Map Worksheet Team: Map method Node Map Sorted Map Link Map Full Map Hash Map clear () 1 1 1 1 del (key) (a. find) N logN 1 1 (b. change) 1 N 1 1 get (key) N logN 1 1 hasKey (key) N logN 1 1 hasVal (val) N N N N N put (key,val) (a. find) N logN 1 1 (b. change) 1 N 1 1 size () 1 1 1 1 1 (12 min) I. Map – Abstract Data Type start time: 12:36 Every published book has a unique 10--digit International Standard Book Number (ISBN); for example, The Mythical Man-Month by Fred Brooks has ISBN 0-201-835-95-9. Similarly, every commercial product has a unique 13-digit Universal Product Code (UPC). The UPC for books is 978 followed by the ISBN, so The Mythical Man-Month has UPC 978-0-201-835-95-3. (You will learn later why the last digit is different.) These unique identifiers (usually a number or character string) are called keys; uniquely identified means that every item has a key and no two items have the same key. The key provides access to other information about the item, collectively called its value; thus, the value for a book includes the author, title, publisher, publication date, etc. The key and its associated value are a (key, value) pair. 1. (3 min) Identify likely keys and values for each of the following: Description Key Value includes a. taxpayers Address XXX Street, City, State, Zip Code b. courses offered at a college or university Course XXX Course #, times,credits c. entries in a dictionary or encyclopedia Word type of word (verb,noun,etc.), pronunciaton, definition In computer science, a data structure to store key-value pairs is called a map (or a dictionary), and might have an interface like this: interface IMap { void clear () // remove all keys & values boolean del (key) // delete key & its value value get (key) // get value for key boolean hasKey (key) // is key in map? boolean hasVal (val) // is val in map? boolean put (key,val) // put key,value in map int size () // return # of pairs } 2. (4 min) Trace the following actions in a map of 2-letter codes to country names. Key-value pairs can be stored in any empty location. Action pairs: Result put("IN", "India") IN/ India true put("CN", "China") CH/ China IN/ India true size() CH/ China IN/ India 2 hasKey("TO") CH/ China IN/ India false put("TO", "Tonga") CH/ China IN/ India TO/ Tonga del("CH") IN/ India TO/ Tonga put("GH", "Ghana") GH/ Ghana IN/ India TO/ Tonga hasVal("IN") GH/ Ghana IN/ India TO/ Tonga true 3. (2 min) An array uses an integer index to access a specific data object. Describe an array using map terminology - what is the key? what is the value? The key is the array. while the value is the index. 4. (2 min) Use map and array terms to explain why maps are called associative arrays. Because a key is essentially an array that is associated with values (idexes). Before you continue, review ...

1. Map Worksheet Team:
Map method
Node
Map
Sorted
Map
Link
Map
Full
Map
Hash
Map
clear ()
1
1
1
1
del (key) (a. find)
N
logN
1
1
(b. change)
1
N
1

2. 1
get (key)
N
logN
1
1
hasKey (key)
N
logN
1
1
hasVal (val)
N
N
N
N
N
put (key,val) (a. find)
N
logN
1
1
(b. change)
1
N
1
1
size ()
1
1
1
1

3. 1
(12 min) I. Map – Abstract Data Type
start time: 12:36
Every published book has a unique 10--digit International
Standard Book Number (ISBN); for example, The Mythical
Man-Month by Fred Brooks has ISBN 0-201-835-95-9.
Similarly, every commercial product has a unique 13-digit
Universal Product Code (UPC). The UPC for books is 978
followed by the ISBN, so The Mythical Man-Month has
UPC 978-0-201-835-95-3. (You will learn later why the last
digit is different.)
These unique identifiers (usually a number or character string)
are called keys;
uniquely identified means that every item has a key and no two
items have the same key.
The key provides access to other information about the item,
collectively called its value;
thus, the value for a book includes the author, title, publisher,
publication date, etc.
The key and its associated value are a (key, value) pair.
1. (3 min) Identify likely keys and values for each of the
following:
Description
Key
Value includes
a.
taxpayers

4. Address XXX
Street, City, State, Zip Code
b.
courses offered at
a college or university
Course XXX
Course #, times,credits
c.
entries in a dictionary
or encyclopedia
Word
type of word (verb,noun,etc.),
pronunciaton, definition
In computer science, a data structure to store key-value pairs is
called a map
(or a dictionary), and might have an interface like this:
interface IMap {
void clear () // remove all keys & values
boolean del (key) // delete key & its value
value get (key) // get value for key
boolean hasKey (key) // is key in map?
boolean hasVal (val) // is val in map?
boolean put (key,val) // put key,value in map
int size () // return # of pairs
}
2. (4 min) Trace the following actions in a map of 2-letter codes
to country names. Key-value pairs can be stored in any empty
location.
Action

5. pairs:
Result
put("IN", "India")
IN/
India
true
put("CN", "China")
CH/
China
IN/
India
true
size()
CH/
China
IN/
India
2
hasKey("TO")

6. CH/
China
IN/
India
false
put("TO", "Tonga")
CH/
China
IN/
India
TO/
Tonga
del("CH")
IN/
India
TO/
Tonga
put("GH", "Ghana")

7. GH/
Ghana
IN/
India
TO/
Tonga
hasVal("IN")
GH/
Ghana
IN/
India
TO/
Tonga
true
3. (2 min) An array uses an integer index to access a specific
data object.
Describe an array using map terminology - what is the key?
what is the value?
The key is the array. while the value is the index.
4. (2 min) Use map and array terms to explain why maps are
called associative arrays.
Because a key is essentially an array that is associated with
values (idexes).

8. Before you continue, review progress with the facilitator.
(12 min) II. Unsorted Array Implementation
start time:12:49
We could implement IMap with 2 unsorted arrays - one for
keys and one for values.
If keys[i] contains an item’s key, then vals[i] contains its value.
class ArrayMap implements IMap {
String[] keys = new String[MAX_MAP_SIZE];
Object[] vals = new Object[MAX_MAP_SIZE];
}
arrayMap1
keys
vals
1. (1 min) What key-value pairs are stored in the diagram
above?
CH/China, IN/India
However, when you see a program where the ith element in one
array corresponds
to the ith element in one or more other arrays, you should be
suspicious.
(We call this a smell – something seems wrong, and we need to
figure out why.)
This smell suggests that another class might be useful, and so

9. we could refactor to:
a) Declare a new Node class that contains an (non-array)
instance field that
corresponds to each array, with appropriate constructor, get &
set methods, etc.
b) Replace the “parallel” arrays with one array of the new Node
class.
class Node {
String key;
Object val;
... // assume appropriate gets, sets, & constructors
}
class NodeMap implements IMap {
String[] keys = new String[MAX_MAP_SIZE];
Object[] vals = new Object[MAX_MAP_SIZE];
Node [] pairs = new Node[MAX_MAP_SIZE];
... // assume appropriate gets, sets, & constructors
}
arrayMap1
pairs
IN
India
CH
China
2. (1 min) What key-value pairs are stored in the diagram
above?
CH/China, IN/India

10. 3. (8 min) Explain (in pseudo-code or English) how to
implement each NodeMap method.
NodeMap Method
Implementation
a.
get(key)
Loop through each Node in the array.
If that node has the given key, return value.
b.
hasKey(key)
Loop through each Node in the array.
If that node has the given key, return true.
If no matching key is found, return false.
c.
hasVal(val)
Loop through each Node in the array.
If that node has the given value, return true.
If no matching value is found, return false.
d.
put(key,val)
Loop through each Node in the array until there is an empty
one.
Then put the key and the value in the empty node.

11. e.
del(key)
Loop through each Node in the array until the given key is
found.
Then the key and the value of it will be deleted.
4. (2 min) In the Map Worksheet column NodeMap,
write the O() performance of each method. (Omit the “O()” to
make it easier to read.)
Note that put() and del() involve 2 steps, which should be
analyzed separately:
a. Find the array element to be changed.
b. Change the array.
Before you continue, review progress with the facilitator.
(6 min) III. Sorted Array Implementation
start time:12:58
We could also implement IMap with an array of Nodes, sorted
by key value.
class SortedMap implements IMap {
Node [] pairs = new Node[MAX_MAP_SIZE];
... // assume appropriate gets, sets, & constructors
}
arrayMap1
pairs

12. CH
China
IN
India
TO
Tonga
1. (2 min) Explain why SortedMap should be much faster for
get() and hasKey(),
but the same for hasVal().
Because once get() and hasKey() only has to go through one
array that is sorted, it would be much quicker to find the key
since the keys are in order, instead of two unsorted arrays.
hasVal() will be the same since the array is sorted by key.
2. (4 min) Explain (in pseudo-code or English) how to
implement each SortedMap method. Write “SAME” next to any
methods that would not change from above.
SortedMap Method
Implementation
a.
get(key)
Go in array where value should be, then go lower or higher
depending on what key is found; until key is found. Return
value.
b.
hasKey(key)

13. Go in array where value should be. If it is there return true, if
it is missing, return false.
c.
hasVal(val)
SAME
d.
put(key,val)
Go in array where value should be. Move other values to make
space for new key. Put key and value in index.
e.
del(key)
Go in array where value should be. Delete value. Moving the
rest of the keys to make sure there is no empty index.
2. (2 min) In the Map Worksheet column SortedMap,
write the O() performance of each method, including each step
in put() and del().
Before you continue, review progress with the facilitator.
(6 min) IV. Linked List Implementation (Optional)
start time:1:23
If you have not studied linked lists, skip this section.
If you have studied linked lists, check with the facilitator before
you start this section.
We could also implement IMap with a linked list of nodes,
sorted from the smallest to largest key value.

