separate shipments. This plan was later advanced by Wu and Chien to come up
with a better loading plan in the same approach that was adopted earlier by Robinson and George
(Tran-Dang, Krommenacker, and Charpentier, 2017). However, none of these approaches
seemed useful because even after being applied for numerous years, loading issues still exist in
the shipping process.
This Dissertation proposes a novel adaptive generic calculation approach that integrates
two-stage actual-number encoding technique and a dynamic space division approach to improve

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the existing solutions to the 3D container loading problem. This solution is sufficient enough to
avoid wastage of space; this method's novelty is described as shown below.
I. Based on the nature of the 3D container loading issue. This approach calls for the
adoption of a two-phase actual-number encoding approach. Here, the design of the
cargo is given priority.
II. An adaptive crossover of dynamic mutation operators designed based on genetic log
to prevent weak convergence that may result from coding changes. Significantly,
strongly and weakly heterogeneous data will be used in this approach concurrently to
test the efficiency of the proposed method. This notion implies that the final solution
will be sufficient enough to solve the 3D container loading problem entirely (Tran-
Dang, Krommenacker, and Charpentier, 2017). The selection of 15 standard sets of
data tests is strategically used in the proposed solution as with it, at no any
circumstance will the utilized space fall below 70%. This notion implies that the
settlement proposed in this Dissertation is the best compared to the earlier solution
proposed in existing scholarly publications, as discussed above. Precisely, this
approach increases space utilization by at least 4.42%
Organization of the Subsequent parts of the Dissertation
The next section presents an in-depth look at the 3D container loading problem. Constraints
and objective functions are also provided in the next section. Chapter 2 will introduce a
literature review of the container loading problem concerning 3D containers. Chapter 3 and 4
presents the proposed solutions while experimental results will be captured in chapter 5,
which will also contain benchmark data. Chapter 6 will attract conclusion and
recommendations.

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1.5. Statement of the Problem
There are various models used in container loading. So, by using integer linear
programming model (MILP) container loading can be done. The main issue that occurs in
this is instability which mainly occurs. It causes damage to products and people are not able
to handle them. Here, generic algorithms are designed which are basis of problem.
Perimeters of the model are:
(i) the length of the container
(ii) The width of the container.
(iii) The height of the container.
Thus, for solving issue time constraint model are taken into consideration. Another model
that can be used is planning horizon in which products with first delivery date are S=1 is put
first and then second S=2 and so on.

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2. CHAPTER TWO: LITERATURE REVIEW
2.1. 3D Containers Loading Approaches
Three Dimensional container loading problem considers all the three dimensions, namely
height, breadth, and length. In the container loading, a set of bins that are intended to be packed
into the container have been greatly minimized by the use of various approaches as captured in
previous studies. The main objective of reducing wastage of space within the container to reduce
the intern costs. According to Gonçalves and Resende (2013), the container can be loaded in
various workstations. However, existing scholarly publications indicate that suitable loading
should be done in not more than one workstation as a way of balancing the problem. The loading
process always starts by laying the foundation, which is well mastered by the primary loader.
This implies that less the primary shipper is transferred to the next workstation, the second
shipper may face challenges in loading the container. As a result, space may be underutilized.
Existing literature related the problem of loading 3D containers with cartons with various
sizes, which may result in overlapping constraints and change in orientation of the boxes.
Because the NP-hardness of the problem is strong, integer programming method can only offer a
solution to situations where few cartons are to be loaded optimally. According to Bortfeldt and
Wäscher (2013), there are three 3D containers loading approaches that are captured in the
existing literature. They include following package, pre-location loading approach, and
simultaneous packing method.Fuzi logic and general concepts were also used over the past few
years to maximize the utilization of space within the container by optimizing the number of
packed bins. However, this approach gave much consideration to the weight of the drawers. For
instance, the more large bins were laid at the bottom of the container.

