FedEx, a global leader in logistics and transportation, has bui lt an
extensive infrastructure to meet the demands of modern commerce and
e-commerce, reaching more than 220 countries and territories. With an
annual revenue of $87.7 bi l l ion, the company operates with a
workforce of over 500,000 employees and handles an average of 16
mi l l ion shipments dai ly.
Its global network comprises more than 200,000 motorized vehicles
and 698 aircrafts, connecting over 650 airports worldwide, ensuring
efficient and fast del ivery across various service l ines, including
express and ground services. FedEx operates more than 5,000
faci l ities, and its website attracts 80 mi l l ion visitors monthly, managing
over half a bi l l ion dai ly package tracking requests.
FedEx revolutionized the logistics industry with its pioneering express
air service in the 1970s, introducing time-definite, overnight del ivery.
This model disrupted traditional shipping and set the company apart.
Over the years, FedEx expanded its portfol io through strategic
acquisitions, such as Flying Tiger Line and Cal iber System, to include
diverse services l ike FedEx Ground, FedEx Freight, and FedEx Office.
This expansion al lowed FedEx to offer comprehensive solutions, from
smal l-package del ivery to international freight.
In addition to its core services, FedEx operates special ized divisions
l ike FedEx Custom Critical and FedEx Logistics, providing solutions for
urgent and sensitive shipments. The company also serves industries
such as healthcare, aerospace, and automotive, where the need for
secure and timely del iveries is critical.
FedEx offers various shipping options, including FedEx International
Priority and Economy services, catering to different customer needs in
terms of budget and del ivery time. For example, express options
typical ly del iver in 2-3 business days, whi le economical options may
take 4-5 days. FedEx’s abi l ity to handle large shipments, such as
those up to 1,000 ki lograms, along with services l ike returns
management and hazardous goods transportation, shows its versati l ity
in meeting industry demands.
FedEx continues to innovate, particularly in the e-commerce space,
where it helps businesses scale with flexible solutions.
About FedEx
FedEx selected the Unit Load Device (ULD) optimization problem for
the Inter IIT Tech Meet 13.0 due to its potential to significantly
enhance operational efficiency, reduce costs, and improve service
rel iabi l ity across its logistics network. ULDs are standardized
containers used in air shipments, varying in shape and size, and have
strict weight and volume l imits. Properly packing these devices
ensures efficient use of space, minimizes costs, and guarantees that
Priority Packages, which are of higher precedence, are shipped without
delay.
The chal lenge is to decide which packages to load into which ULDs,
whi le considering the weight l imits, package dimensions, and ensuring
that Priority Packages are not compromised.
The optimization of ULD packing offers several key benefits to the
logistics industry. First, it increases efficiency by maximizing the
avai lable space in each ULD, al lowing more goods to be transported
per fl ight. This reduces the number of shipments required and leads to
better resource uti l ization.
The company’s FedEx E-commerce Solutions provide end-to-end
support, whi le services l ike FedEx Priority Alert and Del ivery Signature
Options ensure enhanced security for valuable shipments.
Furthermore, FedEx’s commitment to social responsibi l ity is
demonstrated through its global giving initiative, FedEx Cares, which
has pledged $200 mi l l ion to support communities worldwide.
Strategic decisions, such as acquiring TNT Express to strengthen its
European presence and distancing itself from Amazon, reflect FedEx's
drive to remain independent and adapt to changing market conditions.
Under the leadership of CEO Raj Subramaniam, fol lowing founder
Frederick W. Smith’s transition, FedEx continues to prioritize
customer-centric innovation and operational efficiency. This
adaptabi l ity, combined with its vast infrastructure, positions FedEx as
a critical player in the logistics and transportation industry, enabl ing it
to support businesses and individuals in a fast-paced, global ized
marketplace.
Background
By reducing the number of ULDs needed, operational costs, such as
fuel, labor, and handl ing fees, are significantly lowered. Fewer ULDs
also mean less storage and transportation costs, directly impacting the
bottom l ine.
In addition to cost savings, ULD optimization improves timel iness.
Properly packed ULDs ensure that no packages, especial ly Priority
Packages, are left behind, resulting in faster del ivery times. This is
especial ly crucial for time-sensitive shipments, improving customer
satisfaction and overal l service rel iabi l ity.
Moreover, efficient ULD usage leads to higher profitabi l ity. By handl ing
more shipments per trip without significantly increasing costs, logistics
companies can generate additional revenue. Furthermore, optimizing
the use of ULDs reduces inefficiencies, directly benefiting the
company's financial performance.
Environmental sustainabi l ity is another key factor driving FedEx’s
interest in ULD optimization. More efficient packing means less fuel is
consumed per shipment, leading to a reduction in carbon emissions.