14. class LinkMap implements IMap {
Node head, tail;
... // assume appropriate gets, sets, & constructors
}
1. (4 min) Explain (in pseudo-code or English) how to
implement each LinkMap method.
Write “SAME” next to any methods that would not change from
above.
LinkMap Method
Implementation
a.
get(key)
b.
hasKey(key)
c.
hasVal(val)
d.
put(key,val)
e.
del(key)

15. 2. (2 min) In the Map Worksheet column LinkMap,
write the O() performance of each method, including each step
in put() and del().
Before you continue, review progress with the facilitator.
(6 min) V. Full Array Implementation
start time: 1:25
So far, each IMap implementation has performance problems.
Sometimes it helps to explore options that seem impractical, but
which provide useful ideas.
For example, suppose each key was an integer, and was used as
the index for an array of values.
Thus, put(5,"Fri") would put “Fri” at index 5 in the array.
class FullMap implements IMap {
Node [] pairs = new Node[MAX_KEY_VALUE];
... // assume appropriate gets, sets, & constructors
}
1. (4 min) Don’t worry about non-integer keys, at least for now.
Explain (in pseudo-code or English) how to implement each
FullMap method.
Write “SAME” next to any methods that would not change from
above.
FullMap Method
Implementation
a.
get(key)
Go to provided index, return value.
b.
hasKey(key)

16. Go to provided index,
c.
hasVal(value)
SAME
d.
put(key,value)
Go to provided index, put value in index.
e.
del(key)
Go to provided index, delete the value in index.
2. (2 min) In the Map Worksheet column FullMap, write the O()
performance
of each method, including each step in put() and del().
3. (2 min) There is a big problem if the key is long (e.g. a 10
digit ISBN or 13 digit UPC).
Describe the problem, and your ideas (if any) that might help to
help solve them.
It will need a very large array to store all the keys and values.
One way to avoid this would be to have subcategories.
Before you continue, review progress with the facilitator.
(10 min) VI. Hash Functions
start time: 1:38
1. (2 min) A hash function converts a value in a larger range to
a value in a smaller range.
If we have an integer value from 0 to 10,000, which of the
following is a hash function?

17. a.
Divide the value by 100 and take the quotient.
YES
b.
Divide the value by 100 and take the remainder.
YES
c.
Subtract the value from 10,000.
NO
d.
Add all 5 digits together.
NOXXX
e.
Add all 5 digits together, divide by 10, and take the remainder.
NOXXX
2. (2 min) When a hash function converts two or more different
inputs to the same output,
we say there is a collision. In general, good hash functions
should minimize collisions.
Explain why collisions are often unavoidable.
XXX There might be several different ways to get the same
outputs.
3. (3 min) Hash functions can also take non-numeric input. For
example,
a hash function could convert a String into an integer in a
variety of ways.
a. Use the String length, so “alphabet” → 8, “baby” → 4
b. Use the ASCII code of the first character, so “alphabet” →
97, “baby” → 96
Explain why these are both poor hash functions for converting a
String to an integer.
a)Many different strings can add up to the same integer.

18. b)Many different strings can have the same first character.
4. (2 min) Describe at least one better hash function to convert a
string into an integer.
Use ASCII code for each character, then add values.
Ideally, hash functions are both efficient (fast and easy to
compute) and effective
(avoid collisions), but creating such hash functions can be
surprisingly difficult. Be careful!
(18 min) VII. Hash Map Implementation
start time: 1:15
For ISBN, UPC, and many other codes, the last digit is
calculated with a hash function
from the other digits. The last digit is called a checksum, since
it provides a way
to check that a given code is valid, usually from a sum of values
based on the code.
Each code (ISBN, UPC, SSN, etc) must define the hash function
to calculate its checksum;
for technical reasons, the checksum is usually not just the sum
of the other digits.
1. (2 min) Explain why the checksum digit means that 90%
of the possible 10-digit ISBN and 13-digit UPC codes are
invalid.
Since the last digit is invalid, only 10% of the full codes will be
valid. (10^9/10^10 =0.1)

19. 2. (1 min) Explain how all possible 10-digit ISBN values
could be stored in an array of 109 values rather than 1010.
Because the last digit is to validate the first nine.
3. (2 min) Suppose a library with no more than 10,000 (104)
books wanted to store them
in an ArrayMap with 100,000 indices (105) rather than
1,000,000,000 (109) indices
for the ISBN. Describe how we could use part of the ISBN as an
index,
in order to keep FullArrayMap performance.
We could use the last 5 digits to differentiate the books.
4. (1 min) Describe at least one possible hash function for the
previous question.
Add the last 5 digits.
5. (2 min) What problem(s) could arise with this approach?
Several books could have the same sum.
We could use this approach to implement IMap with an
appropriate hash function,
using only a fraction of the memory needed by FullMap.
class HashMap implements IMap {
Node [] pairs = new Node[MAX_MAP_SIZE];

20. ... // assume appropriate gets, sets, & constructors
}
6. (4 min) Explain (in pseudo-code or English sentences) how to
implement HashMap methods. Write “SAME” next to any
methods that would not change from above.
HashMap Method
Implementation
a.
get(key)
SAME
b.
hasKey(key)
SAME
c.
hasVal(val)
SAME
d.
put(key,val)
SAME
e.
del(key)

21. SAME
7. (2 min) In the Map Worksheet column HashMap,
write the O() performance of each method, including each step
in put() and del().
Before you continue, review progress with the facilitator.
8. (2 min) What problems could collisions cause for HashMap?
How could these problems be solved?
Values having the same key after being hashed, could be solved
by altering hash function, or corrected with probing.
(5 min) VII. Java Generics (OPTIONAL)
start time:
As we have seen, in Java we can use type parameters to define
generic classes
that can then be used with any Java type.
1. (1 min) What are the two type parameters used in the code
below?
2. (3 min) Explain why these interfaces and classes need two
type parameters.
interface IMap<K,V> {
void clear () // remove all keys & values

22. boolean del (K key) // delete key & its value
V get (K key) // get value for key
boolean hasKey (K key) // is key in map?
boolean hasVal (V val) // is val in map?
boolean put (K key, V val) // put key,value in map
int size () // return # of pairs
}
class Node<K,V> {
K key;
V val;
... // assume appropriate gets, sets, & constructors
}
class NodeMap<K,V> implements IMap<K,V> {
Node<K,V> [] pairs = new Node<K,V>[MAX_MAP_SIZE];
... // assume appropriate gets, sets, & constructors
}
class HashMap<K,V> implements IMap<K,V> {
Node<K,V> [] pairs = new Node<K,V>[MAX_MAP_SIZE];
... // assume appropriate gets, sets, & constructors
}
Quantifying Supply Chain Trade-Offs Using
Six Sigma, Simulation, and Designed
Experiments to Develop a Flexible
Distribution Network

23. Sameer Kumar1,
Marietsa L. McCreary2,
Daniel A. Nottestad3
1Opus College of Business,
University of St. Thomas,
Minneapolis, Minnesota
23M Company, Stafford Springs,
Connecticut
33M Company, St. Paul,
Minnesota
ABSTRACT This case study quantifies the trade-off between
customer
service and inventory in a multinode supply chain while
assessing system
performance. An integrated and generalized modeling
framework is used
that incorporates define, measure, analyze, improve, control
(DMAIC)
methodology and designed experiments. Many traditional
models require
normality in demand and supply, but this is often not
representative of

24. reality. Therefore, this study leverages discrete-event
simulation to replicate
and understand the variation in a real-world supply chain at a
large multi-
national corporation. The goal of this modeling application is to
provide
dynamic decision support to facilitate effective supply chain
design. The
study uses an innovative three-stage analytical approach to
study a multi-
echelon distribution network. The first stage uses DMAIC to
highlight areas
of variability in the process, enabling identification of key high-
risk inputs
affecting system performance. The next stage, discrete-event
simulation, uti-
lizes DMAIC results in the development of a validated model
that represents
the real-world variability present in the supply chain. The third
and final
stage, designed experiments, is used to analyze the simulation
output and
quantify the factors that drive supply chain performance,
specifically inven-

25. tory levels and customer service (fill rate) at various stages of
the supply
chain. To more effectively respond to stochastic behavior of
customers,
study results impact decision making and facilitate inventory
replenishment
policy changes. The analysis also helped in the proper
allocation of
resources to manage the various stock-keeping units (SKU)
classes and
customer categories. This proactive modeling approach is robust
and readily
replicated in any supply chain.
KEYWORDS designed experiments, discrete-event simulation,
distribution
network, DMAIC, DOE, inventory buffer, six sigma, supply
chain, WITNESSAddress correspondence to Sameer
Kumar, Opus College of Business,
University of St. Thomas, 1000 LaSalle
Avenue, Minneapolis, MN
55403-2005. E-mail:
[email protected]
Quality Engineering, 23:180–203, 2011
Copyright # Taylor & Francis Group, LLC
ISSN: 0898-2112 print=1532-4222 online
DOI: 10.1080/08982112.2010.529481
180

26. INTRODUCTION
It is widely reported that though Six Sigma as a
change and improvement strategy is delivering
significant business benefits to practitioner organiza-
tions, it has not been successfully adapted to deliver
similar benefits across supply chains (Knowles et al.
2005). Knowles et al. (2005) proposed a two-stage
supply chain Six Sigma model in implementing
improved supply chain design. The first stage is
strategic, developing focused projects to generate
maximum business benefit. The second stage is
operational, applying Six Sigma and lean tools in a
define, measure, analyze, improve, control (DMAIC)
cycle to deliver supply chain improvements. This
study showcases the implementation of the two-
stage supply chain Six Sigma model.
The primary objective of this project is to explore