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Zheng, Chien, and Gen (2015) examined the use of GA to solve the problem of 3D
container loading. This method was initially used to maximize the utility of space in 2D
containers. This approach is elaborately used in container loading. For instance, besides dealing
with the classification of the bins and the vessels, it also focuses on generic associate operators
and other techniques. According to Zheng, Chien, and Gen (2015), the GA approach can be used
to solve a variety of issues regarding 3D container loading. According to them, the GA approach
can be used to minimize problem optimization, whose complexity tends to increase with the
increase of geometric parameters. They also borrowed the idea of packing several orders of
clients into multiple 3D containers. Packing maximum number of bins into a bowl limits the
dimensions of the cargo. Based on this notion, Zheng, Chien, and Gen (2015) recommended
packaging of drawers into the container by using an overall approach with the arrangement done
for the container's left-bottom corner. While using this technique, he emphasized that the shipper
should ensure that there is no overlap.
An earlier approach that divided the empty container into columns also seemed suitable
in solving the problem of container loading. The loading method that was devised by Chien and
Wu in 1999 was called a heuristic module and depended on the column to determine the loading
capacity of an empty container. This arrangement pattern was achieved by classifying the bins
based on type and volume. Chien and Wu also recommended the use of various approached in
filling the remaining spaces to ensure that the capacity of the container is utilized maximally.
Another earlier approach that was used to load the tank is a heuristic method, which was devised
by Johannes et al. 2000. However, it is essential to note that this approach should not be entirely
depended on because it was recommended for the arrangement of palates, which differs slightly
from container loading. However, the two concepts are more or less the same.

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The heuristic model depended on Branch and bound method approach in optimization of
the number of smaller rectangular bins before they were loaded into pallets while considering the
stability of the item. Other factors that were equally considered in this approach and that makes it
relevant as far as loading a 3D container is concerned are splitting constraints, placement
constraints, distribution of weight over the pallets, connectivity constraints and the demand of
order (Gonçalves and Resende, 2013). This approach was cost- efficient as transportation costs
were reduced by minimizing the number of the needed pallets. This notion means that there was
a possible deficit on the orders at the long end, this approach focused majorly on filling the
spaces within the container through the systematic arrangement of the pallets and not
maximizing the order quantity. In this regards, it was criticized by Mertello et al. (2000), who
believed that it does not consider the interests of customers. As a result, they provided an
formula of filling multiple containers without reducing the number of pallets.
This approach seemed more affecting than the heuristic model holistic model because it
focused on the maximization of the space within the container, while at the same time
completing the order by providing the required number of bins. Their central assumption was
that bins should be marked and similar trays arranged orthogonally to ensure maximal loading
and utilization of the space within the container entirely. In this regards, they recommended that
for a dynamic 3D container loading, the edges of the bin should be parallel with the boundary of
the container and also with each other (Zhao et al., 2016). In other words, they advocated for
aligning the trays within the edge of the bowl. This approach recommended that bins should be
packed optimally for the space inside the container to be utilized fully. This approach seemed
theoretical useful but may impose further challenges in loading the tank, especially in instances

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where the sizes of the bins vary. As a result, more approaches were devised, including the hybrid
GA.
A simple recursive uniform method that is often referred to as n-triad graph method has
also been used in some instances to load three dimension containers. This approach entails
categorizing input bins according to a bin symmetry format, after which they are parked in sub-
containers to form homogeneity in the containers. It also involved employing rotational and
reflective symmetry concepts to group the bins. The orientation of cartons in 3D containers was
evaluated through the use of a Tabu search framework. This framework was designed by Lodi et
al. in 2012. In application, this approach hardly considers packaging constraints (Bortfeldt and
Wäscher, 2013). The Tabu search framework is a mathematical optimization tool from the
trajectory class. It boosts the performance of the local search approach by employing a memory
structure that describes the visited solutions. This approach generally works by detecting suitable
solutions or ways of loading the 3D container and marking them as "taboo'. However, it still
failed to solve some of the issues such as complex 3D container loading problem. As a result,
more and more research was conducted to provide a universal solution to the 3D container
loading problem.
A tree-based greedy heuristic formula was developed in 2002 to solve various problems
that are associated with container loading. According to Bortfeldt and Wäscher (2013), this
approach solved the problem by grouping identical bins into blocks, after which tree logarithm
was used to load the blocks into a container. This method considered the stability and load of the
vessel. Progressively, a Tabu search approach was developed in 2003, which focused on weekly
different capacities to solve the loading problem. This development was a significant
improvement as it enhanced the container loading process by a more substantial margin. Later,

