SKU Segmentation Strategy for a Global Retail Supply Chain
By
Huiping Jin
MS Finance, Case Western Reserve University, 2013
Master of Business Administration, Tongji University, 2012
SMASSACHUSE[TSINSIJE
OF TECHNOLOGY
JUL 17 2014
And
LIBRARIES_
Brad Gilligan
B.S. Business Administration, Colorado State University, 2010
Submitted to the Engineering Systems Division in Partial Fulfillment of the
Requirements for the Degree of
Master of Engineering in Logistics
at the
Massachusetts Institute of Technology
June 2014
02014 Bradley Michael Gilligan and Huiping Jin. All rights reserved.
The authors hereby grant to MIT permission to reproduce and to distribute publicly
paper and electronic copies of this thesis document in whole or in part in any medium now
known or hereafter created.
Signature of Author ............................... Signature redacted
Master of Engineering in Logistics Program, Engi eering Systems Division
Signature redacted
Signature of A uthor ...................
May 13, 2014
.....
. ...........................................
Master of Engineering in Log~tics.Pr.g.,.giermn Systems Division
May13,2014
Signature redacted'
C ertified by .................................................
Signature
Accepted by .................
r
.........................
Edgar E. Blanco
Thesis Supervisor
Principal Research Associate
Executive Director IT S ALE Network Latin America
redacted MIT Center for Transportation & Logistics
........................................................................
Prof. Yossi Sheffi
Professor, Engineering Systems Division
Professor, Civil and Environmental Engineering Department
Director, Center for Transportation and Logistics
Director, Engineering Systems Division
W
1
SKU Segmentation Strategy for a Global Retail Supply Chain
By
Brad Gilligan
And
Huiping Jin
Submitted to the Engineering Systems Division in Partial Fulfillment of the
Requirements for the Degree of
Master of Engineering in Logistics
at the
Massachusetts Institute of Technology
ABSTRACT
The concept of using different supply chain strategies for different products or product families
is a fairly simple component of supply chain management. This practice, known as SKU
segmentation, is widely used by many companies. However, most research and success stories
involve a relatively stable portfolio of brands and products, and products with easily identifiable
attributes such as profit margins and demand. This thesis attempts to determine if and how a
SKU segmentation can be conducted when product mix is constantly changing and many key
variables used in traditional segmentations are not known in advance. To explore this problem,
we analyze one year of purchase order data and shipment data provided by our sponsor company.
The objective is to use data from purchase orders to predict which items are candidates for
different supply chain configurations (i.e. an expedited supply chain for time-sensitive products
or an efficient supply chain if there is opportunity to reduce cost and still meet demand). We start
by mapping the current supply chain process using historical data and interviews with employees.
The key piece of the process we want to understand is how early or late products arrive at
destination in relation to when those goods are expected in retail stores (a metric we refer to as
"destination dwell time"). We then use visualization and statistical analysis to determine what
PO information is related to the destination dwell time. After testing various multi-factor
regression models to predict the length of this dwell time, we conclude that a neural network
regression model predicts this time most accurately. We then assess whether or not it is feasible
for the sponsor company to use this model to "speed up" or "slow down" the supply chain for
different products as needed.
Thesis Supervisor: Edgar Blanco
Title:
2
ACKNOWLEDGEMENTS
On behalf of Brad Gilligan:
I thank the entire faculty and staff of MIT's Center for Transportation and Logistics for
designing and managing this challenging and rewarding program. I thank my classmates for
enriching this experience with their insight and support, and my thesis partner Huiping Jin and
advisor Edgar Blanco for their contributions to this project. I thoroughly enjoyed working with
such brilliant people and learned so much from both of you.
I thank the many helpful partners at our sponsor company for making this project possible. We
appreciate you taking the time to teach us about your business, arranging tours, and providing
data. It was a pleasure to work with all of you.
I thank my parents, Tim and Jill Gilligan for always challenging me to better myself. You taught
me the value of education and hard work, and none of my achievements would be possible
without you. I also thank Leslie Herring for being by my side throughout this hectic year. Your
love and support made this experience more manageable and enjoyable than I could have
imagined.
On behalf of Huiping Jin:
First of all, I would like to express my deepest appreciation to our thesis advisor, Dr. Edgar E
Blanco, for his support and motivation. His guidance helped me in completing this research and
his enthusiasm in supply chain management really encouraged me to fully commit myself to this
area.
I would also like to give my special thanks to Dr. Bruce C. Arntzen for his guidance in getting
my graduate study at MIT started on the right foot and at the right direction. In addition, my
thanks also go to Jennifer Ademi and Allison Sturchio who had provided endless care to my life
at MIT and valuable advice on my career. You are the ones that made my life at SCM an
enjoyable experience.
I am also indebted to all the faculty members at MIT ESD SCM program for giving me a lot of
insights and help in completing my study and research.
I would like to thank my thesis partner, Bradley M. Gilligan, who has made tremendous
contribution in completing this thesis. I really enjoyed working with you in completing this
research.
Finally, and most importantly, I would like to thank my wife Yefei Gu, my father Yong Jin, and
my mother Lianfeng Tang. It is your support and love that made me this far. I greatly appreciate
for everything you have done for me.
3
CONTENTS
A BSTRA CT....................................................................................................................................
2
A CKN O W LED G EMEN TS.....................................................................................................
3
CON TEN TS.....................................................................................................................................
4
TABLE O F FIGU RES....................................................................................................................
6
TA BLE O F TA BLES .....................................................................................................................
8
1 Introduction..................................................................................................................................
9
1.1
Company-Specific Challenges of SKU Segmentation................................................
1.2
Hypothesis.....................................................11
1.3
A pproach ........................................................................................................................
11
2 Literature Review ......................................................................................................................
12
10
2.1 Purpose of Stock K eeping U nit (SKU) segmentation ......................................................
12
2.2 SK U segm entation dim ensions........................................................................................
12
2.3 SK U segm entation practice for fashion retail industry ....................................................
14
3 M ethods .....................................................................................................................................
15
3.1 D ata Collection ...................................................................................................................
16
3.2 Initial A nalysis of D ata and Supply Chain Process ........................................................
17
3.3 Quantitative A nalysis......................................................................................................
20
4 D ata A nalysis and Results.........................................................................................................
21
4.1 Initial D ata Statistical D escription...................................................................................
23
4
4.1.1 M easuring Tim ing Attributes....................................................................................
24
4.1.2 D efining and M easuring Dw ell Tim e ......................................................................
28
4.2 H ypothesis ..........................................................................................................................
29
4.3 M odel Construction ............................................................................................................
33
4.3.1 Ordered-Probit M ethod.............................................................................................
34
4.3.2 N eural N etw ork M odel.............................................................................................
38
4.4 Tests and Results ................................................................................................................
45
4.4.1 Ordered-Probit Model...............................................................................................
45
4.4.2 N eural N etw ork M odel.............................................................................................
46
4.5 Potential A pplication of M odel (Proof of Concept) ........................................................
48
5 Conclusion .................................................................................................................................
51
A ppendix I - Ordered Probit Model Output:.............................................................................
54
Appendix II - M atlab script for neural network m odel.............................................................
56
References.....................................................................................................................................
57
5
TABLE OF FIGURES
Figure 1 - Initial Understanding of Supply Chain Process and Terminology ...........................
18
Figure 2 - PO Lead Time Histogram ........................................................................................
19
Figure 3 - Lead Time Components..........................................................................................
22
Figure 4 - PO Attributes and Descriptions...............................................................................
24
Figure 5 - PO Create Date to Header Date Statistics (in days)..................................................
25
Figure 6 - Lead Time Components with Statistics ...................................................................
27
Figure 7 - Dwell Time Statistics (in days).................................................................................
29
Figure 8 - A scatterplot showing the days between PO Create and Cargo Receipt on Y-axis, and
Destination Dwell Time on x-axis. Different colors identify different departments, and size of
circle represents order quantity.................................................................................................
31
Figure 9 - Figure 8 has been modified to show a department with more variability than normal.
......................................................................................................................................................
32
Figure 10 - Figure 8 has been modified again to show a department with stable timing.......... 32
Figure 11 - Ordered Probit Model Output Summary...............................................................
36
Figure 12 - Ordered-Probit Prediction Evaluation....................................................................
37
Figure 13 - Model Training and Validation...............................................................................
42
Figure 14 - Error Distribution Histogram.................................................................................
42
Figure 15 - Regress Predicted Value on Actual (In-sample test) ............................................
