The document analyzes algorithms for cargo loading optimization. It discusses several existing commercial software programs and algorithms that can solve the cargo loading problem. The key algorithms described include a dynamic programming approach, a less flexibility first algorithm, a maximal space algorithm, and genetic and parallel tabu search algorithms. It also outlines requirements for developing a cargo loading optimization module, including input/output specifications and the need for a 3D graphical representation of the optimized loading plan. The goal is to select the best algorithm to implement optimized cargo loading for an aircraft or container.

1. To analyze cargo loading optimization algorithm
By: Shahzad Sarwar
To: Development Team + Management
Date: 24th March 2010

2. 1. Objective:
To analyze and plan software development for Cargo Loading optimization module in
Flight Cargo of PCMS, Pegasus Cargo Management System.
1. To Study industry available software for Cargo Load optimization and planning.
2. To study the available algorithm for Cargo Loading optimization in Flight Cargo
module of PCMS, Pegasus Cargo Management System.
3. To analyze requirement specification for Cargo Load optimization and planning.
2. Load Planner Software Comparative Analysis:
There is a very long list of available commercial software that performs cargo load
optimization and planning with full visualization via graphical representation.
Following is brief list of some of the best in industry.
2.1. 3D Load Packer (3DLP) http://www.astrokettle.com
3D Load Packer (3DLP) is the unique space optimizer designed to help to plan quickly
and easily the best compact arrangement of a number of different size 3D rectangular
objects (hereafter called "Boxes") within one or more rectangular enclosures (hereafter
"Containers"). 3DLP is based on the truly three-dimensional, most dense and quick
original packing algorithms.

3. An overall load weight limit and truck axle weight limits may be taken into account as
additional constraints or actual optimization factors. Full control on the allowed box
overhang is also available.
The program has a facility for specifying the associated cost for each box / container item
in order to calculate totals and affect upon optimization as additional priority factors.
Optimizer goal and other main settings are adjustable.
2.2. Cube-IQ http://www.magiclogic.com
The Cube-IQ Load Planning system is built around the best Loading Engine on the
market and will give optimal volume/weight utilization. (Needed - sidebars and quotes
from the industry)
Cube-IQ optimizes the loading of items in one or more containers, optionally of different
sizes.
The system can help to cube-out loads on PC, and also in the actual loading through its
clear, 3-D diagram based loading instructions.
Cube-IQ has a state-of-the-art load optimization engine. Cube-IQ’s database allows to
pre-define containers and boxes, and to store and retrieve any number of complete
loading cases. The system has full data import and export facilities and can both read and
write Excel, XML and other formats.
2.3. AutoLoad Pro http://www.coptimal.com
AutoLoad Pro integrated 3D graphic technology, visual effects and excellent computing
speed help to work out how to load varied shape of goods into varied sizes of containers
efficiently with considering delivery safety of goods, utilization of space, move
convenience and etc. AutoLoad Pro can work out theminimum containers, trucks and
cartons quickly to complete a loading plan and reduce transportation cost as well.
2.4. CubeMaster™ http://www.LogenSolutions.com
CubeMaster™ is a versatile, cost-effective software solution to optimize the cargo load
on your trucks, air & sea containers and pallets quickly and efficiently. It reduces
shipping and transport costs through intelligent loading and optimal space utilization.
CubeMaster™ supports in planning order picking, loading and capacity requirements.
The system delivers clear instructions regarding the work preparation in seconds.
2.5. Load http://www.daubnet.com
Load saves money by optimizing container cargo - includes interactive 3D view
Load saves money by optimizing container cargo:
•includes interactive 3D view
•automatic optimizer
•packing lists are conveniently entered into Load!
•calculates maximum number of items per container