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an enumeration method and an upper bound approach were devised (Gonçalves and Resende,
2013). It entailed the maximum packing number of loads in the container in a significantly short
duration. This method was even more efficient than previous approaches. While it ensured
maximum packaging and utilization of all the spaces within the 3D container, it used an integer
linear programming approach to enhance the stability of the container and reduce the
consumption of fuel.
Other advancements in loading 3D containers were also evident in the flight sector,
where the main container loading objective was to maximize the number of bins being loaded
into the 3D containers. While doing so, measures were also put in place to minimize the amount
of fuel consumed during transportation of the packets through the air and to boost the stability of
the aircraft. This approach entailed modifying First-fit and best fit-decreasing formula to
iterative-best and iterative-first-fit (Gonçalves and Resende, 2013). These two approaches were
used to pack bins inside the container consistently while rotating their shapes continuously until
the optimal solution to the loading problem is achieved. This was a tireless procedure, which
could also lead to wastage of time. It focused much on the utilization of the space within the
containers but failed to consider order delivery time frame. In this regards, issues rose about the
extended time taken in loading the containers.
A step-by-step packing procedure was devised in 2004 to visualize and determine pattern
through simulation, which was aimed at maximizing the number of bits loaded into the container
and enhance the loading speed. This container loading approach was made in a systematic
manner in which similar tins were used to form rips, which were then used to load the container
by attaching them to the wall of the vessel. In this case, key factors such as base area, dimensions
of X-axis, Y-axis, and Z-axis were used to sort the bins. Before, placing the strips, the shipper

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should check the unpacked space inside the 3D container through the use of a formula approach
for placement of every bin (Gonçalves and Resende, 2013). After that, bins are placed in the
unpacked space suitably to march all the dimensions of the area.
In 2001, a significant approach was introduced by Luitpold et al., who packed online tins
into a few containers while considering certain constraints. These constraints included boundary
crossing constraints, overlaying, and taking the shortest time possible to load the tank by using
two heuristic methods. The first one was modified to the first-fit while the second is entailed
arranging the bins differently them using the bulks to fill the spaces within the container
(Gonçalves and Resende, 2013). An approach for prismatic loading bins was developed in 2004
by Macro. The main objective for the Macro's plan was to fit the larger sizes of containers into a
minimal amount of bins, thus saving space and maximizing transportation of packages. In this
arrangement, trays were rotated at 90º to attain orthogonal edges.
The Augmented-Neural-Network was also used to solve the classical bin loading issue.
Augmented-Neural-Network entailed combining an interactive learning approach with a priority-
rule heuristic method to load the container efficiently and within the shortest time possible.
Artificial Neural Network (ANN) is a system used in processing information during loading and
entire loading process. ANN is inspired by nervous systems such as the brain and is also useful
in treating information during shipment. This approach was applied in the 3D container loading
process for the first time in 2004 (Zhao et al., 2016). While it is quite evident that the ANN used
in this case resembles the human brain, it deeds data to train the nervous system efficiently. Out
of the 490 problems that were tested with this approach, 452 were solved entirely. Up to this
stage, it was now clear that modern methods were becoming significantly effective. For example,