27. and optimize finished goods inventory in the
multiple nodes of the distribution network. The
motivation for the project is to design a flexible sup-
ply chain for the manufacturer following a request
for simulation services to align the operational
improvements with capital spending effectiveness.
The goal is to double inventory turns, a key company
metric. A counterbalance to the resulting reduced
inventory is maintaining (or increasing) product
availability to the end-customer. Using DMAIC meth-
odologies, this study leverages simulation as the
enabling technology along with designed experi-
ments to provide decision support to a supply chain
improvement team.
The motivation and value of the supply chain
analysis is twofold:
1. To quantify the trade-off between minimizing
inventory costs and maximizing customer service

28. under normal cause variation; and
2. To assess the performance metrics of the supply
chain and their ability to appropriately evaluate
and reward relevant supply chain nodes
The remainder of the article is laid out as follows.
The following section reviews the existing work
reported in the literature that relates to the study
described in this article. The next section presents
the supply chain network that is the focus of this case
study and outlines the motivation for the analysis.
The next section describes the Six Sigma framework
and the integration of simulation as an enabling
technology to assess the supply chain. Then we
detail the development of the simulation model
and highlight key reporting features. We also focus
on the model’s use in a series of designed experi-
ments. The following section presents the major
findings of this easily replicated approach, and the

29. next discusses the managerial and practical implica-
tions of supply chain analysis. The final section
presents the conclusions.
LITERATURE REVIEW
A significant challenge in today’s manufacturing is
to be both efficient and highly effective in terms of
customer satisfaction. The latter results in emphasis
on both relations with customers and the service
provided to such customers (Hitt et al. 1999). Kotler
(1997) argued, ‘‘Customers are scarce; without them,
the company ceases to exist. Plans must be laid to
acquire and keep customers’’ p. 109. The level of
competition to capture customers in both domestic
and international markets demands that organiza-
tions be quick, agile, and flexible to compete effec-
tively (Fliedner and Vokurka 1997; LaLonde 1997;
Shenchuk and Colin 2000; G. Wang et al. 2005). This
level of flexibility cannot be obtained without coor-

30. dination of the supply chain distribution network
with appropriate supply chain performance metrics
(Lapide 2000).
Time and quality-based competition focuses on
eliminating waste in the form of time, effort, defective
units, and inventory in manufacturing–distribution
systems (Larson and Lusch 1990; Schonberger and
El-Ansary 1984; Schultz 1985). In addition, there has
been a significant trend to emphasize quality not only
in the production of products or services but also
throughout all areas in a company (Coyle et al.
1996, Scalise 2003). Ted Farris of the University of
North Texas reported that 66% of the cash-to-cash
improvements since 1986 in the majority of industry
segments have come from reductions in days of
inventory (Trunick 2005). According to Farris, the
cash-to-cash formula adds accounts receivable to
inventory and then subtracts accounts payable. If

31. any improvement to operations results in a reduction
in the amount of inventory held within the company,
days of inventory are reduced. But if the company is
merely shifting inventories intra-company to hold
the goods somewhere else, there is no change in
181 Quantifying Supply Chain Trade-Offs
the cash-to-cash cycle. This inventory is still carrying
an associated accounts payable tag—it has not shifted
to a receivable because it has not been sold.
The recent application of DMAIC and Six Sigma
principles in the manufacturing and supply chain
arena has led to next-generation supply chain solu-
tions that take full advantage of these initiatives
(Dasgupta 2003; Garg et al. 2004; Keene et al. 2006;
Wang et al. 2004; Yeh et al. 2007). In ‘‘The Next
Stage of Supply Chain Excellence,’’ Schlegel and
Smith (2005) described the elements of the emerging

32. dynamic-on-demand supply chain. In this architec-
ture, Six Sigma DMAIC principles are applied to the
supply chain journey, thereby leveraging their robust
methodologies, along with supply chain best prac-
tices, near real-time data, and on-demand technolo-
gies to achieve a much higher level of performance.
Many companies have developed and implemented
Six Sigma approaches. Among the noted ones are
General Electric (GE), DuPont, Honeywell, and
Samsung (Yang et al. 2007). This study differs from
these approaches in that it offers a three-tiered
approach to solving a dynamic supply chain problem.
The first stage is DMAIC, which identifies key process
parameters. The second stage, discrete-event simula-
tion, enables detailed analysis of the supply chain’s
nodal interactions. Finally, designed experiments
utilize the simulation model to provide robust compar-
isons of supply chain configurations. For a plant

33. operation, Kumar and Nottestad (2006) developed
discrete-event simulation model allied to designed
experiments to design manufacturing capacity realiz-
ing optimal throughput, inventory, and operating
costs. Many supply chain models require normality
in demand and supply, but this is often not represen-
tative of reality. This specific approach uses discrete-
event simulation with normal and=or empirical
distributions to represent the behavior of plants, distri-
bution centers, and customers. Customer demand is
modeled using normal distributions that reflect past
customer ordering patterns. However, manufacturing
lead times are modeled as nonnormal distributions
based on historical fulfillment patterns in the supply
of product from the internal plant to the internal
distribution center (DC).
It is important to consider the underlying assump-
tions that constrain this study. The model predicts

34. supply chain performance under common cause
variation and does not deal specifically with special
cause variation. The DMAIC methodology used in
the study excels at reducing process variation from
common causes.
This easily replicated approach is primarily
strategic but has the capability to analyze tactical
decisions. Strategic decisions such as the inventory
replenishment policy at the internal distribution cen-
ter affect the long-term performance of the supply
chain, whereas tactical decisions such as authorizing
overtime at the factory affect the short-term perform-
ance of the supply chain. The strategic nature aims to
provide a tool for educating both middle and senior
supply chain management on the trade-off between
inventory cost and customer service. How much
does customer service decrease if overall system
inventory is reduced by 25%? This question is easily

35. answered in this study.
SUPPLY CHAIN DISTRIBUTION
NETWORK
Figure 1 shows the supply chain studied. Every day
regional customers order a portfolio of products
from a respective regional third-party distributor.
The third-party distributor tries to immediately fill
demand, but if they cannot fulfill the order it nega-
tively affects the distributor’s customer service. The
third-party distributor periodically reviews their
inventory and replenishes product from an internal,
company-owned distributor that is supplied by the
factory. The internal distributor also directly services
customer orders.
The customer service index (CSI) is the metric
used to measure how well the internal and third-
party distributors are fulfilling customer orders. The
CSI metric tracks both aggregate and stock keeping

36. units (SKU)-specific order fulfillment performance
at both the internal and third-party distributors. For
example, the third-party distributor is penalized each
time an order is not immediately filled from stock.
The formula for CSI is simply:
CSI ¼
Orders immediately filled from stock
Total orders
Perfect service is indicative of a CSI equal to 1.000.
Many firms typically prefer to have less than 100%
delivery service because the inventory costs associa-
ted with flawless service outweigh the marginal
benefits achieved.
S. Kumar et al. 182
In this four-node supply chain (customer,
third-party DC, internal DC, plant), it is not a trivial
problem to examine the trade-offs between inven-
tory holding costs and customer service. Thus, Six

37. Sigma methodology and discrete-event simulation
were used to understand and optimize these trade-
offs (Seifert 2005).
SIX SIGMA FRAMEWORK
The supply chain project team followed the
DMAIC process within a Six Sigma framework
to determine appropriate service metrics in the
division’s supply chain. The five DMAIC phases
and key tools used in each phase are listed
below.
. D ¼ Define
. Project charter
. Stakeholder analysis
. M ¼ Measure
. Process map
. Cause and effect (C&E) matrix
. Initial capability
. A ¼ Analyze
. Failure modes and effects analysis (FMEA)

38. . I ¼ Improve
. Simulation models
. Design of experiments (DOE)
. Pilot study
. C ¼ Control
. Control plan
. Final capability
The five Six Sigma phases are discussed in detail in
this section.
Define Phase
The first phase in a DMAIC project is the define
phase, which uses a project charter to organize the
major project categories. The project goal, scope,
and boundaries are specified in this phase. Major
defect(s) in the system under study are listed. Project
benefits, both financial (hard) and nonfinancial
(soft), are expressed as well as entitlement, a
measure of unconstrained success.
The project charter for this project is as follows:

39. . Project goal: Double inventory turns.
. Scope: Exploration and optimization of the current
supply chain (system).
. Defect definition: Local optimization based on
current understanding and data. Suboptimization
occurs due to ineffective performance metrics that
results in misguided behavior.
. Critical to quality: Customer service index.
. Financial benefits: Significant annual inventory
reduction ($$$).
. Nonfinancial benefits: Better understanding of
effectors on supply chain performance.
. Entitlement: Serve end-customer needs with
minimal working capital investment.
FIGURE 1 Supply chain distribution network.
183 Quantifying Supply Chain Trade-Offs
Measure Phase

40. As part of the measure phase, the team generated
a process map and analyzed key process inputs with
a subsequent C&E matrix.
A process map documents key process steps,
inputs, and outputs. The process map shown in
Figure 2 details the inputs (on the left) to each major
process step. Process outputs from each process step
are listed on the right.
Each of the 15 inputs to the four major process
steps is carried forward into the C&E matrix for
further consideration (Table 1). A C&E matrix
enables the user to prioritize key inputs that affect
the process by rating the importance of the inputs
to the customer in selected outcome categories.
As shown in Table 1, the three outcome categories
are end-user customer service, schedule attainment,
and inventory levels. Each category is ranked on a
scale of 1 to 10 with 10 being extremely important