4. •Optimized packing lists and 3D views can be printed.
2.6. Packer3d Online Service http://www.packer3d.com
The Packer3d Online Service calculates optimal plans for loading different types of
boxes, cylinders, and pallets into containers, trucks, and railroad freight cars.
2.7. packVol http://www.packvol.com
packVol is an Optimization Software for Load Planning, designed to plan the best space
utilization inside containers and trucks, to help to reduce transportation costs. It is an
innovative software for MS Windows™, which has some unique features not found in
other container loading software products. It is truly tri dimensional; the program allows
to manage efficiently complex load planning problems.
2.8. PalletStacking http://www.palletstacking.com
PalletStacking allow users to find the best arrangement of boxes on loading pallets to
warehousing or transportation. This software reduce the costs of palletizing boxes and
calculate the most optimal dimensions of boxes. PalletStaking Solution calculate the best
arrangement of products in a box, calculate box dimensions and show 3D graphics of the
solution. It could be exported to Microsoft Excel to generate reports.
2.9. LoadPlanner http://loadplanner.com/
LoadPlanner is the first system that offers comprehensive load planning and optimization
solution. The heart of LoadPlanner is its sophisticated 3D loading algorithm, the result of
many years of intensive research and cooperation with leading logistics providers. But
what makes us different is that LoadPlanner is an advanced rule-based system. It has
unique capabilities to:
• Classify business objects (items, orders, containers, etc.) into flexible system
of categories.
• Formulate high-level business rules and constraints, and apply them to
selected categories.
• Use business rules and constraints in the process of load planning and
optimization.
• Solve multi-tier load planning problems (packaging - palletizing - container /
trailer loading).
• Produce results in form of easy-to-analyse interactive 3D graphics.
3. Algorithms for loading optimization Problem:
Cargo loading optimization is well known computer science problem and has many well
known algorithms to solve this problem.
Following is brief description about some of the best algorithms to solve this problem.
3.1. Algorithms for the Container Loading Problem

5. By Guntram Scheithauer , Operations Research Proceedings 1991,
Springer-Verlag
This paper covers the three-dimensional problem of optimal packing of a container with
rectangular pieces. It proposes an approximation algorithm based on the "forward state
strategy" of dynamic programming. A suitable description of packings is developed for
the implementation of the approximation algorithm, and some computational experience
is reported. The effective employment of capacity gets a more and more increasing
importance in many problems of production and transportation planning. The reasons in
transportation are e.g. the enlarging trade and growing transportation costs.
Reference:
http://www.math.tu-dresden.de/~capad/PAPERS/clp.ps
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.927
3.2. A Less Flexibility First Based Algorithm
Yuen-Ting Wu
Email: ytwu@cse.cuhk.edu.hk
Yu-Liang Wu
Email: ylw@cse.cuhk.edu.hk
Department of Computer Science and Engineering, the Chinese University
of Hong Kong, Hong Kong
This paper presents a Less Flexibility First (LFF) based algorithm for solving container
loading problems in which boxes of given sizes are to be packed into a single container.
The objective is to maximize volume utilization. LFF, firstly introduced in [An effective
quasi-human heuristic for solving the rectangle packing problem, European Journal of
Operations Research 141 (2002) 341], is an effective deterministic heuristic applied to
2D packing problems and generated up to 99% packing densities. Its usage is now
extended to the container loading problem. Objects are packed according to their
flexibilities. Less flexible objects are packed to less flexible positions of the container.
Pseudo-packing procedures enable improvements on volume utilization. Encouraging
packing results with up to 93% volume utilization are obtained in experiments running on
benchmark cases from other authors.
Reference:
http://www.springerlink.com/content/j02864x28015862j/
3.3. A Maximal-Space Algorithm for the Container Loading Problem
F. Parreño, R. Alvarez-Valdes, J. M. Tamarit, J. F. Oliveira
Department of Mathematics, University of Castilla-La Mancha, Albacete, Spain
Department of Statistics and Operations Research, University of Valencia, Burjassot,
Spain