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the ANN approached only left a gap of about 0.38% (Bortfeldt and Wäscher, 2013). However,
more efforts were needed to fill the remaining gap.
Non-linear decision method was also used to optimize the process of similar packaging
cylinders based on diameter and height into circular and rectangular containers of different sizes.
This approach was majorly based on the concept of batched online tin loading. A batch is a
collection of many bins with a separate sequence for packaging. The main objective of this
approach is to reduce the number of needed containers (Bortfeldt and Wäscher, 2013). In this
context, even though this approach may ensure maximum utilization of the interior space of a
bottle, it might fail to meet the requirements of the order since the focus is shifted to the area and
not on the needed number of containers.
Cranes were also adopted to aid in the 3D container loading activities. Nonetheless, the
cranes could not work independently and required the application of a bound and branch
formula, which was proposed as a solution to the scheduling issue by dividing the terminal of the
containers into square yards (Gonçalves and Resende, 2013). Tanks were also grouped
accordingly to minimize the transportation duration. Observably, this was a mixed integer
mathematical approach. The results indicated that traveling duration increased with an increase
in the problems. As a result, a multi-objective integer programming was developed and used
simultaneously alongside load planning and stowage for loading containers in the yard stack
within the shortest time possible, while at the same time considering spaces and the number of
needed bins (Zhao et al., 2016). Besides, this approach found the stability of the ship and
minimal handling turns. The main focus of this approach was to avoid crushing damages. The
systematic arrangement of tins obtained this objective after arranging them according to on
weight or volume, such that the most massive bins were arranged at the bottom of the container

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while the lighter ones with minimal amount were put at the top. Also, similar tins were arranged
vertically to observe the consistency in the volume pattern. Seemingly, this approach seemed
more efficient compared to its predecessors. However, this arrangement approach left some
spaces in between the cylinders, which were then filled by using bins with enough load and
bearing strength. Trays were also rotated suitably to fill the remaining areas. A similar approach
was applied in loading 3D containers in air cargo, where the linear programming model was used
to determine the lowest bound volume based on the available weight or size of the bins. The
secrecy behind this approach was to formulate a loading plan with minimal deviation from the
lowest point within the container.
The concept of penalties was also adopted in an attempt to solve the 3D container loading
problem. In applying this concept, First-fit, dual next-fit-decreasing, and first-fit-decreasing
methods were selected load bins with high profit and lesser penalty values. In this context,
penalty values were used n loading infeasible bins into the container. The packaging proses in
this context started with optimization of the volume of the container by using the randomized
heuristic container method which optimized similar prismatic bins and using a wall-building
approach to pack them into the container. It also entailed implementation of same data-sets with
and without rotational drawers. This way, it was widely considered that the 3D container loading
problem was significantly reduced, especially if the tins were allowed to obtain self-orientation
through rotation (Zhao et al., 2016). This approach was used on currently with asymptotic worst-
case ratio technique for container loading problem to maximize the use of space within the
container. They were also used in minimizing the number of containers outlined in the order
request. While doing so, the container capacity limit was ensured. Zhao et al. (2016) state that
bins were categorized into three main groups, namely fall back, pure and transition bins,

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denoting small, similar, and highly indexed respectively. A simple meta-heuristic approach was
also adopted to enhance the effectiveness of these approaches according to the first-fit concept
for loading multiple containers (Gonçalves and Resende, 2013). The first-fit concept was applied
to determine the arrangement of bins sequence within the container. This procedure obtained a
series that had alterations obtained through the simulated annealing method, which considered
load constraint, the strength of load bearing, and distribution of weight. In this case, bins of
similar volume were fitted and allowed to rotate in any of the six rotational dimensions,
increasing the effectiveness of this approach. This method was further boosted by using a tertiary
tree formula to pack heterogeneous tins into the larger container.
The multi-layer GA concept was re-adopted to solve container loading problems that
relate to the scheduling problem. It was used to attain a near optimal solution by optimizing the
entire schedule by incorporating crucial shipment factors such as inside yard movements,
containers pre-storage services, loading into the ship, operation discharge, and unloading the tins
from the truck. In the process, the Maximum matching method was employed to enhance GA
performances (Gonçalves and Resende, 2013). Charging and discharging constraints, the use of
automated guided cars, quay, and yard cranes were also considered in this approach. An integer
programming tool was also developed and applied alongside this method to solve loading
problems that are linked to the storage capacity. Suitably, this strategy ensured that the time used
in queuing is significantly reduced. In this regards, it provided timely delivery of the ordered
items. This approach also tested both GA and heuristic, after which it was confirmed that the
latter is only suitable in handling small container loading issues.
On the other hand, the GA approach was found to be suitable for both large and medium
three-dimensional container loading problems. In other words, literature capture no single