41. FIGURE 2 Detailed process map showing key inputs and
outputs to service metrics.
TABLE 1 Cause and Effect Matrix
Rating Scale: 9 ¼ > High High High
3 ¼ > Medium Medium Medium
1 ¼ > Low Low Low
0 (Not Applicable: NA) ¼ > NA NA NA
Rating of Importance to Customer ¼ > 10 3 3
Key Process step Process inputs
End user
customer
service
Schedule
attainment
Inventory
levels
Weighted
total
1 Measuring Forecast Error Demand 9 9 9 144
2 Measuring Forecast Error Forecast 9 9 9 144

42. 9 Measuring Internal DC Performance Inventory Buffers 9 1 9
120
13 Measuring 3rd Party DC Performance Inventory Buffer
Targets 9 1 9 120
14 Measuring 3rd Party DC Performance Desired Customer
Service Levels 9 1 9 120
12 Measuring 3rd Party DC Performance Internal DC Material
Shipments 9 1 1 96
6 Measuring Plant Performance Inventory Buffers 3 9 9 84
5 Measuring Plant Performance Requests for Material 3 9 3 66
3 Measuring Forecast Error Measurement System 3 1 3 42
8 Measuring Internal DC Performance Shipment of Material
from Plant 3 1 3 42
11 Measuring Internal DC Performance Fixed Cycles from
Distribution 3 1 3 42
15 Measuring 3rd Party DC Performance End User Forecasts 3 1
3 42
10 Measuring Internal DC Performance Desired Customer
Service Targets 0 1 9 30
4 Measuring Forecast Error Stratification 1 1 3 22
7 Measuring Plant Performance Desired Plant Performance 0 1 1
6

43. Weighted Subtotals ¼ > 730 141 249
S. Kumar et al. 184
and 1 being not at all important. A weighted C&E
rating is calculated for each input based on the
individual category ratings in each category. For
example, ‘‘demand’’ process input has a total rating
of 144 obtained by multiplying ‘‘end-user customer
service’’ category rating (10) by demand customer
importance rating (9) and adding the remaining
two categories in a similar fashion.
In this case study, five process inputs—demand,
forecast, inventory buffers, inventory buffer targets,
and desired customer service levels—are considered
for further study (see Figure 3). The forecast process
input is eliminated from further study because it is
out of scope of the current project.
The initial capability of an existing system is

44. typically completed in the measurement phase to
document the unaltered state of a system. Because
the proposed system is a business process redesign
that significantly modifies an existing process, initial
process capability will be defined as the baseline
performance of the simulated system. The simulation
model predicts inventory levels over time for the pro-
posed system. Therefore, initial process capability
will be the average of five simulation baseline runs
that track critical-to-quality CSI levels. The baseline
condition used in this study represents existing
behavior of the various supply chain entities in the
distribution network. Existing behavior is defined
by historical operational data such as customer
ordering patterns, inventory replenishment policies,
and variable manufacturing lead times. These beha-
viors and policies are further discussed in the section
on simulation modeling. Table 2 shows the initial

45. capability for the critical-to-quality CSI levels.
A counterbalance ensures that the primary metrics
(inventory levels and inventory turns) are appropri-
ately constrained. Product availability to the end-
customer is the counterbalance for this project. This
customer service metric will be simulated and mea-
sured monthly for the filling of product from the
third-party DC to the customers. Internally, product
availability from the company-owned warehouse to
the third-party DC will be simulated and reported
weekly and monthly.
Analyze Phase
This section will highlight the history, structure,
and benefits of FMEA.
FMEA
The failure modes and effects analysis is a
well-established and systematic process to analyze
potential failures in existing processes. FMEA is used

46. to identify high-risk inputs and prioritize correspond-
ing improvement actions. An FMEA objective is to
reduce variation and its effects for inputs that are
out of control. Inputs to the FMEA include the
process map and C&E matrix as well as process
expertise and process technical procedures. Outputs
to the FMEA include the following:
. The list of chosen inputs to explore further and
potentially control
FIGURE 3 Pareto diagram ranking cause-and-effect inputs.
185 Quantifying Supply Chain Trade-Offs
. Prioritized list of actions to prevent causes or
detect failure modes
. Record of controls and actions taken
. Deep process understanding for the team
The cross-functional project team developed ratings
scales for the FMEA categories ‘‘severity to customer’’

47. and ‘‘occurrence.’’ A scale of 0–10 for both categories
is used. For the severity to customer category, a score
of 10 is extremely severe and a score of 0 is not at all
severe. For the occurrence category, a score of 10 is
routinely occurs and a score of 0 is never occurs. For
the ‘‘detection’’ category, a score of 10 is not detectable
and a score of 0 is always detectable. Risk Priority
Number (RPN) is calculated as the product of the
severity, occurrence, and detection ratings. FMEA
results are shown in Table 3.
The top failure modes to explore and potentially
control are as follows:
. Demand variability too high
. Inventory buffer sized incorrectly
. Incorrect customer service goal
. Forecast accuracy—out of scope
Improve Phase
Simulation and designed experiments anchor

48. the improve phase. Three critical high-risk inputs
identified in the FMEA are explored. A discrete-event
simulation of the multinodal distribution network,
discussed in the section on simulation modeling, pre-
dicts system behavior over time and is the enabling
technology for this study. A designed experiment,
also discussed in the simulation modeling section,
aids in optimization of system performance. The
summary section documents the recommendations
from the simulation and DOE. The section on impli-
cations provides managerial and practical applica-
tions especially regarding the future pilot that will
be used to validate the recommendations.
The potential failures identified in the FMEA
specifically addressed by the simulation are as
follows:
. Demand variability too high
. Inventory buffer sized incorrectly

49. . Incorrect customer service goal
An adjacent initiative with emphasis on sales and
marketing effectiveness, not discussed in this article,
is also implemented to address the potential failures
identified by the FMEA.
Control Phase
The control phase will be developed through
results obtained from a planned pilot study. Inven-
tory replenishment policies will be monitored for
their effectiveness. System capability will record the
actual inventory levels at the internal warehouse
and third-party distributor weekly. In addition, actual
inventory turns at each stocking location will be mea-
sured on a monthly basis in the planned pilot study.
The approach described in this article is easily repli-
cated to similar supply chain configurations with vari-
ation in customer demand and manufacturing supply.
Using the focused and disciplined approach

50. described in this section, customer service failure
modes are identified in the simulation, which is
reviewed in the section on simulation modeling, with-
out disruption of the actual system. To be able to study
supply chain performance in a virtual world allows
learning of system failure modes, maximizing stake-
holder confidence that real world success is achievable.
In the case study, the third-party distributor was
represented on the cross-functional team. Their
understanding of motives for taking on more inven-
tory at the third-party DC while reducing inventory
at the internal DC was paramount for acceptance
and future success of this project. Sharing simulation
results with the third-party distributor gave them the
TABLE 2 Initial Capability for CSI at Internal and External
Distributors
Performance metric Average Run 1 Run 2 Run 3 Run 4 Run 5
Internal DC ‘‘A’’ CSI 0.991 0.984 0.990 0.987 0.997 0.997
Internal DC ‘‘C’’ CSI 0.874 0.866 0.866 0.908 0.874 0.857

51. Internal DC total CSI 0.959 0.951 0.956 0.965 0.963 0.958
External DC ‘‘A’’ CSI 0.992 0.991 0.997 0.982 0.997 0.992
External DC ‘‘C’’ CSI 0.774 0.815 0.762 0.754 0.787 0.753
External DC total CSI 0.916 0.931 0.914 0.904 0.923 0.910
S. Kumar et al. 186
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187 Quantifying Supply Chain Trade-Offs
confidence needed to go ahead with the project. As
with many simulation projects, the underlying models

95. become increasingly robust with time due to increas-
ing knowledge gained from such projects. Various
recommendations outlined in the summary section
are currently being used in numerous operating units
of the company. The trade-off analysis between
customer service and inventory levels is facilitated
by the approach detailed in the next section.
SIMULATION MODEL
WITNESS (Anon. 1998) simulation software
simulates the firm’s supply chain performance by
modeling the different elements that comprise the
distribution network. These elements include custo-
mers, warehouses, plants, and materials, among
others. The role of simulation as the project’s
enabling technology is to evaluate alternatives that
either support strategic initiatives or support better
performance at operational and tactical levels
(Sanchez 2005; Sanchez et al. 1996). This section

96. provides the details for the development of a vali-
dated supply chain model that quantifies customer
service levels when varying inventory buffer sizes,
customer demand, and production lead time.
Model Development
DMAIC’s analyze phase includes the building of
the simulation model to predict supply chain system
performance over time. This project is designed
to explore normal cause variation within the distri-
bution network. Special cause variation is not
included in the model scope.
The model is scaled to include three customers in
a specific region of the country. A third-party
distributor services each customer from their regional
DC. The division’s internal distribution center
replenishes product for the third-party distributor.
Source of supply for the 10 unique products (SKUs)
is a centrally located plant. The model predicts

97. system performance in a small portion of the overall
distribution network. The distribution network and
this project’s area of focus are highlighted in Figure 4.
The product portfolio consists of hundreds of SKUs.
SKUs are categorized using A-B-C analysis to facilitate
the proper allocation of the supply chain manager’s
time and effort (Silver et al. 1998). For simplicity in
modeling, the product mix includes just 10 unique
SKUs. Three of the 10 SKUs are high-demand (‘‘A’’)
products while the remaining 7 SKUs are low-demand
(‘‘C’’) products. The model is fully scalable to allow for
additional SKUs, customers, and distributors.
The main components of the model include the
following:
. Adjustable buffers at internal DC and third-party
(external) DC
. Stochastic customer demand from three major
customers based on historical data