6. Department of Statistics and Operations Research, University of Valencia, Burjassot,
Spain
Faculty of Engineering, University of Porto, Porto, Portugal, and INESC Porto, Instituto
de Engenharia de Sistemas e Computadores de Porto, Porto, Portugal
francisco.parreno@uclm.es
ramon.alvarez@uv.es
jose.tamarit@uv.es
jfo@fe.up.pt
In this paper, a greedy randomized adaptive search procedure (GRASP) for the container
loading problem is presented. This approach is based on a constructive block heuristic
that builds upon the concept of maximal space, a nondisjoint representation of the free
space in a container.
This new algorithm is extensively tested over the complete set of Bischoff and Ratcliff
problems [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of
approaches to container loading. Omega 23 377–390], ranging from weakly
heterogeneous to strongly heterogeneous cargo, and outperforms all the known
nonparallel approaches that, partially or completely, have used this set of test problems.
When comparing against parallel algorithms, it is better on average but not for every class
of problem. In terms of efficiency, this approach runs in much less computing time than
that required by parallel methods. Thorough computational experiments concerning the
evaluation of the impact of algorithm design choices and internal parameters on the
overall efficiency of this new approach are also presented.
References:
http://joc.journal.informs.org/cgi/content/abstract/20/3/412
http://www.uv.es/sestio/TechRep/tr03-07.pdf
3.4. Improved Optimization Algorithm for the Container Loading Problem
Xiamen, China
May 19-May 21
ISBN: 978-0-7695-3570-8
Container loading problem is a kind of space resources optimization problem
which consists of various constraints. The solution can be extended to aircraft, cargo
loading for ships, even the memory allocation for computer, and other applications. This
paper proposes a new algorithm for loading a variety of different goods into a single
container with multi-batches. With the concept of "plane" and "block", the algorithm
uses "depth priority" strategy to locate for the suitable space. The algorithm also allows
goods to rotate in any possible directions, while under the guarantee of efficient space
usage, it improves the placement stability. With the priorities of each goods assigned by
the algorithm, we should could allocate more goods at the same location. The optimal
algorithm is supposed to withdraw when the last batch packing is unsuitable.
Experimental results show that the algorithm is effective to solve such problems.
Reference:
http://www.computer.org/portal/web/csdl/doi/10.1109/WCSE.2009.335

7. 3.5. A Genetic Algorithm for Solving the Container Loading Problem
H. GEHRING and A. BORTFELDT
FernUniversität Hagen, Kleine Straße 22, D-58084 Hagen, BRD
The paper presents a genetic algorithm (GA) for the container loading problem. The main
ideas of the approach are first to generate a set of disjunctive box towers and second to
arrange the box towers on the floor of the container according to a given optimization
criterion. The loading problem may include different practical constraints. The
performance of the GA is demonstrated by a numerical test comparing the GA and
several other procedures for the container loading problem.
Container loading problems may be grouped in different ways. A basic distinction exists
between cases in which a given set of goods has to be loaded completely and cases which
allow some goods to be left behind. Whilst the former type of problem involves more
than one container, the latter is often restricted to a single container (cf. the distinction
made by DYCKHOFF, 1990). Another important distinction concerns the goods to be
loaded. BORTFELDT (1994) considers the loading of rectangular goods, i.e. boxes, and
defines a cargo comprising only identical boxes as 'homogeneous'. He also refers to a
given set of boxes with many different types of boxes as 'strongly heterogeneous'
and one with only a few different types of boxes as 'weakly heterogeneous'. The subject
of this paper is the loading of a strongly heterogeneous set of boxes into a single
container. The literature references given below are focused on this type of problem and
also on genetic approaches.
Reference:
http://www.math.tu-dresden.de/~belov/publ/downl/3D/gehringbortfeldt_container.pdf
3.6. A Heuristic Algorithm with Heterogeneous Boxes
Zhoujing Wang Li, K.W. Xiaoping Zhang Xiamen Univ., Fujian
The container loading problem (CLP) is notoriously known to be NP-hard, an
intrinsically difficult problem that is too complex to be solved in polynomial time on a
system of serial computers. Heuristic algorithms are often the only viable option to tackle
this type of combinatorial optimization problems. This article puts forward a heuristic
algorithm based on a tertiary tree model to handle the CLP with heterogeneous
rectangular boxes. A dynamic spatial decomposition method is employed to partition the
unfilled container space after a group of homogeneous boxes is loaded into the container.
This decomposition approach, together with an optimal-fitting sequencing rule and an
inner-left-corner-occupying placement rule, permits a holistic filling strategy to pack a
container. A comparative study with existing algorithms and an illustrative example
demonstrate the efficiency of this heuristic algorithm.