43
Figure 16 - Regress Predicted Value on Actual (Out-of-Sample Prediction for 100 POs)..... 44
Figure 17 - Predicted Result VS Actual Dwell Time (Out-of-Sample Prediction for 100 POs).. 44
Figure 18 - Performance Sensitivity Relative to Change of Model Size (Number of
prediction= 1,000 PO s)..................................................................................................................48
6
Figure 19 - Histogram of Actual Cargo Receipt to First Keytrol.................................................
50
Figure 20 - Histogram of Actual Dwell Time for 100 POs ..........................................................
51
Figure 21 - Histogram of Improved Dwell Time for 100 POs .....................................................
51
7
TABLE OF TABLES
Table 1 - Factors influencing supply chain segmentation ........................................................
13
Table 2 - Ordered Probit Model - Test Result for 1,000 POs .................................................
45
Table 3 - Test Results without updating the model (model size=3,000, gap=3,000)...............
47
Table 4 - Test Results with updating the model (model size=3,000, gap=3,000)........................
47
Table 5 - Model Parameters Used in the Application Example ...............................................
49
Table 6 - Segment Predicted Dwell Time into Predefined Categories......................................
49
Table 7 - Example Strategies for Supply Chain Segments........................................................
50
8
1 Introduction
Before describing SKU segmentation, it is important to clarify what is meant by the term "SKU".
SKU is an abbreviation for Stock Keeping Unit and refers to a specific product within a
company's catalog. As consumers, we see SKUs every day in the form of barcodes. If you walk
through any large retail store, you will realize there are thousands of different SKUs, and each
one can have very different characteristics such as size, price, and demand. A SKU segmentation
is a simple concept that suggests there is a benefit to handling certain products differently.
To illustrate this concept, consider the way you may buy and care for a suit or dress for a special
event, and compare it to the way you buy socks. You would likely spend a lot of time shopping
around for the suit or dress and try on several different products. You would make sure to hang it
safely in your closet and would have it cleaned by a professional dry cleaner. When buying
socks, you would grab the product that is easiest to find and reasonably priced, and store them
and clean them with little care. The advantage of these different approaches is that you get a
quality suit or dress and you do not waste too much time or effort worrying about socks. This
exact same principle applied to an organization can tell them which products they should focus
on and which can be handled with little effort. The advantages are satisfying customers while
minimizing supply chain costs.
Our research explores how this concept can be utilized by a global retailer that procures and sells
a wide range of products in multiple regions. To simplify this project we focus only on items that
are procured in China for sale in the USA, but the intent is for this approach to be scalable and
repeatable to be applied to other parts of the business. We start by looking at their existing
product mix and supply chain process, then identifying which SKUs might need to be handled in
a more proactive and responsive manner, and which SKUs could be handled more economically.
9
1.1 Company-Specific Challenges of SKU Segmentation
A SKU segmentation can be very straightforward and useful for companies with a mostly static
product base. For example, a company with a very high-cost high-margin product line with
volatile demand would obviously benefit from a flexible and responsive supply chain. They can
afford to spend more on transportation in order to meet demand. On the other hand, a company
that sells a low-cost everyday item with stable demand can utilize a slow and economical supply
chain to control costs. In the real world, these segments of SKUs are not always so easily
identifiable. What if the company's product mix changes and they do not know in advance what
their margins and their demand will be? What if some SKUs are inherently more difficult to
handle and require additional time in the supply chain regardless of traditional attributes? These
are questions difficult to answer while working with a company that has a unique business
model.
Currently, our sponsor company treats every single product the same in terms of procurement,
transportation, and storage. This approach can result in high-value products being delivered to
stores late and missing sales, while low-value items could be delivered too early and
consequently take up valuable space in a distribution center. The company sells a large variety of
products, with price points that range from under ten dollars to several hundred dollars and
annual sales between a single unit and over one million units. This wide range of products
suggests there is definitely potential to customize the supply chain process for different SKUs,
but the company's business has some unique complexities that make this segmentation
challenging.
To begin, the company has a very dynamic product mix and an equally dynamic pool of
suppliers. Their business is seasonal, and consumer preferences change quickly and frequently. It
10
is very rare for them to sell the same SKU more than once, and their product assortment changes
constantly. The supplier market is highly fragmented and competitive, so they are constantly
working with new suppliers depending on where they can get products at the best value. Because
a SKU segmentation relies on the attributes and behavior of suppliers, products, and customers
over time, this volatility makes the process much more difficult.
1.2 Hypothesis
Even with the challenges presented by this business model, there is potential to identify SKUs
which can be handled differently to achieve improvements in cost and/or service. Because the
products and suppliers are constantly changing, we will look at higher level attributes of SKUs
such as merchandise departments, order sizes, and origin locations rather than lower level
attributes such as specific suppliers and styles, the most traditional segmentation attributes.
1.3 Approach
We used a combination of qualitative and quantitative analysis to identify when and how this
company could treat certain SKUs differently. The qualitative piece involved working with
stakeholders to clearly understand and map out their supply chain process from procurement to
store delivery. The quantitative piece involved statistical analysis to predict lead times and
demand for products based on SKU attributes. The deliverable is a model that could tell this
company which SKUs should be expedited in order to meet demand, which could be held or
processed differently to reduce costs, and which fit the current process.
11
2 Literature Review
SKU segmentation is not a new or innovative idea. Research on the topic is readily available, and
the technique is already used by many companies to improve supply chain performance.
However, because every company has a different mix of SKUs and different feasible supply
chain configurations, every segmentation requires a unique approach. Our sponsor company's
business model proved to be an exception to many of the conventional rules used to segment
SKUs.
In this literature review, we will discuss the history and purpose of SKU segmentation, the
typical and widely used methods, and industry-specific considerations. We will then describe
how the traditional approach to segmentation did not work for our sponsor company.
2.1 Purpose of Stock Keeping Unit (SKU) segmentation
A segmentation strategy is a systematic method of separating products into different buckets for
a certain purpose, which can include maximizing market share, minimizing risk, improving
efficiency, etc. The approach to SKU segmentation is usually to group SKUs based on criteria
that indicate which supply chain management strategies can be used to maximize a firm's value.
It can also be described as a process of understanding the nature of the demand for different
SKUs and devising supply chain strategies that can best satisfy that demand (Fisher, 1997).
2.2 SKU segmentation dimensions
SKUs can be segmented based on many dimensions. The most traditional way is the ABC
classification method, which is to segment the SKUs based on the dollar sales volume. The
underlying theory of this segmentation method is the 20-80 Pareto principle, which suggests that
12
20% of the SKUs account for roughly 80% of total revenue, and those 20% should deserve the
most attention from management.
The benefits of using the ABC segmentation method are that it is very easy to implement and
there are many established inventory control strategies based on it, such as continuous review (s,
Q)
inventory strategy, period review (R, S) inventor strategy, order-up-to (s, S) inventory
strategy etc. The shortcoming of this method is that it utilizes only one dimension to segment the
SKUs. Under ABC segmentation method, SKUs within the same bucket can still have very
different characteristics. For example, two SKUs may have similar dollar value contribution, but
one may have high unit value but low demand, and the other may have low unit value but high
demand. Obviously, it is not appropriate to apply the same strategy to both SKUs.
Due to the limitations of the ABC method, many other dimensions have been used for
segmentation. Additional product characteristics include profit margin, volume, demand
volatility, etc. Anthony Lovell summarized these dimensions as shown in table 1. (Anthony,
2005)
Table 1 - Factors influencing supply chain segmentation
Group
Product
Market
Factor
Life cycle
Variety within product group
Product type: functional or innovative
Handling characteristics
Shelf life
Physical size and weight
Value
PVD
Demand location/dispersion
Demand level (throughput)
Demand variability
Service expectations
Limitations on raw material
Source
Economies of scale
13
Production flexibility
Lead-time
Geographic and commercial environment
Existing infra-structure
Transport mode availability
Customs/duties/trade areas
Legislation
In addition to introducing new dimensions, SKUs can be segmented using multiple dimensions
instead of just one or two. A common approach is to first segment the SKUs based on two
dimensions, then add another dimension as a new axis to further slice the SKUs. An example
could be segmenting the SKUs based on volume ani volatility first, then adding profit margin as
the third axis to form a 3-dimensional segmentation.
In general, segmentation dimensions are industry specific or company specific. There is no
universal list of attributes that can be applied for all companies and all situations. Therefore,
when developing a segmentation strategy for our sponsor company, it becomes very important to
understand their industry and business model.
2.3 SKU segmentation practice for fashion retail industry
The retail fashion industry, from a supply chain management perspective, is usually described as
a perishable-goods industry. It is assumed that all the goods purchased during the period will be
sold out by the end of the season. This assumption is quite reasonable because the industry is
highly seasonal and excess inventory is usually sold via mark-downs. Therefore, the supply
chain model is often characterized as a single-period model. A classic example of this is the
newsvendor model, which assumes that every unit of supply will be sold or salvaged by the end
of a given time period with known demand distribution and fixed cost.