98. FIGURE 4 Supply chain distribution network—area of focus.
S. Kumar et al. 188
. Fulfill backorders prior to new orders
. Reorder point replenishment for internal DC
. Periodic order cycles for third-party distribution
(fixed cycle, variable quantity)
. Time-series charts of inventory levels at specified
nodes
. Stock-out duration record keeping
. Stochastic production lead times from internal
plant to internal DC based on historical data
Modeling Customer Behavior
Capturing and modeling customer ordering pat-
terns is paramount to a valid model. Each customer
has its own unique demand for products. On a daily
basis, the three customers place orders to the third-
party DC. If the product is in stock at the external

99. DC, the order is filled. If the product is not in stock
at the external DC, the order is placed on backorder
and customer service is decremented.
Customer behavior is modeled for each individual
customer. The order frequency and order size for
each of the 10 SKUs are modeled as normal distribu-
tions with a given mean and standard deviation.
These values are based on historical performance
and it is assumed that future behavior will follow
the past. For simplicity, the distributions for order
frequency and order quantity are identical for the
three customers. It should be noted that empirical
distributions could have also been easily used to
describe this behavior.
Modeling Inventory
Replenishment Policies
Replenishment orders for restocking third-party
DC inventory from internal DC inventory are placed

100. differently based on a product’s sales volume.
High-demand (‘‘A’’) products are replenished on a
weekly cycle, whereas low-demand (‘‘C’’) products
are replenished on a 6-week cycle. Partial shipments
from the internal DC are allowed and backorders are
modeled as an integral part of the distribution
process. Backorders are filled before new orders.
The internal DC reorder point (r) is a function of
safety stock and work-in-process for each SKU. The
reorder point is monitored and changed as required
by the supply chain manager. A replenishment order
is generated when the inventory level for a given SKU
falls below the reorder point. The replenishment
order quantity (Q) equals the amount of inventory
to replenish inventory to the buffer target capacity.
The factory fills all replenishment orders and a
replenishment lead time is assigned. The inventory
buffer target parameter is a function of customer

101. demand and safety stock.
The third-party DC’s replenishment order is filled
from the internal DC within a given period of time,
based on historical delivery performance, as long
as product from the internal DC is available. How-
ever, if product is not available at the internal DC,
the third-party DC is not restocked and the internal
DC customer service is negatively affected. If, during
this restocking procedure, product falls below a set
reorder point at the internal DC, a replenishment
order is placed with the factory. Historical delivery
performance from the plant to the internal DC is
modeled with an empirical distribution for each
SKU. A manufacturing lead time is assigned from
the appropriate distribution and product is replen-
ished to its inventory buffer target capacity after the
lead time has expired. The distribution network is
simulated in this manner for 2 years. The model is

102. programmed in days and weekends are ignored.
This process flow and programming strategy are
shown in Figure 5.
Modeling Supply Variation
The manufacturing lead time for a specific SKU
varies, potentially causing delays in the order
fulfillment process and the holding of inventory at
different nodes in the supply chain. The internal
DC places replenishment orders with the internal
plant. The manufacturing lead time varies and is non-
normal. Discrete-event simulation is well suited to
handling nonnormal distributions. Historical plant
performance is analyzed using distribution fitting
software such as ExpertFitTM (Averill M. Law and
Associates) to properly model the variation in supply
times to the internal DC. Figure 6 represents the
manufacturing lead time distribution for SKU 10 that
is typical of other SKUs in the model. SKU 10 manu-

103. facturing lead time is best represented by a Weibull
distribution with WITNESS function:
SKU 10 Manufacturing Lead Time ¼ 3:96263
þ Weibull ð1:015826; 9:627193Þ
189 Quantifying Supply Chain Trade-Offs
Model Output and Analysis with
Design of Experiments
Within the project—as with successful simulation
projects—first, the objectives and scope were clearly
set. Next, subject-matter experts and reliable data
helped build the underlying assumptions and simpli-
fications of the model. Throughout the project, the
simulation was methodically validated against logical
and historical expectations. Lastly, structured studies
and analysis were performed.
The customer-accepted simulation is validated
and verified after critical assessment by project

104. stakeholders and with buy-in from business leaders.
FIGURE 5 Supply chain distribution network process flow.
FIGURE 6 Manufacturing lead time distribution for SKU 10.
S. Kumar et al. 190
Validation assessment involved supply chain
managers and Six Sigma coaches as well as
critical project stakeholders including product
planners, schedulers, and internal and external DC
representatives.
The simulation-building process creates a highly
functional decision tool that accurately characterizes
the supply chain. Model validation consists of base-
line performance comparisons of the simulation
model with the actual system data. Real-world vari-
ation in customer demand and manufacturing supply
is analyzed and fit to normal and nonnormal distribu-
tions in the model using ExpertFitTM software. Each

105. continuous distribution used in the simulation model
passed both the Anderson-Darling and Kolmogrov-
Smirnov goodness-of-fit tests. This approach lends
credibility and confidence to the project team that
the model accurately predicts reality. It is assumed
that past behavior is representative of future beha-
vior in this specific supply chain.
Responses from the simulation include the
following:
. Customer service (CSI)
. Aggregate at internal DC
. Aggregate at third-party (external) DC
. Detailed
. By item
. Combination of items (‘‘A’’ or ‘‘C’’)
. Backorder duration for SKUs at both DCs
. Inventory
. Daily snapshot of inventory position at both

106. DCs
. Graphical view of inventory
. Orders
. Historical record of order size
. Historical record of order pattern (frequency)
As model runtime progresses day by day, inven-
tory enters and leaves each DC. Initial inventory
levels are set equal to inventory buffer capacity,
resulting in maximum inventory at model runtime.
As time passes, inventory reaches steady state where
natural variation in order behavior (frequency and
quantity) occurs and the replenishment model is
fully functional. Two-year simulation duration
appears sufficient in allowing the model to warm
up in the first year to steady-state conditions.
The robust simulation model allows customized and
informative reporting of system performance under
varied conditions. For example, consider that inven-

107. tory is recorded to a data file on a daily basis for each
SKU. To highlight the benefit of this functionality,
Figure 7 charts this variation in daily inventory value
at both DCs for a single simulation run for low-demand
SKU 9. The 6-week replenishment policy for
low-demand ‘‘C’’ products can be readily seen in
Figure 7 as inventory is depleted each week until the
6-week cycle is completed and product is replenished
at the third-party DC. A similar pattern is observed in
high-demand ‘‘A’’ products that have a one-week
replenishment cycle. Further analysis of Figure 7
shows that the internal DC never stocked out but the
third-party DC stocked out on numerous occasions.
Also note that the stock-out duration at the third-party
DC is quantified using this analysis method.
A series of designed experiments from the
discrete-event simulation model was implemented
FIGURE 7 Daily inventory for a low-demand product.

108. 191 Quantifying Supply Chain Trade-Offs
to quantify the impact of the following supply chain
variables on CSI.
. Internal distributor’s inventory buffer size
. Third-party distributor’s inventory buffer size
. Production lead time
. Customer demand
The results from a 34 full-factorial (81 experi-
ments) DOE are included in Appendix B.
The simulation-generated reports and subsequent
graphical analysis, statistical analysis, and designed
studies enable decision makers to assess process
parameters as well as business rules, policies, and
metrics.
SUMMARY OF MAJOR FINDINGS
The major findings of the simulation analysis and
simulation DOE are documented in the following

109. subsections.
DOE Results Confirm Conventional
Wisdom
The simulation model quantifies customer service
levels when varying customer demand, inventory
buffer sizes, and production lead time. The general
outcomes from the DOE analysis predict and quan-
tify conventional wisdom as follows:
. Increases in customer demand variation result in
lower customer service.
. Decreases in customer demand variation result in
higher customer service.
. Long-term backorder events cause significant
performance problems.
. Short-term backorder events are absorbed by the
supply chain.
Customer demand variation and lead time variation
have significant effects on the performance of both
the internal and external DCs. The effects differ by

110. item type in that high-demand products have a dif-
ferent replenishment policy from the low-demand
products.
Varying buffer sizes at the third-party DC does
affect customer service. However, the third-party
DC customer service performance in this system is
not very sensitive to the inventory carried at the
internal distributor.
Process Improvement
Recommendations
As stated previously, the motivation and value of
the simulation model and DOE analysis is twofold:
1. To quantify the trade-off between minimizing
inventory costs and maximizing customer service
under normal cause variation; and
2. To assess the performance metrics of the supply
chain and their ability to appropriately evaluate
and reward relevant supply chain nodes.