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approach that can solve loading problems of different nature. For instance, just like these
approaches, the online bin loading technique is suitable for small and large issues but not
medium-sized items. This technique is not universal to all types of container loading problem. At
the same time, it fails to consider the required number of bins as per the order as it focuses
majorly in filling the spaces within the container. These deficits form the basis of this
dissertation. Precisely, this dissertation aims at developing a universal solution to container
loading problem by considering the order request, storage time, and stability of the container and
general efficiency of the loading process.
2.2. Summary of Literature Review
This literature review has revealed various approaches and strategies that were applied by
researchers to solve the 3D container loading problem. Variable sized containers were also used
to accommodate the smaller vessels (bins), which were then used to form a strip or pellet. The
pallets and pieces were then used to load the containers. Generally, most of the approaches used
in this fielded considered three-dimensional containers. In this context, it is justifiable to rule out
the different sized bottles as was used in most procedures discussed above, because at times the
bins may have the same sizes.In most cases, the bins are always heterogeneous. The literature
review much ignores this perspective. However, the literature has stressed that a simple
mathematical approach cannot be used to solve the various 3D container loading problems,
especially for the multi-constrained and multi-objective issues.
Significantly, the literature has provided an elaborate framework that can be used to solve
container loading problems, including the ones associated with continuous variables and discrete.
However, it was also noted that virtually all the literature ignored crucial shipment concepts.
Precisely, factors such as weight constraint, stability, placement constraint, load-bearing

3D Container Loading 21
constraint, boundary-crossing constraint, and orientation constraint. Mostly, the existing
scholarly publications compared developed it while putting the minimal focus on the output
format. Based on this notion, this dissertation attempts developing a conceptual framework in
solving 3D container loading challenge entirely. The solution that this dissertation provides will
also help in the development of an optimal solution for various objective issues by considering
various container loading constraints. Precisely, this desertion aims at providing an effective
solution to 3D container loading problem that will not only ensure that the space within the
container is maximally utilized but that also the stability of the container is ensured. Most
importantly, the solution will provide maximum packaging within the shortest time possible. In
this context, a more reliable and exciting container loading and shipment will be established.
Progressively, the open-ended container was used to design a bound and branch heuristic
for strip loading issue. The main objective of this development was to reduce the utilized length
of the container. This approach was applied alongside a search process to determine layer depth,
strip, and bets strip dimension. Since the method does not value any constraint, simplification did
not affect the performance of this approach as far as loading a 3Dcontainer was concerned. To
these end, 3D container loading problem was as good as simplified and solved. However, some
issues still rose regarding the capacity of the container. Precisely, it was noted that while it was
recommendable to not the space within the vessel was maximally utilized; it was pointed out that
in some instance, some bins were left unpacked. The stowage plan was optimized for the second
time for containers that are transported by ships. This development assumed that all bins would
fit in the ship hence, sorting the capacity deficit. The total weight of the container was also
checked through the use of weight constraint. Notably, the shipper using this approach should
always ensure that the weight constraint that is used to test the capacity of the total number of

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loaded items should be less or equal to the bins bottom layer. Equally, placement constraints
were valuable in this procedure as they were used to monitor things placement based on
unloading and loading locations. However, it seemed non-dependable as new practices were
needed to enhance the stability of the whole container. In this regards, bin loading concept was
adopted that recommended loading of bins into a block first, after which the blocks are loaded
into the container. This approach seemed useful because not only would it enhance the stability
of the, but also ensure that the bins are tightly packed and cannot move with ease.