This al igns with FedEx's commitment to sustainabi l ity and
environmental ly friendly logistics practices.
The key constraints in optimizing ULDs include not exceeding weight
l imits, ensuring al l Priority Packages are shipped, and fitting the
packages within the ULD’s dimensions.
The optimization solution seeks to balance these constraints whi le
minimizing costs, including the risk of packages being left behind or
the need to spread Priority Packages across multiple ULDs.
In summary, FedEx's selection of the ULD optimization problem stems
from its potential to streaml ine logistics operations, reduce operational
costs, and enhance customer satisfaction. By improving space
uti l ization, increasing efficiency, and ensuring timely del iveries, the
optimization of ULD packing offers significant advantages for both the
company and its customers.
Packing Unit-Load Devices for
Air Shipments
Figure: 1. A picture of ULDs at an airport (Source: www.fedex.com)
Figure 2: ULDs come in different shapes and sizes
The packages that are being transported are usual ly stacked inside
large standard sized containers, cal led Unit Load Devices (ULDs), that
are then loaded onto the aircraft.
These ULDs are avai lable in various standard sizes, meant for carrying
different types and quantities of packages. Each of them have specific
shapes, dimensions, weight, volume and a l imit for how much load they
can carry. Some of the varieties of ULDs are shown in the pictures
below:
Many ULDs have tapered or rounded edges on one of their sides in
order to enable ful l uti l ization of space inside the aircraft. For the
purposes of this problem statement, assume that al l avai lable ULDs
are cuboidal in shape. The packages, which are smal ler in comparison
to the ULDs, also come in various shapes and sizes.
Problem Statement
For a given fl ight, a given set of ULDs that must travel in that fl ight,
and a l ist of packages that need to be flown in that fl ight, we would
l ike to decide which package should be packed in which ULD and how
it should be packed (coordinates and orientation inside the ULD).
A solution must satisfy al l the fol lowing requirements:
1. Total weight of al l packages in a ULD should not exceed its l imit.
None of the Priority Packages must be left behind (some economy
packages can be left behind).
2.
3. Al l packages assigned to a particular ULD must fit into that ULD.
Amongst the many possible solutions that satisfy the above
requirements, the one with the lower ‘total cost’ is preferable. Total
cost has the fol lowing components and are explained later below:
1. Cost of packages left behind
2. Cost of spreading the Priority Packages into too many ULDs
Again, assume that al l packages are cuboidal in shape and they can
only be oriented along the axes inside a ULD. That means the edges of
the package must be paral lel to the wal ls of ULD (and not incl ined at
other angles).
Thus, there are 6 possible orientations for each package inside a ULD.
It is further given that there are two types of packages: Priority and
Economy. Priority Packages are higher valued than Economy
Packages. If there are more packages than space avai lable then
Priority Packages are given priority. Also, Priority Packages should be
grouped into as few different ULDs as possible so that they can be
unpacked and del ivered faster.
ULD Identifier Length (cm) Width (cm) Height (cm) Weight Limit (kg)
ULD-1
…
ULD-m
Package Identifier
Length
(cm)
Width
(cm)
Height
(cm)
Weight
(kg)
Type
(P/E)
Cost of
Delay
P-1
…
P-n
Inputs
The fol lowing inputs are provided:
Table: 1. Format of a table describing ULD attributes
Table: 2. Format of a table describing package attributes
1. List of ULDs: A l ist of ULDs is provided in the fol lowing tabular form
2. List of Packages: A l ist of packages is provided in the fol lowing
tabular form
3. Cost ‘K’ for each ULD that carries a Priority Package in the
solution. Thus, for example, if a total of 7 ULDs have one or more
Priority Packages in them, a total cost of 7K is incurred.
Expected Output
As an output, it is expected that for each package we get:
The ULD identifier in which it must be loaded or NONE in case it
can not be loaded.
1.
The coordinates of the cuboidal packages inside a ULD using the
fol lowing convention.
2.
Also expected in the output is the total cost incurred of the proposed
solution. This cost is the sum of (a) delay-cost of al l packages that
could not be loaded plus (b) the cost of spreading Priority Packages in
multiple ULDs, computed as K x (number of ULDs that have Priority
Packages).
In this competition we are assuming that a package inside a ULD wi l l
be al igned along its axes. This assumption makes it easy to represent
the position of a package inside a ULD by means of coordinates (three
dimensional) of its two diagonal ly opposite corners. In this convention
we fol low two rules:
The coordinate system is al igned to the axis of the ULD with the
origin (0,0,0) at the front, left, bottom corner.The length of the ULD
is measured along the x axis, width along y and height along the z
axis.
1.