111. Considering these motivations, the designed experi-
ments analysis, simulation results, and recommenda-
tions for advancing the project to the improve phase
are as follows:
. Leave high-demand ‘‘A’’ items at baseline inven-
tory levels
. Redefine CSI performance metrics toward the
end-customer
. Preposition inventory closer to the end-customer
on the lower demand ‘‘C’’ items
. Decrease service level requirements on ‘‘C’’
items at the internal DC
. Inventory reduction is possible through this
reallocation process
. Strive for lead-time variability reduction
. Fixed cycles with variable quantities
. Move toward a true periodic review inventory
policy

112. Support for each recommendation is detailed in this
section as shown in Figures 8 thru 13.
Leave High-Demand ‘‘A’’ Items at Baseline
Inventory Levels
High-demand products should remain at the base-
line conditions for inventory buffer targets. Figures 8
and show the CSI of high-demand ‘‘A’’ products for
the internal and third-party DCs, respectively. Con-
sidering the normal cause of system variability, the
high CSI (above 90% CSI for various buffer sizes)
and small variation (4% CSI) at the internal DC is
negligible. Similarly, for various buffer sizes the
external DC maintains a CSI above 86% and does
not vary much more than 3% CSI overall.
S. Kumar et al. 192
Redefine CSI Performance Metrics to Focus
on End-Customer

113. One issue with customer service arises when the
internal DC stocks out but the external DC does
not. In this case, the end-customer does not see any
problem with delivery performance yet the CSI metric
indicates poor (or reduced) performance at the inter-
nal DC. This issue is illustrated in the stock-out history
chart shown in Figure 10. For low-demand SKU 8, the
internal DC stocks out five times in 2 years, whereas
the third-party DC only stocks out twice during the
same time frame. Stock-out duration at the internal
DC is twice as long as stock-out duration at the exter-
nal DC. Because the main objective is high customer
satisfaction, measuring customer service performance
at the internal DC that does not affect the end-
customer is counterproductive.
The converse also occurs where the internal DC
rarely stocks out but the external DC frequently does.
Here, the internal DC appears to have outstanding

114. performance but the customer(s) cannot get the pro-
duct they want when they want it. Figure 11 shows
this situation for numerous SKUs. SKUs 4, 7, 9, and
10 all exhibit this behavior.
Thus, it is imperative to examine and redefine the
current performance metrics to reward service that
productively affects customer satisfaction.
Preposition Inventory Closer to Customer
on the Lower Demand ‘‘C’’ Items
This section highlights when the CSI performance
metric can incorrectly punish or reward a DC for
customer service. Specifically, on lower demand
‘‘C’’ product it is common that the internal DC rarely
stocks out but the external DC frequently does. This
trend results in product interruptions for customers
and indicates that additional inventory (or a varied
replenishment policy) is required at the external DC.
FIGURE 9 Third-party DC high-demand product ‘‘A’’ CSI—
interaction plot.

115. FIGURE 8 Internal DC high-demand product ‘‘A’’ CSI—
interaction plot (data means).
193 Quantifying Supply Chain Trade-Offs
To increase inventory at the external DC and
maintain or reduce the total system inventory, inven-
tory at the internal DC must be reduced or the
internal DC target CSI metric must be reduced. This
may seem intuitive when considering overall inven-
tory costs but not necessarily when considering CSI.
Figures 11 and 12 show that the range of CSI for
the external DC, which directly impacts the end
customer, can be significantly lower (10–90% CSI)
than the internal DC (70–90% CSI) even under the
same conditions.
These combined observations and Figures 11 and
12 indicate:
. Prepositioning inventory closer to the end-

116. customer on the lower demand ‘‘C’’ items should
result in improved end-customer service.
. Decreasing service level requirements on ‘‘C’’
items at the internal DC has a limited effect on
end-customer service.
. Inventory reduction is possible through this reallo-
cation process.
There are many benefits to reducing inventory,
including (1) increased cash flow, (2) reduced oper-
ating expenses, (3) acceleration of new product to
market due to less old product inventory in the pipe-
line, (4) reduction in obsolescence risk, and (5) the
ability to quickly address quality concerns in the
supply chain with minimal inventory cost.
Arguably, the primary benefit of reduced inventory
is increased inventory turns. As stated previously, the
project goal is to double inventory turns. As shown
in Figures 11 and 12, customer service is the

117. FIGURE 10 Stock-out history at the internal and third-party
distributors.
FIGURE 11 Third-party DC low-demand product ‘‘C’’ CSI—
interaction plot.
S. Kumar et al. 194
counterbalance to reduced inventory and must also
be considered in corresponding recommendations.
Strive for Production Lead Time Variability
Reduction
The reduction in production lead time variability
has many positive effects on the overall performance
of the supply chain. A factory is likely to be more
responsive when its lead time variability is reduced
as its ability to consistently fill customer orders
within a specified lead time is enhanced. Flexibility
is also improved, resulting in supply chain nodes that
function efficiently with less system inventory. As
lead time variation is reduced, the CSI for ‘‘C’’ pro-

118. ducts increases at the internal DC. In other words,
the internal DC is able to more consistently fulfill
external DC orders as a result of tighter lead times.
Figure 12 shows this trend.
Trade-Off Analysis
Inventory reallocation within the nodes of the
supply chain, if done correctly, has the potential to
significantly increase customer service while main-
taining or decreasing total system inventory. As an
example, consider the baseline case compared with
a case that has reduced internal DC inventory to
75% and increased external DC inventory to 125%.
In both cases, the overall system volume remained
relatively constant. This comparison quantifies the
changes in CSI at the internal DC and third-party
DC for a simple reallocation of inventory closer to
the end-customer without considering increases or
decreases in customer demand and production lead

119. time variation. Results are shown in Figure 13.
Positioning inventory closer to the customer
reduces internal DC total CSI. However, this change
increased the external DC total CSI and significantly
FIGURE 12 Internal DC low-demand product ‘‘C’’ CSI—
interaction plot.
FIGURE 13 CSI box plots for simulated inventory levels for
inventory reallocation to the external DC for ‘‘C’’ items and all
items
(baseline inventory level ¼ 1.00).
195 Quantifying Supply Chain Trade-Offs
reduced the variability in CSI. The majority of the
improvement occurs for the low-demand ‘‘C’’ items,
thereby supporting the recommendation to leave
high-demand ‘‘A’’ items at baseline.
MANAGERIAL/PRACTICAL
IMPLICATIONS
There are a number of important issues to con-
sider when implementing changes in the real supply
chains. The company is currently investigating a

120. change to customer service metrics by focusing on
on-time-in-full (OTIF) performance that may affect
the pilot implementation planned for in the improve
phase. Also, the question remains, ‘‘Will forward
deployment of inventory be acceptable to third-party
distributors?’’ The pilot system is designed to handle
normal cause variation. How will we manage special
cause events? Special cause events have great poten-
tial to create long-term backorder problems that are
difficult to recover from. How do we address these
special cause events in the pilot?
The next steps in the improve phase of the Six
Sigma framework are as follows:
. Identify a pilot area for testing
. Baseline data collection in the pilot area
. Develop parameter changes for service metrics
. Implement changes to internal and vendor-
managed inventory systems

121. . Track progress over a minimum 12-week period
Identifying the pilot area is an important decision.
The pilot should be of sufficient size to provide mean-
ingful results yet not too large to hinder management
of the pilot study. Management needs to set the
appropriate expectations for those involved because
change acceptance is important. Historical and cur-
rent performance of pilot operations is required to
provide an accurate baseline for which to compare
pilot performance. The proper service metrics need
to be identified to reward intended performance
and highlight underperforming areas requiring atten-
tion. Negotiating mutually beneficial contracts with
third-party distributors is imperative to the success
of the pilot because internal inventories will be
reduced at the same time that third-party inventories
are increased, the net result of which will be a
reduction in overall system inventory. Finally, the

122. pilot will need time to function and progress will be
tracked over a minimum of 12 weeks.
CONCLUSIONS
The three-tiered approach described in this article
exploits the synergies between Six Sigma, discrete-
event simulation, and designed experiments. First,
DMAIC methodology identifies and prioritizes the
objectives and process for the simulation. Second,
the distribution network simulation model provides
a comprehensive study of the supply chain’s per-
formance. Third, the relationship between inventory
and customer service is better understood and
quantified using the model coupled with designed
experiments. Even though DMAIC’s improve and
control phases were not fully completed, the results
from this study impacted decision making, facilitated
inventory replenishment policy changes, and
addressed the stochastic behavior of customers.

123. Finally, with the study helping to enable the proper
allocation of resources, the company is now able to
effectively manage various SKU classes and customer
categories.
A direct outcome of this study has resulted in an
analysis template that is currently implemented in
numerous supply chains within the company. A
proactive decision support tool is now available to
perform a wide array of analyses. ‘‘What If’’ scenario
analysis can predict how the distribution network
responds to increases in demand or changes in
replenishment policies. The model is scalable to
include more customers, SKUs, DCs, and so on. Simu-
lation of the distribution network leads to improved
trade-off analysis, maximizing the confidence of the
business team that changes in policy have proven
successful in the virtual world. The model can
be used as a cost–benefit analysis tool to support

124. changes in business or inventory management
policies. This innovative and robust approach lends
itself well to replication in distribution networks
across a diverse range of industries.
ABOUT THE AUTHORS
Dr. Sameer Kumar is currently a professor of
operations and supply chain management and
Qwest Endowed Chair in Global Communications
S. Kumar et al. 196
and Technology Management in the Opus College of
Business, University of St. Thomas. Major research
interests include optimization concepts applied to
various aspects of global supply chain management,
information systems, technology management, pro-
duct and process innovation, and capital investment
justifications.
Marietsa L. McCreary holds a bachelor’s degree

125. and two master’s degrees in mechanical engineering
from the University of Michigan, Georgia Institute of
Technology (Fluids & Thermo dynamics), and
L’Ecole Nationale Superieure D’Arts et Metiers
(Manufacturing & Materials), respectively. She is an
advanced design engineer at the 3M Company. As
a senior resident project engineer, she provides
manufacturing and business systems analysis, as well
as decision modeling and analysis for 3M Divisions
and 3M corporate quality initiatives.
Daniel A. Nottestad is an engineering specialist at
the 3M Company. He provides manufacturing and
business systems analysis for 3M Divisions and 3M
corporate quality initiatives. In addition to engineer-
ing analysis, his work experience includes design,
project, and plant engineering. He has a bachelor’s
degree in mechanical engineering from the University
of Wisconsin at Madison in 1991. He was awarded a