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3. CHAPTER THREE: METHODOLOGY
The research methodology provides a framework which allows conducting study in
proper manner. The scholar is able to identify various methods that are used in research. It
includes research philosophy, data collection, data sampling, etc. however, it is necessary to
identify relevant methods so that it becomes to complete it in given time. Moreover, user is
able to identify what methods are been used in study. The methodology is described below in
detail :-
Research philosophy –
In this first research method the scholar provides a brief overview of how entire research
will be done. The philosophy describes how study will proceed further. With this it become
easy for scholar to conduct research in systematic way. So, there are different philosophies
available which can be selected. They are positivism, realism, pragmatism, etc. In positivism
only theoretical knowledge is developed. Also, no human interest is taken and study is
independent. Moreover, role of researcher is limited in data collection and interpretation. In
pragmatism there is no single view point on basis of which data is gathered. The focus is on
research question and results are generated. The realism philosophy is based on assumption
of developing knowledge.
Interpretivism is applied to take human interest into consideration but knowledge is
developed on basis of positivism philosophy. Thus, emphasis is on issues that relates with
topic.
So, the scholar will use interpretivism philosophy which will enable in finding out what
issues are been faced in 3-D container loading. Furthermore it will be easy to identify factors
in container loading.
Research type-
Research approach –
Here, it is defined that how data and information will be gathered and analyzed in overall
research. It consists a plan which refers to methods of data, collection procedure, etc. The
research approach is based on nature of research and problem which is been addressed.

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Basically, there are three common methods of which is used in it. They are inductive,
deductive and abductive.
Research design
Data collection- It is the most important part of research because here appropriate data has to
be collected. The data gathered should be from relevant sources in order to generate precise
and accurate outcomes. It depends on scholar that how data and informant is gathered from
varied sources. Data collection is process in which data is gathered to examine research
objectives.
Usually, there are two types of data collection method that is primary and secondary. In
primary, data is gathered for first time. Here, survey or questionnaire is used to gather data.
By using primary data is becomes easy to generate proper outcomes and attain research aims
and objectives.
In secondary method, data is gathered from previous articles, journals, etc. Here, the main
focus is on analyzing what other authors or researcher views and opinions are regarding
study. Here, most of the times theoretical info is gathered in secondary method to conduct
study in depth.
In present study secondary data collection method is used to gather data. For this
previous articles, journals, etc. will be used and reliable sources are used to collect data. The
scholar will analyze how 3-D container loading are manufactured, what formulas are applied,
what amount of weight is loaded, etc. It will be easy to get in depth info about research topic
Data analysis- This is also a crucial element of research as overall study results are based on
it. It is a process of analyzing and interpreting data in order to obtain relevant outcomes. The
scholar is responsible to analyze data in proper way. He or she should have knowledge about
various tools and techniques of data analysis and how it is applied or used. In order to

3D Container Loading 25
interpret data there are different tools and techniques available. But it also depends on nature
of study and researcher willingness that what tool can be used. The data analyzed has to be
done in effective way to obtain precise and accurate outcomes.
In this study thematic data analysis method is used. Here, themes will be developed and
on basis of that data is interpreted. It will enable in finding out how 3-d container are
prepared and what calculation is done to load a container.
Ethical consideration
It is essential for researcher to follow several ethics while conducting research. This is
because it enables in ensuring that norms are followed and study is conducted in systematic
way. Here, scholar will follow several ethics such as. First of all the data and information
security and privacy will be maintained. The data will not be shared with third party or any
other person. It will be stored in database and servers. Beside this, the individual who are
participating in study will be respected. Their dignity will be maintained. Alongside it,
scholar will ensure that no person is intentionally harmed during study.
Reliability and validity
It means the extent to which right elements have been used by researcher is conducting
research and interpreting data. It is necessary to use right tools so that outcomes will not get
affected. Research validity is divided into two i.e. internal and external. Internal refers to how
findings are related with reality whereas, in external, results will be simulated in outside
environment. Here, research consideration has been kept by the researcher. This is an
important part of study. It has helped in looking for the extent to which research could be
carried out in most effective and efficient manner. Also, researcher has maintained the
validity of findings by ensuring that data has been collected from authentic sources. The data
analysis tools were tested and then used. It was useful in validating the data and obtaining
outcomes.