14
Based on this model, SKU segmentation for this industry has focused on lost sales, demand
patterns, margin, lead time, and holding cost.
Different supply chain strategies are then
developed to manage the flow of the goods from suppliers to retail stores. The goal is to balance
the tradeoff between lost sales due to stock outs and the cost of excess inventory.
On a higher level, those supply chain strategies can be categorized into several groups, such as a
"responsive" supply chain focused on reacting quickly to changes in demand, or an efficient
supply chain that aims to use the most economical transportation and storage options.
Our sponsor company's suppliers and product mix are constantly changing. This prevents us
from using many traditional dimensions used for segmentation such as demand variability.
Another caveat that made the segmentation even more challenging was that the sponsor company
requested that price and margin be excluded from the analysis because product availability is a
critical component of their strategy, regardless of profitability.
In order to segment their products, we will look at patterns and trends in the import process for
different categories of products. They currently treat all items in their supply chain equally, but
because they know that some items sit in their distribution centers for extended periods while
others are delivered late to retail stores, they believe that certain products have more urgency
than others. The objective of this thesis is to identify groups of SKUs that may warrant a
different supply chain process in order to reduce costs or better meet customer demand.
3 Methods
A traditional Stock Keeping Unit (SKU) segmentation begins by segmenting products based on
cost, profit margin, and the volume and variability of demand. Because the sponsor company did
not want to consider the cost of an item, and because they rarely sell the same SKU more than
15
once, we could not utilize profit margin or historical demand. This segmentation started by
identifying items that had abnormally long lead times, then working backward to find out what
characteristics could be contributing to those lead times. This process involved gathering data
from the sponsor company and learning about its supply chain through site visits and interviews,
plotting data to identify patterns and trends, and then building a regression model and
simulations to test and validate the correlation of variables.
3.1 Data Collection
The first step was a face-to-face meeting with the key stakeholders of this project (VP of
International Logistics and Trade Compliance and VP of Logistics Development) at their
corporate headquarters. This meeting served as an introduction to the company's supply chain
process and provided an opportunity to ask questions to determine which variables could be
relevant to the project. The next step was to tour facilities that receive and ship goods, in order to
see the supply chain in action and observe the physical flow of materials. These facilities
included a third party deconsolidator (crossdock) and a company distribution center.
After developing an understanding of the company's end-to-end supply chain, we then looked at
one year of historical data. In order to narrow the focus of the project, we looked at only data for
shipments from China to the US. The data included 298,754 records (rows) and 48 fields
(columns). Each record represented one shipment of one SKU. Shipments that contained
multiple SKUs were listed in more than one record, and multiple shipments of a single SKU
were also listed separately. The data included 491 unique suppliers, 38,306 unique Purchase
Orders, and 33,566 unique SKUs.
16
3.2 Initial Analysis of Data and Supply Chain Process
Once we received the data, we tried to tie each element of data to the specific supply chain
processes that were explained by the company and witnessed at their facilities. We also clarified
when each element of data was created and how it was generated (i.e. the PO Quantity is
generated at the time the PO is created by the buyer). After validating the source and meaning of
the data, we then attempted to validate the actual dates and numbers. After identifying records
with missing and incorrect data, we made revisions before continuing the analysis. An overview
of the supply chain process and definitions of key dates and terms is shown in Figure 1 on the
following page.
17
ORIGIN LEAD TIME
Supplier
PO Create Date = Sponsor company agrees to buy goods.
Start Ship Date = Sponsor company agrees to accept shipments of this PO.
Book Date = Supplier arranges shipment of goods.
Con Can Date = The last day the sponsor company will accept shipments of this PO.
Consolidator (accepts shipments on behalf of sponsor company and arranges ocean shipping)
Cargo Receipt Date = Goods are received by the consolidator.
Consolidation Date = Goods are in an ocean container and ready to be shipped.
Origin Port
ETD = Estimated time of departure. This is the date the goods leave the port.
OCEAN TRANSIT TIME
DESTINATION LEAD TIME
Destination Port
ETA = Date the vessel reaches US port.
Deconsolidator (receives containers and ships goods to sponsor company distribution centers)
Arrive Decon = Goods received by deconsolidator.
Distribution Center (DC)
1st Keytrol Date = Goods received by distribution center.
IRetail Store
LP Date = Goods expected in store.
Figure 1 - Initial Understanding of Supply Chain Process and Terminology
The next stage of the qualitative analysis entailed looking for high-level patterns and trends in
SKU lead times. We used a range of visualizations to reveal patterns and found histograms, boxplots, and scatter-plots to be the most useful. The analysis started by looking at the total lead
time from the creation of a purchase order to distribution to retail locations. The following
histogram shows the distribution of this lead time.
18
130K
120K
110K
100K
90K
80K
70K
60K
SOK
40K
30K
20K
10K
OK
Null
0
50
100
150
200
250
300
350
400
550
Days from PO Creation to Retail Store Distribution
Figure 2 - PO Lead Time Histogram
After looking at this total lead time, we focused on anomalies and looked at additional details to
determine which specific processes were contributing to the long lead times. For example, were
the long lead times a result of the time spent getting from the supplier to the origin port, or the
result of time spent at the company's DC in the destination country?
After identifying the outliers that could be causing unpredictability and unnecessary costs in the
supply chain, we looked for factors that these records had in common in an effort to determine
19
causality. We developed theories about product departments, seasons, and other variables that
could be correlated with lead time.
3.3 Quantitative Analysis
Using the variables identified during the qualitative analysis, we built regression models to
explore how well lead time could be predicted using specific variables. For instance, do products
in certain departments or products sold in certain seasons take longer to get from origin to
destination? To build the regression model, we focused on the top seventeen SKU categories by
order quantity, which account for 80% of total volume. We set lead time to be the dependent
variable and ran several iterations using different independent variables in order to identify those
that were most correlated with the lead time.
Once the regression model was working reasonably well, we used it to estimate lead times for a
sample of 100 SKUs. The advantage of an accurate estimation of the lead time is to give the
sponsor company more predictability in their supply chain. This predictability will allow them to
take advantage of opportunities to handle certain SKUs with more cost-effective supply chains.
For example, if they know a product will have a three month lead time, they do not need to
import it immediately and hold it in their distribution center. They can hold the item at origin and
use more economical storage and transportation options.
In order to demonstrate this value, we use our model to delay the export of shipment of SKUs
that we predict will have an abnormally long lead time. We can simulate the resulting time spent
at DCs and compare it to the actual time spent at DCs to predict potential savings.
20
4 Data Analysis and Results
We analyzed 2013 purchase order data for shipments from China to US. The analysis consisted
of four stages: 1) initial statistical data description; 2) hypothesis; 3) model construction; 4) tests
and results.
In the first stage, we looked at transit time statistics for shipments from China to US, including
averages, standard deviations, and distributions. Then, we broke down the total lead time into
several components in order to understand how each part behaved and contributed to the total
lead time, as shown in Figure 3.
21
i*
fD
P0 Create - Cargo Received
PO Creat Date Book Date
Confirmation Date
Month
PO CreateI Sail Date
Actual Receipt Date
lConsolidation Date
CY
Book Date
Con Can Date
CFS
Actual Receipt Date
Consolidation Date
Ui|
PO Create Datel
Itrt Shp Date
PROCESS DETAILS
ORDER DETAILS
ecpected at
ETD
Load Port
Origin Service
PO CreateDC Receipt
kI
Estimated Arrival
SaIlate -,
I
1
Estimate Arrival Deconsolidator Arrival
Delivery
BookedHeader Date
. .......
....
..
....
Destination Service
I
First KeyL Date -
Last Keytrol Date
DC Receipt
I
I
Deconsollor Date -
Last Header
Place of
Arrive Decon
Discharge Port
Store Ready
EFA
PO Create Date - Header Date
Actual Weight
Actual Measurement
Actual Packages
Actual Quantity
Vndor
The purpose of this study was to find out how different supply chain strategies can be applied in
order to reduce the dwell time at destination DCs and the relevant logistics costs. In order to do
this, the second stage of our analysis focused on hypothesizing on what attributes on a given
purchase order may help to explain why the dwell time at DCs behaved differently. Data
visualization is used to help to build our initial hypothesis. Based on the visualization result,
certain attributes are selected to be included in our hypothesis that can help to explain the
variation of the dwell time at destination DCs.
In the model construction stage, regression models are used to verify the correlation between the
ten attributes and dwell time at DCs. Specifically, two types of regression models are used to
carry out the analysis: multi-factor based regression model and ordered-probit regression model.