8. Reference:
http://ieeexplore.ieee.org/Xplore/login.jsp?reload=true&url=http%3A%2F
%2Fieeexplore.ieee.org%2Fiel5%2F4273787%2F4274604%2F04274749.pdf
%3Farnumber%3D4274749&authDecision=-203
3.7. A parallel tabu search algorithm for the container loading problem
A. Bortfeldt , H. Gehring and D. Mack
FernUniversität, Fachbereich Wirtschaftswissenschaft, Postfach 940, 58084, Hagen, Germany
This paper presents a parallel tabu search algorithm for the container loading problem
with a single container to be loaded. The emphasis is on the case of a weakly
heterogeneous load. The distributed-parallel approach is based on the concept of multi-
search threads according to Toulouse et al. [Issues in designing parallel and distributed
search algorithms for discrete optimization problems, Publication CRT-96-36, Centre de
recherche sur les transports, Universitéde Montréal, Canada, 1996] i.e., several search
paths are investigated concurrently. The parallel searches are carried out by differently
configured instances of a tabu search algorithm, which cooperate by the exchange of
(best) solutions at the end of defined search phases. The parallel search processes are
executed on a corresponding number of LAN workstations. The efficiency of the parallel
tabu search algorithm is demonstrated by an extensive comparative test including well-
known reference problems and loading procedures from other authors.
Reference:
http://www.sciencedirect.com/science?
_ob=ArticleURL&_udi=B6V12-487V02C-4&_user=10&_coverDate=05%2F31%2F200
3&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=
1247995731&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&
_userid=10&md5=24ffd9fe7e654b1de2c46c093e4ab8ab
4. Requirement specification for Load Plan PCMS:
a. To develop an efficient algorithm which can generate loading plan for goods in an
aircraft or container.
b. Input Data for Algorithm:
1. Job cards data with number of pieces of goods to be filled in a
aircraft/container with dimension(volume)

9. 2. Dimension of aircraft’s area to be filled or dimension of container
to be filled.
c. Out put data for algorithm:
1. To provide list of jobs card that would be filled in the aircraft or
container.
2. To provide the exact location of goods to be placed in aircraft or
container.
d. There would be an option to offload a particular job from container or aircraft.
Algorithm will automatically provide re-scheduled information after this change.
e. There would be an option to load a particular job to aircraft or container as
priority. Algorithm will automatically provide re-scheduled information after this
change.
f. A email alert will be generated to all the clients, shipper, consignee, agent,
operation person and prepared by persons.
g. There would be 3-D graphical representation for load planning showing details
of exact items loaded in aircraft or container.
5. Future Guide lines:
• To contact the corresponding algorithm providers for possibility of getting code
of implementation of algorithms.
• After getting feedback from algorithm providers, best suited can be selected.
• A implementations are found in c language, so there is a need to transform that
logic in C#, then modify the algorithm as per our need. This need code
exploration in C.
• To do R & D related to 3-D graphical representation of objects in .Net specifically
WPF.
• Third party graphical libraries like ceometric can be explored to get help in 3-D
virtualization of objects.
6. References:
http://www.diku.dk/hjemmesider/ansatte/pisinger/codes.html
http://www.astrokettle.com/
Algo for container Loading problem:

10. http://portal.acm.org/citation.cfm?id=1295701
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.927
http://www.springerlink.com/content/j02864x28015862j/
http://joc.journal.informs.org/cgi/content/abstract/20/3/412
http://www.uv.es/sestio/TechRep/tr03-07.pdf
http://www.computer.org/portal/web/csdl/doi/10.1109/WCSE.2009.335
http://www.math.tu-dresden.de/~belov/publ/downl/3D/gehringbortfeldt_container.pdf
http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org
%2Fiel5%2F4273787%2F4274604%2F04274749.pdf%3Farnumber
%3D4274749&authDecision=-203
http://www.sciencedirect.com/science?
_ob=ArticleURL&_udi=B6V12-487V02C-4&_user=10&_coverDate=05%2F31%2F200
3&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=
1247995731&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&
_userid=10&md5=24ffd9fe7e654b1de2c46c093e4ab8ab
Code:
http://www.diku.dk/hjemmesider/ansatte/pisinger/codes.html
http://www.ceometric.com/support/examples/g-a-loading-problem.html
http://loadplanner.com/library.html