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This study used a qualitative approach in two main dimensions, namely primary data
collection and analysis of secondary data. To begin with, a personal interview was conducted at
two major ports. These surveys targeted shippers and managers of the ports as the primary
respondents. Data were collected in ten ports across Europe and took not more than one hour. In
total, 30 participants were engaged in the interviews. These participants were selected randomly
based on readiness and availability. The study entailed the use of questionnaire forms containing
both structured and semi-structured questions. All questions tested the experiences and opinions
of shippers in regards to the container loading process. After filling the questionnaire forms, they
were collected and analyzed for two days through the use of Stata 13 model.
On the other hand, secondary data was collected through an online search. Precisely,
keywords such as "3D container loading problem" were fed in the Google search engine to
generate relevant scholarly publications. Numerous articles were made. However, only six were
used to extract data regarding 3D container loading problem. The most relevant scholarly
publications were selected based on content relevancy and age. This notion means that besides
addressing specific issues about 3D container loading, only five years and younger articles were
valued for this dissertation. Just like in the case of primary data, secondary data were analyzed
through the use of Stata 13. This tool was also used to analyze the reliability of the data sources
and whether the selected population and data sources were sufficient enough to represent all
container loading ports across the world and available publications about 3D container loading
problem respectively. Using a double approach to collect data in this dissertation was valued
because dual procedure narrows the error risks. Hence, since primary data coincided with the
secondary data, the findings were considered as reliable.

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4. CHAPTER FOUR: RESULTS

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5. CHAPTER FIVE: DISCUSSION
It can be analyzed from literature review that there are different types of container which
carry goods. Due to their different dimension goods are loaded as per their capacity. The
containers are loaded on ships as per its requirements. There are many activities which is
performed in container loading. This results in arising of various issues and problems. The
shipper has to ensure that container capacity is utilized at maximum. However, many times it is
not possible as load weight vary as compared to container dimension. The shipper plays crucial
role in loading of goods in container (Saikia and et.al., 2018). The containers are designed by
applying specific formula. Now, many companies are using 3- D containers in shipping of goods.
But in recent times, the main issue is non deterministic polynomial (ND) which is based on
mathematical formula. Moreover, another issue evaluated is ineffective planning and loading of
goods. The ND problem is not been solved by using mathematical approaches. So, due to this
many issues has arise in recent times making it difficult to load goods into container. But on
contrary it is observed that formulas and algorithms are not helpful in solving multi constrained
and multi objective issues. So, in replacement of it various strategies are used.
It is evaluated that in order to solve ND problem different methods are applied. This is done
to increase capacity of container. Each container is having a dimension on basis of which their
capacity is decided. Many shippers focused on using integer programming method to solve ND
issue. It has helped in maximizing capacity of container. Alongside it, another approach which is
beneficial in solving issue is using GA. It has benefited in reducing problem optimization and
increasing complexity of parameters. The shippers are able to identify that no load gets
overlapped. Thus, it is ensured that container capacity is utilized to maximum.
GA is an approach that is used to calculate container capacity. It benefits shipper to ensure
that container capacity is improved. In addition to it, complex issues are solved easily. But many
shippers said that with advancement in technology a tree based formula is helpful in solving
complex problems (Razumov, 2016). It has transformed the way of loading container. In present
times artificial neutral network is used to solve 3-D container problems. It process and solves
complex data and information in effective way. It fulfills the gap that occurs in container
loading. However, this method eliminates loading time and identify shortest time in which