Finally, in the result and test stage, out-of-sample data are used to test the accuracy of the
regression models' predictions, and simulation is further used to test the effectiveness of the
segmentation strategy based on the regression results.
4.1 Initial Data Statistical Description
One year's Purchase Order data for shipments from China are given to perform the analysis.
There are total 298,711 specific order lines. Unlike traditional segmentation approach, which
typically used attributes such as profit margin, demand volume, demand volatility, value density
etc., the challenge for our study is to segment the SKUs using only the attributes on the Purchase
Orders. Figure 4 is the list of the attributes and their descriptions on a typical Purchase Order.
23
Dat
Element
Element Description
If N then only TJX po data; If Y then Damco shipment Data; APLL older PO Data
PO Shipped
Division
PONumber
)
Oracle
Agent Num
Date
UP
(M/Y
Po Create Date
Strt Shp Date
PO Merchandise Type
Pretkt ind
Prepk
Vendor
Numn
Po Page Num
Po Line Num
Nesting Code
Con Can
1Dte
ind
Style
Ladder
into
Sku
Indicator
Style
of set
Indicates if Item Is
Set Indicator
Arrive Decon
1st Keytrol
Last Header
Deconsoliator Date - DC Receipt
PO Create - DC Receipt
First Keytrol Date - Last Keytrol Date
PO Create Date - Header Date
PO Create -Cargo Received
PO Create -Sail Date
Sail date -Estimated Arrival
Estimated Arrival - Deconsolidator Arrival
PO Create Date - Book Date
Booked -DC Receipt
-Header Date
Booked
Equipment Number
Book Date
Confirmation date
Actual Receipt Date
Create
of
goods
received origin
origin
arrived
of arrival
at
umber
goods
is
of
Consolidation Date
ETD
ETA
Carrier
Service
Destination
Load Port Country
Load Port
Discharge Port Country
Discharge Port (Damco)
Place of Delivery
Ordered Quantity
Actual Quantity
Actual Packages
Actual Weight
Actual Measurement
Origin
Division Number
PO Number
PO Department Number
TiX
TJX Agent Number
PO Cancel date at freight forwarder
PO
Plan Month (expected at DC)
Date po was entered
mainframe
Earliest date Vendor can deliever the goods to consolidator
Po
Type
Preticket Indicator
PrePak
Vendlor
Number
Page on Po for style number
Line on PO for style number
Code for pack together
From ACT part a
Date the goods arrived atthe deconsolnoator (US)
First Date of cargo receipt at DC
Date that goods were worked at the DC
Timing: Arrival at Deconsolidator -Arrival at DC
Timing: Po Create date - Arrival at DC
Timing: First Date cargo receipt at DC - Date that goods were worked at the DC
date - Date that goods were worked at the DC
Timing: Po
Timing: Po Create date - date
were
at
Timing: Po Createe dat
e goods sailed from
Timing: Transit time for goods on the water
port - Date goods
at econsolidator
Timing: Date
Timing: PO Create date - Vendor booking date
Timing: Vendor booked date - Arrival DC
were worked at the DC
Timing: Vendor booked date - Date that
Container N
Vendor Booking Date
Date Damco confirmed booking
Actual cargo receive date
date that
Consolidation date cargo: CF the date the container stuffed, CY
the cargo has been received at the po
Estimated Vessel Departure Date
Estimated Vessel Arrival Date
ship
factory
Mode (Consolidated by forwarder
Destination Mode (Port Move
Door Move)
Export Country
ExportPort
Country discharge Port
Port Arrival
Final Destination on BL
Po Ordered Units
PO Shipped Units
PO Shipped Cartons
POShippedWeight(kgs)
Po Shipped Cubic meters
#
Dept Num
AP Vendor (Lawson
Service
line Carrier
Steam
Origin
of
vs
or
the
load)
of
Figure 4 - PO Attributes and Descriptions
We first wanted to understand how the different timing attributes behaved across the whole data
set and statistically measure the time spent in different stages of the supply chain process, along
with the variation and distribution of this timing. Most importantly, we wanted to understand
how dwell time at destination DCs varies across different Purchase Orders, since this is the
attribute we try to explain and predict in our analysis.
4.1.1 Measuring Timing Attributes
We first looked at the total time spent for moving shipments from China to US in the given data
set. We used PO Create - Header Date to measure this time attribute. This measure is equal to
24
the number of days between when a PO is created and when it is finished being processed at a
DC and ready for distribution to retail stores.
PO Create Date - Header Date
tMspwiofPO OatDt- HOdr Date
One Variable Summary
Mean
Variance
Std. Dev.
Skewness
Kurtosis
Median
Mean Abs. Dev.
Mode
Minimum
Maximum
Range
Count
m
117.00
34.14
112.00
34.00
630.00
3rd Quartile
Interquartilo Range
56.00
Ist Quartile
MO1I
baw0
596.00
284497
35660800.00
95.00
151.00
Sum
e g a m
125.35
186114
43.14
0.8370
4.0091
g
g
Figure 5 - PO Create Date to Header Date Statistics (in days)
As it is shown in Figure 5, the company spent an average of 125 days moving shipments from
China to US, with a median of 117, standard deviation of 43 days, minimum of 34 days, and
maximum of 630 days. So, its distribution is skewed to the right with a skewness of 0.837 and a
kurtosis of 4.
We then broke down this total lead time into several sub-components and looked at how they
behaved statistically, as shown in Figure 6. Because our study will be used to help the company
determine different supply chain strategies for moving future shipments, only the time attributes
that cannot be determined at the time of decision making are of particular interest. Those time
attributes are:
25
1) Estimated Time of Departure from origin port to Estimated Time of Arrival at destination
port (ETD to ETA)
2) ETA to Arrival at Deconsolidator Warehouse
3) Deconsolidation Date to receipt at company Distribution Center (DC)
4) Date goods received at company DC to date goods were processed at DC
Of these four attributes, the first three can be used as lead time distribution inputs in order to
simulate the outcome of using different supply chain strategies. The fourth element partially
captures the dwell time spent at destination distribution centers. Since destination dwell time
(days between arrival at a DC and actual demand at retail store) is the key attribute we tried to
explain and predict, our next focus is on how to define and measure this attribute appropriately.
Figure 6 on the following page quantifies the different lead time components that were identified
earlier.
26
II
a
I
rilli I
I
I
5|-|3
I
I
~I
-j
I~I
I
I
51 +;
2
II
'Ia
1;I I
2
I
II
611111
AI 'III
I
Figure 6 - Lead Time Components with Statistics
27
4.1.2 Defining and Measuring Dwell Time
Dwell time is the time difference between the goods received at DCs and the actual demand
window. In order to correctly measure the dwell time, we first need to understand when the
shipments were received at destination DCs and when they left. In the data set given, First
Keytrol Date (as shown in Figure 1) represents the time the shipments are received. To measure
the time shipments left a DC, our original thought was to use Last Header since this attribute
represents the last date that the goods were worked at DC. However, during interviews with the
company, we were told that the Last Header is not an accurate measure of the date a shipment
leaves the DC for two reasons. First, Last Header is the date the last item was processed at DC.
In many occasions, the majority of the inventory has already left the DC and any remaining
pieces, no matter how small the quantity, would lead to an unrealistically late Last Header date
for the entire PO. Second, the actual demand may happen before a shipment arrives at DC. In
other words, the shipment was late and the Last Header date will be beyond the actual demand
date.
Therefore, in addition to the Purchase Order dataset, the company gave us the actual Ladder Plan
dates to represent the actual demand window. The dwell time at DC is then equal to the number
of days between the First Keytrol Date and the Ladder Plan Date. If the result is negative, it
means the shipment was delayed and failed to fulfill the demand on time.
28
First Key to LP
One Variable Summary Updated LP Date
Histogram of First Key to LP/ Updated LP
Variance
1.42
890.26
20OW
Std. Dev.
29.84
16M
Skewness
Mean Abs. Dev.
5.3008
46.7737
-2.00
15.85
Mode
-4.00
Minimum
-108.00
Maximum
399.00
507.00
Mean
Kurtosis
Median
"ane
Date
33O
1
M
LZM
0COO
WW
Figure 7 - Dwell Time Statistics (in days)
As shown in Figure 7, the historical dwell time averages about I to 2 days with a standard
deviation of almost 30 days, which indicates the historical dwell time is very volatile. Also, with
the median of -2 days, more than 50% of shipments failed to arrive before the actual demand
window. In the next section, we will build our hypothesis regarding which attributes can help to
explain this dwell time variation.