Convention for Representing a Package
Position Inside a ULD
Figure 3: Coordinate axes for a ULD
ULD Identifier Length (cm) Width (cm) Height (cm) Weight Limit (kg)
ULD-1 100 80 80 250
ULD-2 100 80 80 250
2. For placing a package, we need to specify the reference corner of
the package which is selected as fol lows in our convention. Amongst
the eight corners of the package, select the ones that wi l l have the
smal lest z-coordinate when placed inside the ULD.
Amongst al l such corners, select the one that has the smal lest y value.
The position of the package is specified using the coordinates of the
reference-corner and the corner diagonal ly opposite to it. For instance,
a package of size (2x25x2) with location specified by (5,0,0)-(30,2,2)
wi l l be placed l ike this inside ULD at the bottom surface, 5cm to the
right of the origin:
Figure 4: Package inside a ULD
Faces (sides) of the packages may touch the wal ls of the ULD, as wel l
as sides of other packages, for compact packing.
Table 3: ULD attributes for Example Problem
Example: Here is a fictitious toy example of only 2 ULDs and 4
packages. Suppose K=40 and the other inputs are as fol lows:
Package
Identifier
Length
(cm)
Width (cm)
Height
(cm)
Weight
(kg)
Type (P/E)
Cost of
Delay
P-1 70 40 50 100 Priority -
P-2 70 40 50 100 Priority -
P-3 70 40 50 150 Economy 20
P-4 70 40 50 150 Economy 30
Table 4: Package attributes for Example Problem
Three feasible solutions (not necessari ly optimal) are provided for
i l lustration purposes.
Solution-1
Both the ULDs get one Priority package and one Economy package
each.
Here, the position of P-1 in ULD-1 according to our convention is:
(5,0,0) - (45,70,50) and that of P-3 in ULD-1 is (45,0,0)-(85,70,50).
The cost of this solution is (40x2) 80 as there are two ULDs with
Priority packages and no package is left out.
Solution-2
One ULD has two Priority packages, and the other has two Economy
packages.
The cost of this solution is 40 as only one ULD has priority packages,
and no package is left out. However, this solution is not acceptable
because the second ULD is loaded beyond its capacity of 250KG
The ful l problem data (Chal lenge Problem Data) that wi l l be used to
judge the winners wi l l be released on 18th November. It wi l l include
about 9 ULDs of different sizes and no more than 500 packages. ULDs
wi l l not be bigger than 240 x 320 x 240 cm3 and package dimensions
wi l l vary from 4cm to 100cm (along each of the three coordinates).
Challenge Problem Data
Solution-3
Here, one ULD has two Priority packages, whi le the other one has only
one Economy package (P4).
The cost of this solution is (40 for Priority +20 for delaying package
P3) 60 units.
The fol lowing must be submitted in the final solution:
Each contesting team should prepare a short report on the method
they used to solve the problem. The method should be explained in
simple, concise Engl ish so that it is understandable by non-experts.
It can be supported by technical detai ls including detai ls of the
algorithm, flowcharts, example computations, figures etc. The report
should mention the difficulties faced and the ideas tried. The report
should also clearly mention any l imitations or drawbacks of the
proposed approach. This report should be submitted in a PDF
format (up to 10 pages).
Code used to solve the problem, without any third-party or
commercial l ibraries should also be shared. Code can be in any
programming language. A short how-to on running the code must
accompany this submission.
Final ly, the output obtained by solving the chal lenge problem
released for the competition should be submitted in the fol lowing
format.
Solution Deliverables
Participants wi l l be required to submit a plain text fi le in the fol lowing
format:
The first l ine of the fi le should contain total cost (an integer value)
computed for the solution, the total number of packages packed in
al l ULDs and the number of ULDs with Priority Packages separated
by commas (no spaces).
1.
For example:10200,380,4
2. Subsequent l ines should contain detai ls of one packet per l ine in the
format: Package-ID,ULD-ID,x0,y0,z0,x1,y1,z1
where Package-ID is the ID of the package, ULD-ID is the ID of the
ULD to which the packages is assigned, (x0,y0,z0) are the coordinates
of the reference corner of the package and (x1,y1,z1) are the
coordinates of the diagonal ly opposite corner (see convention above).
If a particular package is not al lotted to any ULD then its ULD-ID
should mention NONE and the coordinates be -1,-1,-1,-1,-1,-1.
Output Format
Evaluation Criteria
The teams wi l l be judged on the fol lowing criteria:
Qual ity of the solution to the chal lenge problem submitted in the
above format (60%). Solutions should try to meet al l primary
requirements (al l priority packages must be shipped, weight of
ULDs should not exceed the l imit, al l selected packages must be
ful ly inside their respective ULDs and no two packets should
spatial ly overlap). Cost is a secondary goal.
Qual ity of presentation and the fol lowing question and answer
session (20%).
Qual ity of the report submitted (15%).
Qual ity of the code submitted (5%). propose a solution for this problem statement