126. master’s degree in manufacturing systems engineer-
ing in 2002 by the University of St. Thomas, St. Paul,
Minnesota.
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APPENDICES
Appendix A contains the selected analysis
of variance (ANOVA) for the DOE analysis.
Appendix B contains the simulated supply chain
performance data and results from DOE and simu-
lation studies.
197 Quantifying Supply Chain Trade-Offs
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S. Kumar et al. 198
Analysis of Variance for Internal CSI ‘‘A’’
Source DF Seq SS Adj SS Adj MS F P
Regression 14 6,455.92 6,455.92 461.14 112.46 0.000
Linear 4 4,686.59 4,686.59 1,171.65 285.74 0.000
Square 4 1,547.86 1,547.86 386.96 94.37 0.000
Interaction 6 221.47 221.47 36.91 9.00 0.000
Residual error 66 270.62 270.62 4.10
Total 80 6726.55
Estimated Regression Coefficients for Internal CSI ‘‘A’’ Using
Data in Uncoded Units

154. Term Coef
Constant 54.8419
Customer variation �18.0431
Lead time variation 87.9234
External buffer �1.94991E-14
Internal buffer 3.19533
Customer variation � Customer variation �2.43467
Lead time variation � Lead time variation �37.0100
External buffer � External buffer 7.05246E-15
Internal buffer � Internal buffer 1.80533
Customer variation � Lead time variation 8.90933
Customer variation � External buffer 1.51425E-14
Customer variation � Internal buffer 6.06333
Lead time variation � External buffer 2.62404E-15
Lead time variation � Internal buffer �6.28200
External buffer � Internal buffer �1.12832E-14
Appendix B
TABLE B1 Aggregate Table of CSI for Various
Customers/Various Product Types
Aggregate customer service performance
Location Product type Customer orders Service penalties CSI

155. (%)
Third-party DC Customer 1 A 517 3 99.4
C 272 33 87.9
Total 789 36 95.4
Customer 2 A 515 1 99.8
D 281 38 86.5
Total 796 39 95.1
Customer 3 A 522 4 99.2
C 269 37 86.2
Total 791 41 94.8
All customers A 1554 8 99.5
C 822 108 86.9
Total 2376 116 95.1
Internal DC A 312 1 99.7
C 119 15 87.4
Total 431 16 96.3
199 Quantifying Supply Chain Trade-Offs

156. TABLE B2 Third-party DC Customer Service Performance for
Customer 3 Only
Location: Third party DC Customers: Customer 3 only
X
SKU 1 SKU 2 SKU 3 SKU 4 SKU 5
Period Orders Hits CSI Orders Hits ISC Orders Hits CSI Orders
Hits CSI Orders Hits CSI
1 7 0 100.0 3 0 100.0 9 0 100.0 5 0 100.0 2 0 100.0
2 7 0 100.0 7 0 100.0 8 0 100.0 1 0 100.0 3 0 100.0
3 7 0 100.0 5 0 100.0 8 0 100.0 3 0 100.0 2 0 100.0
4 7 0 100.0 4 0 100.0 8 0 100.0 3 0 100.0 3 0 100.0
5 6 0 100.0 8 1 87.5 7 0 100.0 2 0 100.0 2 1 50.0
6 7 0 100.0 7 0 100.0 7 0 100.0 3 0 100.0 2 1 50.0
7 5 0 100.0 6 0 100.0 7 0 100.0 3 0 100.0 0 0 100.0
8 7 0 100.0 6 0 100.0 7 0 100.0 1 0 100.0 2 0 100.0
9 8 0 100.0 5 0 100.0 8 0 100.0 2 0 100.0 2 1 50.0
10 6 0 100.0 8 0 100.0 7 0 100.0 3 0 100.0 2 0 100.0
11 7 0 100.0 4 0 100.0 8 0 100.0 3 0 100.0 3 0 100.0
12 8 0 100.0 4 0 100.0 8 0 100.0 0 0 100.0 3 0 100.0
13 7 0 100.0 4 1 75.0 7 0 100.0 3 0 100.0 2 0 100.0

157. 14 4 0 100.0 5 0 100.0 6 0 100.0 2 0 100.0 1 0 100.0
15 8 0 100.0 5 0 100.0 9 0 100.0 2 0 100.0 4 0 100.0
16 8 0 100.0 5 0 100.0 6 0 100.0 1 0 100.0 3 1 66.7
17 8 0 100.0 8 0 100.0 6 0 100.0 2 0 100.0 3 0 100.0
18 8 0 100.0 7 0 100.0 9 0 100.0 3 0 100.0 1 1 0.0
19 6 0 100.0 3 0 100.0 9 0 100.0 3 0 100.0 3 0 100.0
20 6 0 100.0 7 0 100.0 6 0 100.0 2 0 100.0 2 0 100.0
21 7 0 100.0 4 0 100.0 8 0 100.0 3 0 100.0 1 0 100.0
22 8 0 100.0 6 0 100.0 8 0 100.0 2 0 100.0 2 2 0.0
23 8 0 100.0 7 1 85.7 7 0 100.0 4 0 100.0 4 0 100.0
24 5 0 100.0 6 1 83.3 7 0 100.0 2 0 100.0 3 0 100.0
25 8 0 100.0 6 0 100.0 7 0 100.0 3 0 100.0 2 0 100.0
26 7 0 100.0 7 0 100.0 8 0 100.0 2 0 100.0 2 0 100.0
SKU Totals 180 0 100.0% 147 4 97.3% 195 0 100.0% 63 0
100.0% 59 7 88.1%
X SKU 1 SKU 2 SKU 3 SKU 4 SKU 5
TYPE A A A C C
Third Party Total Orders 791 Third Party ‘‘A’’ Orders

158. Third Party Penalties 41 "A’’ Penalties
Third Party Total CSI 94.8% Third Party ‘‘A’’ CSI
(Continued )
S. Kumar et al. 200
TABLE B2 Continued
NOTE: (1) PERIOD ¼ (1) MONTH ¼ (20) SIMULATION
DAYS
SKU 6 SKU 7 SKU 8 SKU 9 SKU 10 OM summary customer 3
Orders Hits CSI Orders Hits CSI Orders Hits CSI Orders Hits
CSI Orders Hits CSI Orders Hits CSI
1 0 100.0 2 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 32 0 100.0%
2 0 100.0 1 0 100.0 1 0 100.0 0 0 100.0 1 0 100.0 31 0 100.0%
1 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 30 0 100.0%
0 0 100.0 2 0 100.0 1 0 100.0 1 0 100.0 0 0 100.0 29 0 100.0%
2 0 100.0 1 0 100.0 1 1 0.0 1 0 100.0 1 0 100.0 31 3 90.3%
1 0 100.0 2 1 50.0 1 0 100.0 2 1 50.0 1 1 0.0 33 4 87.9%
2 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 0 0 100.0 26 1 96.2%
2 0 100.0 2 0 100.0 1 0 100.0 0 0 100.0 0 0 100.0 28 0 100.0%

159. 2 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 31 2 93.5%
3 0 100.0 1 0 100.0 1 0 100.0 2 0 100.0 2 1 50.0 35 1 97.1%
2 1 50.0 0 0 100.0 1 0 100.0 1 0 100.0 0 0 100.0 29 1 96.6%
1 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 0 0 100.0 27 0 100.0%
2 1 50.0 1 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 29 3 89.7%
1 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 23 1 95.7%
2 0 100.0 1 1 0.0 1 0 100.0 0 0 100.0 1 1 0.0 32 2 93.8%
3 1 66.7 1 0 100.0 1 0 100.0 2 0 100.0 1 1 0.0 31 3 90.3%
2 1 50.0 1 1 0.0 1 0 100.0 1 0 100.0 0 0 100.0 32 2 93.8%
2 1 50.0 1 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 34 3 91.2%
1 0 100.0 2 0 100.0 1 0 100.0 0 0 100.0 1 1 0.0 29 1 96.6%
2 0 100.0 1 0 100.0 1 0 100.0 1 0 100.0 0 0 100.0 28 0 100.0%
2 0 100.0 2 0 100.0 1 0 100.0 1 0 100.0 1 1 0.0 30 1 96.7%
2 0 100.0 2 0 100.0 0 0 100.0 1 0 100.0 1 1 0.0 32 3 90.6%
2 0 100.0 2 1 50.0 1 0 100.0 1 1 0.0 1 1 0.0 37 4 89.2%
1 0 100.0 1 1 0.0 0 0 100.0 1 0 100.0 1 1 0.0 27 3 88.9%
3 0 100.0 1 1 0.0 2 0 100.0 2 0 100.0 0 0 100.0 34 1 97.1%
1 0 100.0 2 1 50.0 0 0 100.0 1 0 100.0 1 1 0.0 31 2 93.5%

160. 45 5 88.9% 34 7 79.4% 23 1 95.7% 26 3 88.5% 19 14 26.3%
791 41 94.8%
SKU 6 SKU 7 SKU 8 SKU 9 SKU 10 Summary Customer 3
C C C C C ALL
522 Third Party ‘‘C’’ Orders 269
4 "C’’ Penalties 37
99.2% Third Party ‘‘C’’ CSI 86.2%
201 Quantifying Supply Chain Trade-Offs
TABLE B3 DOE Results from Simulation
DOE
DOE factors DOE responses
Eval
Customer
variation
Lead
time
variation
External