4.2 Hypothesis
There are many factors or attributes that may have some level of explanatory power of the dwell
time variation. In this study we are limited to the attributes on the purchase orders, and only the
attributes that are available before moving shipments from their port of origin can be used.
Attributes that are created after that are hind-sighted information and therefore cannot be used to
predict dwell time. The attributes that can be used for this study are listed below:
1) Division - The sponsor company operates multiple retail chains. Each one is a
considered a division in this data.
29
2) Department - Each item has a department number that represents the category of
item (i.e. shoes, menswear, etc.)
3) Vendor - Each supplier is assigned a unique ID.
4) Agent - Some products are sourced through agents, which are also assigned
unique IDs.
5) Start ship date - The date that suppliers are able to begin shipping product.
6) Con cancel date - The deadline for suppliers to arrange shipment of product.
7) Merchandise Type - Proprietary
8) Ladder Plan Month - The month that an item is expected to be for sale in retail
stores.
9) Place of Delivery - Destination location
10) Loading Port - Origin port
11) Style Ordered Quantity
12) Actual Quantity
13) Actual Packages
14) Actual Weight
15) Actual Measurement
16) Pre-ticketed - Whether or not an item has a price tag at the time it leaves the
supplier facility.
17) Pre-packed - Whether items are packaged for store delivery by the supplier, or
the company must repack them at their distribution center.
18) Time between PO create and Cargo Receipt at origin
19) Time between PO create and Start to Ship
30
.~
.....
....
...
...
.........
..
We then used data visualization to quickly identify which of those attributes can help to explain
the dwell time variation.
Sheet
1
Dept Num
101
102
400
103
109
350
112
113
C
300
114
115
C
110
*120
S124
geC
200
150
*120
128
U129
131
*133
0
235
CC...4.
50
100
236
6
238
*1A
150-
3500
2350
130
*362
*363
*366
PO Ordered Quantity
-100
0
50
100
150
200
PO to Cargo Received
250
300
350
4130
1000
147000
Figure 8 - A scatterplot showing the days between PO Create and Cargo Receipt on Y-axis, and Destination
Dwell Time on x-axis. Different colors identify different departments, and size of circle represents order
quantity.
For example, in Figure 8, we plotted the number of days cargo spent at the company DC (DC
receipt to ladder plan date) against the number of days between the date the PO was created and
the date the cargo was received at origin, based on Department Number and Ordered Quantity
attributes. Visually, we can quickly identify that it seems that as PO to Cargo Received time
increases, the dwell time will decrease. In Figures 9 and 10, we see that Dept 236 has much more
dwell time variation when compared to Dept 346.
31
Sheet
Dept Nun,
1
4W0
350
e.,
150
:
.
a
-
250
I
*
ON
*
IM
PO
100
Ordered Quantity
S500DO
50
100
200
PO to Cargo
250
300
350
1 OD0O
147000
400
Recoied
Figure 9 - Figure 8 has been modified to show a department with more variability than normal.
Dept Num
Sheet I
400
350
300
250
200
150
100
ME
50
ii
PO
Ordered Quantity
) 50000
50
100
20
150
PO
to Cargo Re ~e
250
300
350
400
1001
147000
Figure 10 - Figure 8 has been modified again to show a department with stable timing.
32
By using this data visualization approach, we narrowed down the original attributes to create the
following list:
1) Department (Binary Variable)
2) Merchandise Type (Binary Variable)
3) Ladder Plan Month (Binary and Numerical)
4) Place of Delivery (Binary Variable)
5) Dvision (Binary Variable)
6) Pre-ticketed (Binary Variable)
7) Pre-packed (Binary Variable)
8) Time between Cargo Receipt and LP month (Numerical Variable)
9) Time between PO create and LP month (Numerical Variable)
Our hypothesis is that these nine attributes can help explain the dwell time variation. In order to
test our hypothesis and understand the numerical relationship between these nine attributes and
dwell time, a numerical model must be constructed. In the next section, we discuss our model
construction and results.
4.3 Model Construction
In the previous section, we hypothesized that there are nine attributes that may help to explain
the dwell time variation. At this stage, we use various multifactor regression models to test this
hypothesis and determine the numerical correlation between the variables and the dwell time.
The company is particularly interested in segmenting future shipments into the following groups
so they can use different supply chain speed to improve on-time performance:
1) Late shipment: dwell time is less than negative 21 days
33
2) On time shipment: dwell time is between negative 21 days and 0
3) Early shipment: dwell time is greater than 0.
The remainder of this section documents the development of an ordered-probit regression model
and a neural network regression model that proved to be most effective in identifying correlation
and predicting dwell time. We then provide an example of how a regression model can be used
to form a segmentation strategy for the purchase orders based on the predicted dwell time and
simulate the impact on on-time performance.
4.3.1 Ordered-Probit Method
Since our objective is to determine a method to segment future purchase orders into three groups,
we decided to use ordered-probit method to construct our model instead of using simple linear
regression method. We assumed this model would be more accurate and reliable because it
predicts the probability of dwell time falling in a given range rather than predicting an exact
number of days as in a linear regression. Unlike standard linear regression models where the
dependent variable needs to be numerical, an ordered-probit method is a technique used to
regress categorical values against the chosen attributes. Instead of a predicted value, the output
of a probit model is the likelihood of the occurrence of each category given a set of inputs. A
tyical ordered probit model can be described as follows (Chris Brooks, 2008):
=i
xi /3 + EL
Where ei are independent and identically distributed random variables, xi
is the independent
variable matrix, and 0 is the coefficient matrix. Then, yi is determined from yi* according to the rules
below:
34
if y* :5 y1
ify1<yt<y2
if yi* > Y3
1
yi =
2
(3
Then, the probabilities of observing each value y are given by:
P(yj = 11x,f, y) = F(y1 - xi' f)
F(y 1 - x i)
P(y = 21xi,f, y) = F(y2 - xi'
P(y = 31x,fl,y) = 1 - F(y2
- xi #)
The yi, the threshold values, and f , the coefficient matrix will then be estimated according to
the natural log likelihood function:
Maximize: L( 53, y)
ln(P(y1
=
= jIxi, fl,
y))
(yi = j)
i=1 j=1
is a logical value. If y = j is true it will take a value of 1,
In the above formula, 1(y =
j)
otherwise it will be 0. F( y
x' f
-
) is the
cumulative probability function of the error terms,
which is assumed to be normally distributed.
To build an ordered-probit regression model, the dependent variable - dwell timein this case - is
translated into three categorical ranges. Before running the model, we still have to transform the
original dwell time values into the categorical values, which are detailed as follows:
" Categorical value: 1, for dwell time <=-21 days
* Categorical value: 2, for dwell time >-21 days and <= 0 day
o Categorical value: 3, for dwell time > 0 day
Next, we constructed the model in EViews, which is an econometrics software. In choosing the
maximizing optimization method, the default Quadratic hill climbing method is used, the model
output is summarized in Figure 11:
35
Pseudo R-squared
Schwarz criterion
Hannan-Quinn criter.
0.364280
1.247907
1.237530
Akaike info criterion
Log likelihood
Restr. log likelihood
1.232705
-23118.32
-36365.56
LR statistic
26494.47
Avg. log likelihood
-0.614571
Prob(LR statistic)
0.000000
Figure 11 - Ordered Probit Model Output Summary
The correlation coefficient between the dependent and independent variables as well as the
significance level can be found in Appendix I. Since this is an ordered probit model, those
coefficients cannot be directly interpreted as how much the dependent variable will change by
changing one unit of the independent variables. Usually, marginal effects are calculated and used
to measure how much the probability of the dependent variables will change given a unit change
of the independent variables. Nevertheless, those coefficients can still be used to get a sense of
the relative strength in correlation with the dependent variables among the independent variables.
Specifically, the higher the coefficient, the higher is the chance that the dependent variable will
fall into category 3.
Regarding the model fitness, as indicated in Figure 11, the Pseudo R-squared value is 36%.
However, since this is an ordered-probit model, this R-square cannot be directly interpreted as a
measurement of goodness-of-fit. To better measure this model's predictability, the model
outcome should be compared to the constant probability in the original dataset. This is to
measure how the model performs in prediction relative to always choosing the category that has
the highest historical number of occurrence, which in our case will be category 2 that has 45%
occurrence in the past. Figure 12 shows the comparison of the model ability to predict the dwell
time:
36
Prediction Evaluation for Ordered Specification
Equation: EQ02PROBIT
Date: 04/20/14 Time: 11:15
Estimated Equation
Dep. Value
Obs.
Correct
Incorrect
% Correct % Incorrect
1
4233
1438
2795
33.971
66.029
2
17034
14570
2464
85.535
14.465
3
16350
13543
2807
82.832
17.168
Total
37617
29551
8066
78.558
21.442
Constant Probability Spec.