3D Container Loading 29
container can be loaded. On contrary, the GA approach is suitable for both large and medium 3-
D container loading problems. In other words, no single approach that can solve loading
problems of different nature. For instance, just like these approaches, the online bin loading
technique is suitable for small and large issues but not medium-sized items. This technique is not
universal to all types of container loading problem. At the same time, it fails to consider the
required number of bins as per the order as it focuses majorly in filling the spaces within the
container.
By interpreting secondary data it can be stated that now container height, weight, etc. is
identified and then only the issue is solved. This has become easy for shipper to identify gap and
utilize it. Furthermore, open containers are designed and then loaded. It helps in improving their
efficiency and making it easy to load things. Alongside it, the faults are identified and proper
measures are taken to compare capacity of container with loads. Basically, a separate model is
required to find out dimension. It has become important for shippers to solve loading problems
(He and et.al., 2019). Now, problems are solved but not to that much extent. The generic
algorithm is useful in determine fitness value of container. Thus, it has reduced uncertainty and
labor usage in loading process. The process starts from initiating population and ends at selecting
best one. The software is implemented which process data from database. So, every dimension
info is analyzed which makes it simple to evaluate container capacity. This approach is
successfully implemented in DC in Texas. It is highly benefited in improving efficiency of
container and solving issues. With this the ability of port has increased as well.
It has been analyzed that in genetic algorithm uses parameters. Here, the highest and
lowest score is taken into consideration. This has been useful in achieving load goals and
objectives. GA turns down score coefficients to suit problem instead of solving it. Hence,
each container is analyzed from software and determines its new order delivery, delay time,
etc. But the implementation of GA approach require more improvements. There needs to be
redesigning of load plans that helps in finding out spaces. Shippers are using two load plans
one is loading 20ft container and second is loading of two consolidation pallets. Through
this, they are able to determine container efficiency and spaces between them. Thus, they
compare them and accordingly change design. The pallets method is simple as here many
bins are loaded and then empty space area is determined. Along with it, load plans are

3D Container Loading 30
evaluated on basis of set standards. From that constraints are figured out and solved. So, it
gives an idea to modify design of container. As elucidated by () the problems are categorized
at 5 stages and then resolved. This support in reducing complexity of problem and breaking
down into smaller units. However, the most common strategy used to solve problem is
finding out time of overall process of loading and unloading of container.

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6. CHAPTER SIX: CONCLUSION AND RECOMMENDATIONS

3D Container Loading 32
References
Bortfeldt, A., and Wäscher, G., 2013. Constraints in container loading–A state-of-the-art
review. European Journal of Operational Research, 229(1), pp.1-20.
De Azevedo, A.T., Ribeiro, C.M., de Sena, G.J., Chaves, A.A., Neto, L.L.S. and Moretti, A.C.,
2012. Solving the 3D container ship loading planning problem by representation by rules
and beam search. ICORES, 12, pp.132-141.
Gonçalves, J.F., and Resende, M.G., 2013. A biased random-key genetic algorithm for 2D and
3D bin packing problems. International Journal of Production Economics, 145(2),
pp.500-510.
He, G. and et.al., 2019. Container terminal, container loading-unloading method and container
collection-evacuation method. U.S. Patent Application 16/065,678.
Razumov, S.N., 2016. Loading desired container sequence onto board of container carriage in
storage system. U.S. Patent Application 14/333,199.
Saikia, S. and et.al., 2018. Evolutionary RL for Container Loading. arXiv preprint
arXiv:1805.06664.
Tran-Dang, H., Krommenacker, N., and Charpentier, P., 2017. Containers are monitoring
through the Physical Internet: A spatial 3D model based on wireless sensor networks.
International Journal of Production Research, 55(9), pp.2650-2663.
Zhao, X., Bennell, J.A., Bektaş, T., and Dowsland, K., 2016. A comparative review of 3D
container loading algorithms. International Transactions in Operational Research, 23(1-
2), pp.287-320.
Zheng, J.N., Chien, C.F., and Gen, M., 2015. A multi-objective multi-population biased random-
key genetic algorithm for the 3-D container loading problem. Computers & Industrial
Engineering. 89. pp.80-87.