Shipping Estimation Algorithm Predicts Container Needs

Introduction
The Solution
Algorithm
Output
End Product
Operation Pack-Man: Shipping Estimation
Eric Bentley, Christian Bottenﬁeld, Michael Garver, Christopher
Lindeman, Namita Matharu, Surya Padinjarekutt, Sylvia Ujwary
University of Pittsburgh
May 1, 2015
BIG Problems, Math Dept., Univ. of Pittsburgh, Spring 2015 Operation Pack-Man: Shipping Estimation

Introduction
The Solution
Algorithm
Output
End Product
The Client
The Problem
Redirects still-useful materials away from US landﬁlls to
support public health programs in targeted communities
throughout the Western Hemisphere

Introduction
The Solution
Algorithm
Output
End Product
The Client
The Problem
Redirects still-useful materials away from US landﬁlls to
support public health programs in targeted communities
throughout the Western Hemisphere
http://www.globallinks.com

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The Solution
Algorithm
Output
End Product
The Client
The Problem
The Problem
Global links needed a way to predict how many shipping
containers should be ordered for each shipment

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The Solution
Algorithm
Output
End Product
The Client
The Problem
The Problem
For a collection of n items {wi }, where wi = (xi , yi , zi , hi ), we
seek a mapping ϕ := {wi } → R3

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The Solution
Algorithm
Output
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The Client
The Problem
The Problem
More speciﬁcally, for a partition representing the clinics
C = {Ci } of the items {wi }, and a subspace of R3 called S,
we seek the mapping ϕc := {Ci } → S. S is given by a
rectangular prism with a corner at the origin, and restricted by
maximum values of KXC , YC , ZC .

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The Solution
Algorithm
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The Client
The Problem
The Problem
More speciﬁcally, for a partition representing the clinics
C = {Ci } of the items {wi }, and a subspace of R3 called S,
we seek the mapping ϕc := {Ci } → S. S is given by a
rectangular prism with a corner at the origin, and restricted by
maximum values of KXC , YC , ZC .
K is the total number of containers needed and (XC , YC , ZC )
are the dimensions of said container.

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The Solution
Algorithm
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Stochastic Rotation
Machine Learning
Statistics
The Solution
An algorithm that takes inventory data and packs each object
into a truck

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Stochastic Rotation
Machine Learning
Statistics
The Solution
into a truck
Inputs:
- Dimensions of each object

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The Solution
Algorithm
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Stochastic Rotation
Machine Learning
Statistics
The Solution
into a truck
Inputs:
- Dimensions of each object
- Height priority of each object

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The Solution
Algorithm
Output
End Product
Stochastic Rotation
Machine Learning
Statistics
Stochastic Rotation
We stochastically turn and reorder items

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Stochastic Rotation
Machine Learning
Statistics
Stochastic Rotation
For wi = (xi , yi , zi , hi ), generate βi ∈ (0, 1)and αi ∈ (0, 1)

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Stochastic Rotation
Machine Learning
Statistics
Stochastic Rotation
If βi < αi then wi = (yi , xi , zi , hi )

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Stochastic Rotation
Machine Learning
Statistics
Stochastic Rotation
If βi < αi then wi = (yi , xi , zi , hi )
We leverage the Central Limit Theorem to converge upon the
true mean of containers needed.

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Stochastic Rotation
Machine Learning
Statistics
Machine Learning
With our machine learning component, we approximate the
real-world solution more closely each time

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Stochastic Rotation
Machine Learning
Statistics
Machine Learning
We adjust the dimensions based oﬀ of a formula derived by:
Ti = ˆTi + N(ˆξ − 1)3

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The Solution
Algorithm
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Stochastic Rotation
Machine Learning
Statistics
Machine Learning
We adjust the dimensions based oﬀ of a formula derived by:
Ti = ˆTi + N(ˆξ − 1)3
We then average all past error factors to derive a current error
estimate.

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The Solution
Algorithm
Output
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Stochastic Rotation
Machine Learning
Statistics
Statistics
Algorithm will generate and output estimates of the mean,
standard deviation, and error factor ξ for the number of
necessary containers.

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Pseudocode
Algorithm
Pseudocode

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Pseudocode
Algorithm
Algorithm
We ﬁrst consider the y direction.

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Pseudocode
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Algorithm
If space exists in this direction, we ﬁll the given space.
Otherwise, we move on to and repeat for the z direction and
then the x direction.

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Pseudocode
Algorithm
Algorithm
If space exists in this direction, we fill the given space.
Otherwise, we move on to and repeat for the z direction and
then the x direction.
In this way we are able to fit items on top of one another
before taking up more floor space

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Efficiency
Definition (Packing Efficiency)
Packing efficiency is the ratio of the sum of all item volumes and
the volume of all containers estimated as needed.
i (xi yi zi )
KXcYcZc

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Efficiency
Definition (Packing Efficiency)
Packing efficiency is the ratio of the sum of all item volumes and
the volume of all containers estimated as needed.
i (xi yi zi )
KXcYcZc
This number does not represent how close we have come to
any goal, as a one item overflow into a new container could
cause a drastic reduction in the calculation.

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Summary
Reception
Versatility
By interfacing with Excel, this solution can be adopted by
numerous businesses.

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Summary
Reception
Versatility
Since the container size is user-deﬁned, any form of transport
can be used, whether it be by ship, air, truck, etc.

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The Solution
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Summary
Reception
Versatility
Since the container size is user-deﬁned, any form of transport
can be used, whether it be by ship, air, truck, etc.
This program could beneﬁt nearly anyone involved in
transporting and packing of goods.

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Summary
Reception
Implementation and Eﬀects
Having the ability to determine, with certainty, the number of
shipping containers required to ship the requested supplies,
the user can know, in advance, the shipping costs that will be
associated with the order.

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Summary
Reception
This knowledge allows the user to accurately convey a proper
valuation of their shipment and bill the recipient properly.

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The Solution
Algorithm
Output
End Product
Summary
Reception
This knowledge allows the user to accurately convey a proper
valuation of their shipment and bill the recipient properly.
The recipient may then opt to adjust the size of their order,
either to ﬁll a nearly full container, or to empty a barely-ﬁlled
one.

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Summary
Reception
Thank you to Mathematical Association of America for giving us
the opportunity to participate in this initial oﬀering of PIC Math

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Learning Outcomes
Throughout this project we have learned
Creation of Excel Macros

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Summary
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Learning Outcomes
MatLab Programming

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Summary
Reception
Learning Outcomes
MatLab Programming
Machine Learning

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Algorithm
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Summary
Reception
Learning Outcomes
MatLab Programming
Machine Learning
Stochastic Processes

Introduction
The Solution
Algorithm
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Summary
Reception
Learning Outcomes
MatLab Programming
Machine Learning
Stochastic Processes
Heuristic Algorithm Development

Shipping Estimation Algorithm Predicts Container Needs

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