Dep. Value
1
2
3
Total
Obs.
4233
17034
16350
37617
Correct
Incorrect
4233
0
16350
20583
0
17034
0
17034
% Correct % Incorrect
0.000
100.000
0.000
45.283
100.000
0.000
100.000
54.717
Gain over Constant Prob. Spec.
Dep. Value
Obs.
Constant
Equation
% Incorrect % Incorrect Total Gain*
Pct. Gain**
33.971
1
4233
66.029
100.000
33.971
2
17034
14.465
0.000
-14.465
NA
3
16350
17.168
100.000
82.832
82.832
Total
37617
21.442
54.717
33.275
60.812
Figure 12 - Ordered-Probit Prediction Evaluation
Overall, this model achieves about 78% prediction accuracy. When compared to the constant
probability, the model improves prediction performance by 33%. However, the limitation of this
model is that it can only predict categories two and three with high accuracy. Its accuracy for
category one is only 33%. Moreover, since this model incorporates many binary variables, it will
frequently encounter multicollinearity problems, that were fixed in the final models, but could
resurface when running the model over new datasets.
37
4.3.2 Neural Network Model
Due to the limitations of the ordered-probit model, we used a neural network regression model in
an effort to improve prediction accuracy, goodness-of-fit, and application feasibility.
4.3.2.1 Neural Network Model Mathematical Equations and Algorithm
Neural network is usually referred to the various mathematical models that imitate human brain
functions (Huangjin Tang, Kay Chen Tan and Zhang Yi, 2007). It has wide applications in areas
such as artificial intelligence, information processing, engineering, and finance for pattern
recognition, function approximation, forecasting purposes. In statistical forecasting, unlike
traditional regression model which relies on modeler's ability in guessing the causal-and-effect
function between the inputs and the outputs, neural network method provides a way directly
learn the internal relationship between the variables in a system (Ke-Lin Du & M.N.S Swamy,
2014). This feature is very helpful when the underlying relationship between the inputs and
outputs in a system cannot be very well estimated.
The most widely used neural network model in statistical forecasting is feed-forward networks.
A typical feed-forward network structure consists of a layer of inputs, a single or multiple hidden
layers and an output layer. A typical feed-forward neural network model's mathematical
equations can be described as follows:
1. Input variables and non-linear transform function:
=(S j)
Xj
0
d(l-1)
)
(-
(1w 1=
38
6(S)
es - e-s
es + e-s
=
Where:
1
1
L (1 stands for which layer in the model, L is the largest layer in the model)
0
i
1
j < d(') (i stands for which output in the model, d is the number of outputs)
d(-')(i stands for which input in the model, d is the number of outputs)
x
is the ith output at layer (1 - 1)and the ith input at layer I
x!is the jth output at layer 1
w!- is weight
0(S)is a tansigmoidnonlineartransform function for the input variable
2. Output and error term:
The final output of the model is a linear output. The error term, which is the difference between
the model output and actual value, is often measured by mean squared error. Based on the
equations for the input variables, the error term is essentially a function of w!b . To minimize the
error term, w!b can be determined by:
de(w)
Ve(w):
de(w)
a
(1
awi
de(w)
sl
__S_
aw(1)
Since:
39
x.
, so only
8w
(w) needs to be calculated.
S~l
3. Back propagation:
To find the optimal weight, neural network regression models use a method known as back
propagation. The error terms are run through the network layers in reverse order, then a gradient
descent method is used to determine the optimal weight that minimizes the error term (Ke-Lin
Du & M.N.S Swamy, 2014). Its mathematical equation usually can be described as follows:
80)
=e(w)
as~l
Starting from the last layer:
d(l)
-ae(w)
81 d =1
i
j=1
a
_ x>
e(11)l
=x
i
i
d(1)
_
i
=
8
x1w0f(
x 6' (SO'~)
j=1
4. Algorithm:
A typical back propagation neural network algorithm follows the following steps:
a) Randomly initialize w (1
b) Forward compute all x! in the net
)
c) Back propagate all 6(1
d) Update wf
e) Iteration
f)
Find the optimal wf that gives the lowest e(w)
The neural network mathematical structure also has many derivatives which can use different
non-linear transform functions, error term measurements, layer structures and so on. In this
study, the modelling is based on the back-propagation feed forward model described above.
40
More specifically, the neural network model used in this study has one input layer, one output
layer, and 10 neurons.
4.3.2.2 Model Building in Matlab
To build, run, and test the neural network model, we used Matlab technical computing software.
3,000 purchase orders are first used to build the model. A rolling forecast mechanism is designed
to roll the model over the entire 37,617 purchase orders in order to fully test the accuracy and
robustness of the model. Parameters such as model size, variables to be included, and which part
of the dataset to use to build the model and forecast, can be entered as the script starts to run.
Because the sponsor company would only be able to use data from POs that have been delivered,
we include a gap of 3,000 purchase orders in the initial model to represent the time gap needed to
update the model. The size of this gap is another parameter that can be controlled. The detailed
Matlab script for our model is presented in Appendix II.
Also, in choosing the input variables, we narrowed down number of input variables from the
nine variables used in the ordered probit model to five variables, which are Merchandise Type,
Pre-ticked, Pre-packed, Division, and Time between Cargo Receipt and LP Month. The reason is
that in building our neural network model, we found that adding the Department, Time between
PO creation and LP month, and Place of Delivery variables didn't help to improve the
performance of the model, and adding them into the model will simply complicate the
application of the model, since it will ask users to provide more inputs than necessary.
We use this script and the first 3,000 purchase orders in the dataset to build, train, and validate a
neural network model. Figures 13, 14 and 15 show the resulting model construction.
41
Best Validation Performance is 106.2722 at epoch 7
10
-
10,
0
h
Train
Validation
Test
Best
3
So
10
_
102
10
10 0
_k
0
4
2
6
8
12
10
13 Epochs
Figure 13 - Model Training and Validation
Error Histogram with 20 Bins
700
Training
Validation
Test
Zero Error
600
500
0
500-
400
300
200
100
C
9
Errors = Targets - Outputs
Figure 14 - Error Distribution Histogram
42
Validation: R=0.9243
Training: R=0.96247
t
250
d
a
+
o
250
Data
Fit
Y= T
-200
CP
Data
Fit
---- Y = T
200
150
150
100
D
0
100
50
50
0.
o05
100
0
+
0
250
C4
200
150
All: R=0.95947
250
0'
200
LM 150
150
100
100
0
50
100
Test: R=0.965
Data
Fit
Y =T
-
50
Target
/
0
0
200
Target
50
0
200
250
0
Data
-- -Fit
Fit
0'
0
0
o -5o
-50
0
100
Target
200
0
100
200
Target
Figure 15 - Regress Predicted Value on Actual (In-sample test)
As shown in figure 13, after training and validating, the model found the minimized MSE, which
is the mean squared error between the actual value and predicted value, is at 106. Figure 14
shows and compares the error term distributions, which is the difference between the predicted
value and actual value, during model training period, validating and train periods. The allocation
of the sample data for training, validating and testing is 70%, 15% and 15% respectively. In
figure 15, the predicted value, which is the output of the model, is regressed on the actual value,
which is the target of the model. The dashed line represents the ideal situation where the output
value is exactly equal to the target value and the R squared value is 1, while the solid line
represents the actual fitness. Overall this model has very good fitness as indicated by the high R
43
squared value. Next the model is used to predict the dwell time for 100 out-of-sample purchase
orders. Figures 16 and 17 show the result:
: R=0.99273
o
200
-
Data
Fit
--
'0
Cl!
150
'D
100
50
0
0
0
50
100
150
200
Target
Figure 16 - Regress Predicted Value on Actual (Out-of-Sample Prediction for 100 POs)
I
I
I
I
I
I
I
I
I - -
-
I
I
I
I
I
-
I
I
I
- -
-
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
60
SI
1
10
20
30
4
I
0
0
8
100
Figure 17 - Predicted Result VS Actual Dwell Time (Out-of-Sample Prediction for 100 POs)
In this out-of-sample prediction, the model achieves fitness of 99% with a constant bias of 4.2
days. In the following section, more tests are performed to evaluate this model's accuracy and
robustness.
44
4.4 Tests and Results
In this section, both the ordered-probit model and the neural network model are tested and
evaluated in terms of their predictive abilities, fitness, and feasibility in application.