161. buffer
Internal
buffer
Internal
CSI ‘‘A’’
Internal
CSI ‘‘C’’
Internal
CSI total
External
CSI ‘‘A’’
External
CSI ‘‘C’’
External
CSI total
0 0.5 0.5 0.75 0.75 82.956 94.225 86.906 69.947 84.226 74.966
1 0.5 0.5 0.75 1 85.565 94.447 88.459 75.937 84.261 78.85
2 0.5 0.5 0.75 1.25 90.542 94.452 91.81 77.709 84.297 80.006

162. 3 0.5 0.5 1 0.75 84.905 93.683 87.89 72.223 94.087 79.909
4 0.5 0.5 1 1 88.069 94.105 90.059 78.683 94.087 84.085
5 0.5 0.5 1 1.25 88.605 94.315 90.43 80.832 94.087 85.476
6 0.5 0.5 1.25 0.75 85.895 92.423 88.051 75.716 97.111 83.223
7 0.5 0.5 1.25 1 86.732 93.895 89.051 80.684 97.111 86.437
8 0.5 0.5 1.25 1.25 88.662 93.895 90.352 82.009 97.111 87.297
9 0.5 1 0.75 0.75 99.676 91.19 97.477 99.387 70.09 89.082
10 0.5 1 0.75 1 99.919 91.655 97.777 99.387 70.09 89.082
11 0.5 1 0.75 1.25 99.919 91.887 97.837 99.387 70.09 89.082
12 0.5 1 1 0.75 99.513 90.303 97.118 99.961 78.673 92.477
13 0.5 1 1 1 99.919 90.768 97.538 99.961 78.708 92.489
14 0.5 1 1 1.25 99.919 91.688 97.778 99.961 78.708 92.489
15 0.5 1 1.25 0.75 99.432 88.693 96.638 100 81.696 93.562
16 0.5 1 1.25 1 99.837 90.076 97.298 100 81.696 93.562
17 0.5 1 1.25 1.25 99.919 90.076 97.358 100 81.696 93.562
18 0.5 1.5 0.75 0.75 99.676 93.445 97.948 99.387 84.902
94.293
19 0.5 1.5 0.75 1 99.919 93.867 98.242 99.387 84.902 94.293
20 0.5 1.5 0.75 1.25 99.919 93.868 98.241 99.387 84.902

163. 94.293
21 0.5 1.5 1 0.75 99.513 89.688 96.778 99.961 93.732 97.774
22 0.5 1.5 1 1 99.756 90.53 97.188 99.961 93.91 97.836
23 0.5 1.5 1 1.25 99.919 93.475 98.125 99.961 94.087 97.898
24 0.5 1.5 1.25 0.75 99.513 89.688 96.779 100 97.04 98.959
25 0.5 1.5 1.25 1 99.756 92.843 97.832 100 97.111 98.984
26 0.5 1.5 1.25 1.25 99.837 93.053 97.949 100 97.111 98.984
27 1 0.5 0.75 0.75 78.731 90.445 83.002 58.861 29.557 48.677
28 1 0.5 0.75 1 83.963 90.664 86.48 59.207 29.617 48.925
29 1 0.5 0.75 1.25 84.325 90.883 86.633 64.392 29.647 52.316
30 1 0.5 1 0.75 79.978 88.965 83.342 59.774 77.759 66.024
31 1 0.5 1 1 83.091 89.805 85.532 63.787 77.759 68.643
32 1 0.5 1 1.25 84.732 90.046 86.639 67.169 77.819 70.871
33 1 0.5 1.25 0.75 79.218 84.076 80.992 63.391 91.339 73.113
34 1 0.5 1.25 1 80.97 85.58 82.603 66.66 91.339 75.248
35 1 0.5 1.25 1.25 81.878 86.222 83.477 67.093 91.339 75.524
36 1 1 0.75 0.75 98.3 89.199 95.967 96.928 25.095 71.948
37 1 1 0.75 1 99.352 89.199 96.749 97.023 25.095 72.01

164. 38 1 1 0.75 1.25 99.595 89.435 96.99 97.023 25.125 72.021
39 1 1 1 0.75 98.298 84.705 94.816 99.713 60.999 86.24
40 1 1 1 1 98.947 84.941 95.359 99.823 61.029 86.323
41 1 1 1 1.25 99.352 86.587 96.082 99.839 61.121 86.365
42 1 1 1.25 0.75 98.054 79.532 93.31 99.936 73.466 90.728
43 1 1 1.25 1 98.865 80.947 94.274 99.952 73.466 90.739
44 1 1 1.25 1.25 99.514 82.12 95.058 99.968 73.466 90.749
45 1 1.5 0.75 0.75 97.896 88.655 95.325 96.816 29.135 73.279
46 1 1.5 0.75 1 99.11 88.866 96.26 96.974 29.225 73.414
47 1 1.5 0.75 1.25 99.353 89.076 96.494 97.023 29.346 73.488
48 1 1.5 1 0.75 97.165 83.613 93.393 99.744 78.12 92.215
(Continued )
S. Kumar et al. 202
TABLE B3 Continued
DOE
DOE factors DOE responses
Eval
Customer

165. variation
Lead
time
variation
External
buffer
Internal
buffer
Internal
CSI ‘‘A’’
Internal
CSI ‘‘C’’
Internal
CSI total
External
CSI ‘‘A’’
External
CSI ‘‘C’’

166. External
CSI total
49 1 1.5 1 1 98.703 84.454 94.737 99.807 78.18 92.278
50 1 1.5 1 1.25 99.108 88.235 96.082 99.839 78.54 92.424
51 1 1.5 1.25 0.75 97.487 77.941 92.047 99.952 91.459 96.997
52 1 1.5 1.25 1 98.703 79.622 93.392 99.952 91.789 97.112
53 1 1.5 1.25 1.25 99.189 80.462 93.977 99.968 91.879 97.154
54 1.5 0.5 0.75 0.75 76.757 84.087 79.537 46.68 11.098 34.258
55 1.5 0.5 0.75 1 77.493 84.306 80.022 48.27 11.098 35.292
56 1.5 0.5 0.75 1.25 80.031 88.097 83.162 49.741 11.098 36.25
57 1.5 0.5 1 0.75 73.303 81.538 76.473 51.964 19.861 40.76
58 1.5 0.5 1 1 74.421 85.156 78.501 53.482 19.861 41.748
59 1.5 0.5 1 1.25 77.235 88.737 81.721 53.803 19.861 41.956
60 1.5 0.5 1.25 0.75 73.982 68.585 71.815 53.239 59.065
55.277
61 1.5 0.5 1.25 1 73.486 72.65 73.121 53.589 60.332 55.947
62 1.5 0.5 1.25 1.25 73.88 73.719 73.8 57.655 60.388 58.614
63 1.5 1 0.75 0.75 95.955 81.604 92.289 87.609 10.243 60.598

167. 64 1.5 1 0.75 1 98.786 81.604 94.398 87.817 10.243 60.733
65 1.5 1 0.75 1.25 99.11 85.377 95.602 87.846 10.243 60.752
66 1.5 1 1 0.75 94.741 79.717 90.904 97.88 16.496 69.469
67 1.5 1 1 1 97.087 79.717 92.651 98.247 16.496 69.708
68 1.5 1 1 1.25 98.382 84.434 94.819 98.437 16.496 69.832
69 1.5 1 1.25 0.75 94.498 66.19 87.319 99.662 42.146 79.585
70 1.5 1 1.25 1 97.006 71.19 90.459 99.78 43.193 80.027
71 1.5 1 1.25 1.25 97.816 72.619 91.425 99.838 43.304 80.104
72 1.5 1.5 0.75 0.75 91.789 81.513 88.929 86.185 11.098
59.971
73 1.5 1.5 0.75 1 96.602 81.723 92.465 87.549 11.098 60.858
74 1.5 1.5 0.75 1.25 98.22 85.294 94.626 87.787 11.098 61.012
75 1.5 1.5 1 0.75 90.431 76.05 86.429 96.634 19.53 69.719
76 1.5 1.5 1 1 93.689 79.832 89.836 97.951 19.668 70.624
77 1.5 1.5 1 1.25 96.926 86.134 93.925 98.319 19.668 70.863
78 1.5 1.5 1.25 0.75 89.391 63.787 82.28 98.582 57.905 84.385
79 1.5 1.5 1.25 1 93.366 68.204 86.382 99.398 59.256 85.388
80 1.5 1.5 1.25 1.25 96.683 69.118 89.019 99.794 59.589
85.762

168. 203 Quantifying Supply Chain Trade-Offs
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“Six sigma framework in supply chain” is an example of how
six-sigma tools can be implemented to make better decisions
and save money for a huge supply chain. Following are the
expectations from your report:
1. Give me a report of 4-5 pages (12 point Times New Roman,
single spacing) on the case study “Six sigma framework in
supply chain”.
2. Your report need not be an extensive description of the case
study including all details. For example,
a. you do not have to focus on how the simulation model and the
experimental design work. But you should briefly identify the
different components of the model inputs, the outputs and the
specific conclusions from the analyses. (I understand some of
you may not be completely familiar with
simulation/experimental design)
b. your report should not include any data or figures from case
study. Just reference them with indices used in the case study.
3. You should write elaborately on what are the different six-
sigma tools used and how they are used, as part of the DMAIC

169. process.
4. If possible, make a table or flow chart of different tools used
at each stage of the DMAIC, as part of your report.
5. Other information to include in your report are:
a. Objective of the case study,
b. Brief description of the supply chain network
c. Metrics used at different stages of DMAIC,
d. Results from each part of the DMAIC,
e. Conclusion with a couple of suggestions that you think would
have improved the analysis.
6. A suggestion for organization of the report:
a. Executive summary
b. Introduction
c. DMAIC
d. Conclusion