4.4.1 Ordered-Probit Model
Due to the multicollinearity problem caused by the use of binary variables, testing for model by
choosing different sample size becomes difficult. The chosen binary variables that work over the
first 10,000 samples may have multicollinearity problems when the model is built from the next
10,000 samples, and the binary variables that cause this problem will have to be deleted from the
model, which will make the test results become incomparable. Therefore, we kept 36,617
purchase orders as our sample size, and run the model to predict the dwell time for the remaining
1,000 purchase orders in the dataset. Below is the result:
Table 2 - Ordered Probit Model - Test Result for 1,000 POs
Actual
Predicted correctly
Accuracy
Category 1
111
25
22.52%
Category 2
Category 3
467
422
128
290
27.41%
68.72%
Total
1000
443
44.30%
S
J
The prediction accuracy for this test is 44.3%, which indicates that the out-of-sample prediction
power of the ordered probit model is not accurate enough for the company to make business
decisions. One approach often used to improve the forecasting performance is to reduce the
number of categories to be predicted. however, in our study, when we used logit model to predict
one category, the forecast accuracy was even worse with the accuracy lower than 10%.
45
4.4.2 Neural Network Model
Unlike the ordered-probit model, using binary variables in a neural network model does not
cause any problems in running and testing the model. Therefore, the neural network model can
be tested over any portion of the given dataset. There are two ways to do this:
1) Build a single model to predict the entire dataset
Under this method, the first 3,000 purchase orders are selected to build the model. This model is
used to predict the remaining purchase orders.
2) Build initial model then update it on a rolling basis to predict the rest of the dataset
Under this method, the first 3,000 purchase orders are selected to build the model. This model is
then updated using the rolling window method to predict the rest of the dataset. For example, if it
is set to predict 500 purchase orders per run, it will use the first 3,000 POs to build the model and
predict the dwell time for the POs from 6,001 to 6,500 (including the timing gap size of 3,000
POs). For the next run, POs from 1 to 500 will be excluded from the model and POs from 3,001
to 3,500 will now be included in the model used to predict dwell time for POs from 6,501 to
7,000.
In either case, it is important to know how far this model can predict into the future while
maintaining an acceptable accuracy level and what sample size results in the most accurate
predictions. In other words, how frequent the model should be run in application to achieve the
highest accuracy.
The following table summarizes the test results under the two approaches:
46
Table 3 - Test Results without updating the model (model size=3,000, gap=3,000)
How far into the future
100 POs
500 POs
1000 POs
5000 POs
10000 POs
30000 POs
Fitness
99.27%
98.23%
98.30%
97%
96.50%
92%
Coefficient
1
1.1
1.1
1.1
0.98
0.89
Bias (days)
4.2
4.9
5.9
2.9
1.8
0.69
Table 4 - Test Results with updating the model (model size=3,000, gap=3,000)
Number of POs updated per run
100 POs
500 POs
1000 POs
1500 POs
3000 POs
Fitness
86%
86%
85.80%
83.70%
82%
Coefficient
0.92
0.87
0.88
0.93
0.82
Bias (days)
1.5
1.5
1.4
1.5
1.4
As indicated in Table 3, when tested under approach one the model achieves at least 92% fitness.
The coefficient
,
which measures the slope of the linear relation between the actual value and
predicted value, with one as the perfect forecast performance, averages at one and the bias is
between one and six days. When tested under approach two, the model achieves at least 82%
fitness, the coefficients vary between 0.82 and 0.92, and bias is 1.5 days.
Based on these results, two observations can be generalized:
1) Prediction accuracy will drop as the time horizon is extended
2) The rolling approach results in less fitness accuracy but is less biased
In the initial tests, the model size is fixed at 3,000 POs. The next step was to test the sensitivity
of the model performance relative to the model size. Figure 21 indicates that increasing the
47
model size generally improves performance. Additionally, once the model size crosses a
threshold the performance becomes less sensitive to changes in model size.
Fitness Coefficient
0.34
0.59
500
Model Size
700
0.94
Bias
3
1.1
2.5
1000
0.98
1
5.9
2000
3000
4000
0.97
0.98
1
1.1
-10
5.9
0.986
5000
6000
7000
0.97
0.95
0.97
1
0.97
0.93
0.99
2.21
3.5
2.5
10000
0.965
0.92
2
1.6
02
04
02
0
0
r
4400
M
60-tj
8000I
Figure 18 - Performance Sensitivity Relative to Change of Model Size (Number
1 X IL
IP
)X)
of prediction=1,000 POs)
4.5 Potential Application of Model (Proof of Concept)
Because the neural network model showed a clear advantage in prediction accuracy, we will not
explore the potential use of the ordered-probit model.
The predictions from the neural network model only solve part of the actual problem. How to
segment the POs based on the predicted dwell time and how to apply different supply chain
speed to improve on-time performance are the next steps to be taken for this model to be useful.
The following example demonstrates how this model can be implemented by the company.
First, 3,000 POs are chosen to build, train, and validate the model. As mentioned previously, the
next 3,000 POs are excluded from this simulation to represent POs that have not been delivered
and therefore do not have complete data. The detailed parameters of the model are summarized
in Table 5:
48
Table 5 - Model Parameters Used in the Application Example
Model Size
Gap Size
Input Variables
Number of POs to be predicted
3,000 POs
3,000 POs
Merchandise type, Preticked, Prepacked, Division, Cargo Received, LP Month
100 POS
The output of the model will be the predicted dwell time for the next 100 POs. Then, the 100
POs will be segmented into the three predefined categories:
*
*
*
Categorical value: 1, for dwell time <=-21 days
Categorical value: 2, for dwell time >-21 days and <= 0 day
Categorical value: 3, for dwell time > 0 day
Table 6 demonstrates how this part of the process would look in application:
Table 6 - Segment Predicted Dwell Time into Predefined Categories
PO
6001
6002
6003
6004
6005
6006
600
6008
6009
6010
6011
6012
6013
601
6015
6016
6017
601
6019
6020
6021
6022
6023
6024
6025
Predicted
5
5
133
5
5
163
5
5
-19
4
-19
3
3
-21
-15
13
13
13
-17
-21
3
3
-21
-21
-19
Actual
13
13
125
13
13
167
13
13
-15
13
-15
17
17
-14
-15
13
13
13
-15
-21
7
6
-11
-11
-13
Predicted Category Actual Category
3
3
3
3
3
3
3
3
3
3
3
3
2
3
2
3
3
2
2
3
3
3
2
1
3
3
2
2
2
3
3
3
3
2
3
2
3
3
2
2
3
3
3
2
1
3
3
2
2
2
Accuracy
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
The next step is to determine how the company can adjust supply chain speeds based on the
predicted segments in order to improve on-time performance and/or reduce costs. For
demonstration purpose, it is assumed that the company will adopt the following strategy as
shown in Table 7:
49
Table 7 - Example Strategies for Supply Chain Segments
Shipment Definition
Category 1 Late shipment
Category 2 On time shipment
Category 3
Early shipment
Supply Chain Speed TransitTime
Average-l1 days
Fast
Average
Normal
Slow
Average+predicted dwell time
In Table 7, the average transit time refers to the historical average Cargo Received Date to First
Keytrol Date, which is 32 days with its distribution shown in Figure 13.
Sheet 3
Figure 19 - Histogram of Actual Cargo Receipt to First Keytrol
Next, the transit time for those 100 POs (number of days between cargo receipt at origin and
delivery to TJX at destination) is changed according to the strategy in Table 7. Then, a new
dwell time for those 100 POs is calculated based on this change.
50
Actual Dwell Time
1
2C
X
45
C
0
ac
Figure 20 - Histogram of Actual Dwell Time for 100 POs
Improved Dwell Time
w
Figure 21
-
%fP
aa
C
60
2C
5C
C
90
C
Histogram of Improved Dwell Time for 100 POs
As Figures 26 and 27 indicate, before the improvement, 6% of POs arrived late and 58% of the
POs arrived too early. Among the POs that arrived early, 93% of them arrived at least 20 days
earlier than needed. If the company were to use the simple segmentation strategy determined by
the model, there would have been no late POs and 60% of them would have arrived exactly on
time. The remaining 40% of the POs would still arrive early, but would be early by fewer than 10
days.
5 Conclusion
Based on the tests of the models, we concluded that the neural network model achieves much
greater prediction accuracy than the ordered-probit model in this study. Additionally, the neural
network model can be easily updated to incorporate new information. This is a very useful
51
feature in actual application, especially for a company with seasonality. The ordered-probit
model cannot be updated as easily due to muliticollinearity problems caused by binary variables.
Therefore, the neural network model can be used by the company to predict the dwell time and
segment the POs based on the result. However, one limitation of the neural network model is that
the w! is initialized randomly when running the model, this stochastic process can sometimes
make the model generate high errors. In this study, the model typically has a MSE between 30
and 100. When the MSE is above 200, the model prediction accuracy tends to become unstable.
One way to correct this problem is to run and train the model several times until the error term is
down to a desired level.
The simulated application of this model shows that it is feasible to implement a segmentation
strategy based on the output of the neural network model and on-time performance can be
improved significantly. The six percent of POs that were delivered late could be expedited and
potentially increase sales. The shipments that arrive slightly early (less than a month) could be
shipped using slower and more economical transportation options. In the simulation, this
accounted for about half of the POs which means the potential savings are very significant. The
shipments that arrive very early are perhaps the highest area of opportunity. These purchases can
be acquired later from suppliers, or could be stored at origin. This will reduce holding costs at
destination DCs and free up space in their network that is used to store early shipments. This is a
great benefit to the sponsor company as it will allow them to increase volume without making
costly expansions their distribution network.
To maximize the performance of the model, we suggest the company capture additional data that
could be relevant to supply chain timing when creating POs. For instance, when touring
distribution centers we observed a lot of volatility in the amount of time different SKUs spend in
52
the distribution center before they are ready to be shipped to stores. This required processing
time is currently invisible to the company, but could be recorded and used to improve adjust
transit times for future orders. This information and additional data such as historical on-time
performance of different suppliers and buyers, or a metric that buyers can use to communicate
the urgency of POs, could be used to improve future versions of the model. Because there is
always uncertainty when using a predictive model, these metrics could also help the company
decide when they should buffer the model output.
53
Appendix I - Ordered Probit Model Output:
Variable
Coefficient
Std. Error
z-Statistic
Prob.
PRETICKTY
PREPKTY
JAN
MAR
MAY
JUN
AUG
SEP
OCT
NOV
TYPE_1
TYPE_2
TYPE_3
TYPE_6
-0.074357
0.085350
-0.059730
-0.295996
0.380402
0.004634
0.063681
-0.349777
0.233088
0.078296
-6.456124
-6.356646
1.364158
-6.202059
0.044614
0.023546
0.029739
0.026030
0.029859
0.028680
0.028568
0.025396
0.026165
0.022754
2389.213
2389.213
2404232.
2389.213
-1.666660
3.624768
-2.008460
-11.37137
12.73993
0.161569
2.229140
-13.77313
8.908471
3.440889
-0.002702
-0.002661
5.67E-07
-0.002596
0.0956
0.0003
0.0446
0.0000
0.0000
0.8716
0.0258
0.0000
0.0000
0.0006
0.9978
0.9979
1.0000
0.9979
TYPE_7
-6.278583
-6.519581
2389.213
-0.002628
0.9979
TYPE_8
2389.213
-0.002729
0.9978
POD_881
-0.627139
0.188543
-3.326244
0.0009
POD_884
-1.701864
0.450726
-3.775824
0.0002
POD_885
POD_955
POD_964
POD_970
NUM102
NUM103
-1.602656
-2.004570
-1.317218
-1.628698
-0.026699
-0.186398
0.257253
0.062149
0.024036
0.033680
0.058170
0.065245
-6.229885
-32.25430
-54.80076
-48.35846
-0.458972
-2.856896
0.0000
0.0000
0.0000
0.0000
0.6463
0.0043
NUM111
-0.130785
0.140679
-0.929671
0.3525
NUM112
NUM116
NUM120
1.487328
-12.63921
-0.720489
0.588088
1649925.
0.138239
2.529090
-7.66E-06
-5.211902
0.0114
1.0000
0.0000
NUM124
-0.326453
0.083075
-3.929623
0.0001
NUM128
NUM129
NUM236
NUM346
NUM347
NUM348
NUM349
NUM356
NUM358
NUM359
NUM360
NUM362
NUM363
NUM366
NUM450
NUM451
NUM452
NUM453
NUM455
-0.791264
0.032269
0.181421
0.037849
-0.317279
3.847498
-0.283656
0.287244
0.067265
0.020737
-0.021652
-0.064302
0.134225
0.258893
-0.322776
-0.359345
-0.457402
-0.367397
-0.024978
0.133675
0.065884
0.048861
0.039086
0.039231
1744173.
0.054707
0.041984
0.159771
0.040866
0.049639
0.055149
0.055393
0.049101
0.044953
0.051123
0.037862
0.048793
0.101328
-5.919305
0.489777
3.713000
0.968342
-8.087480
2.21E-06
-5.185038
6.841804
0.421010
0.507434
-0.436180
-1.165955
2.423134
5.272661
-7.180389
-7.029051
-12.08081
-7.529682
-0.246511
0.0000
0.6243
0.0002
0.3329
0.0000
1.0000
0.0000
0.0000
0.6737
0.6119
0.6627
0.2436
0.0154
0.0000
0.0000
0.0000
0.0000
0.0000
0.8053
54
113.0017
-2.708509
0.0976
0.2060
0.0244
0.0012
0.3927
0.2182
0.1039
0.0973
0.0000
0.0007
0.1212
0.0001
0.1411
0.0000
0.0000
0.0000
0.0068
-0.002321
-0.001413
0.9981
0.9989
0.212175
0.128076
1.656635
0.131815
-1.264550
2.251281
NUM539
NUM541
-0.166687
0.095850
0.306472
-0.049565
-0.228738
0.116640
0.201158
0.566689
0.199860
0.292992
0.203503
0.093107
NUM643
-0.345179
PO_TO_LP
CTOL
DIVISION 1
0.001152
0.066607
-0.101180
NUM469
NUM472
NUM475
NUM479
NUM480
NUM481
NUM484
NUM485
NUM486
NUM489
NUM490
0.042576
0.094646
0.057992
0.185760
0.071732
3.238086
-0.854689
-1.231368
1.626063
0.121329
1.657953
0.104034
0.058857
0.189039
0.052181
0.063268
0.064372
0.000258
0.000589
0.037356
5.447132
3.395705
1.549900
3.899922
1.471636
-5.362276
4.467529
Limit Points
LIMIT_2:C(66)
LIMIT_3:C(67)
-5.545330
-3.376751
2389.213
2389.213
1.232705
0.364280
Akaike info criterion
Schwarz criterion
1.247907
Log likelihood
-23118.32
Hannan-Quinn criter.
LR statistic
Prob(LR statistic)
1.237530
Restr. log likelihood
Avg. log likelihood
-0.614571
Pseudo R-squared
26494.47
-36365.56
0.000000
55
Appendix II - Matlab script for neural network model
"Dwell Time Forecast
start=input('Enter
starting
row number:');
ending=input('Enter ending row number:');
s=input('Enter size of the model:');
gap=input('Enter gap size:');
incr=input('Enter the number of POs to be predicted:');
sv=input ('Enter starting
variable number:');
ev=input('Enter ending variable number:');
storedprediction=[];
storedactual=[];
for n=(start:incr:ending)
in=inputmatrix(n:(n+s-1),sv:ev);
output=outputmatrix(n:(n+s-1),l);
inputs = in';
targets = output';
Create a Fitting Network
hiddenLayerSize = 10;
net = fitnet(hiddenLayerSize);
Set up Division of Data for Training,
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;
Validation,
Testing
% Train the Network
[net,tr]
= train(net,inputs,targets);
Test the Network
outputs = net(inputs);
errors = gsubtract(outputs,targets);
performance = perform(net,targets,outputs);
% Predict dwell time
predictinput=inputmatrix( (n+s+gap) : (n+s+gap+incr-1) ,sv:ev);
predictoutput=net(predictinput');
storedprediction=[storedprediction;predictoutput];
storedactual=[storedactual;outputmatrix( (n+s+gap) :(n+s+gap+incr-1) ,1)];
end
storedprediction=storedprediction';
storedactual=storedactual';
result=storedprediction(:);
actual=storedactual(:);
[r, c]=size(result);
figure
plot(l:r,result,'r')
hold on
plot(1:r,actual)
legend('result','actual')
grid on
figure
plot(1:r,actual)
plotregression(actual,result)
errorscalar=actual-result;
squarederror=errorscalar.^ 2 ;
meansqurederror=sum(squarederror)/r;
56
References
Brooks, C. (2007). Introductory Econometrics for Finance. Cambridge University Press.
Du, K.-L., & Swamy, M. (2014). Neural Networks and Statistical Learning. New York:
Springer.
Fisher, M., Hammond, J., Obermeyer, W., & Raman, A. (1997). Configuring a Supply Chain to
Reduce the Cost of Demand Uncertainty. Production and Operations Management, 211225.
Lovell, A., Saw, R., & Stimson, J. (2005). Product value-density: managing diversity through
supply chain segmentation. The InternationalJournalof Logistics, 142-158.
Tang, H., Tan, K. C., & Yi, Z. (2007). Neural Networks: Computational Models and
Applications. New York: Springer.
57