White_Paper_on_the_Impact_of_Inventory_on_Network_Design_v2

Published by Opex Analytics . 2014
White Paper:
Impact of Inventory on Network Design
Written as Research Project at Georgia Tech
with support from people at IBM, Northwestern, and Opex Analytics
Released: January 2014
Georgia Tech Team Members
Chandreshekar Sundaresan
MS SCE Graduate Student
Sundaresan3@gatech.edu
Seth Webster
MS SCE Graduate Student
Seth.webster@gatech.edu
Sponsor Writers
Michael Watson, Ph.D
Adjunct Professor, Northwestern
Partner, Opex Analytics
m-watson2@northwestern.edu
(312) 613-8008
Sara Lewis
Opex Analytics
Sara.Lewis@opexanalytics.com
Faculty Advisor
Dr. Alan Erera
Associate Professor
alerera@isye.gatech.edu
(404) 385-0358
Chandrashekar Sundaresan
Seth Webster

Introduction
Supply chain network design is about determining the right number, location, and size of
facilities in your network. It is a critical factor in determining the overall effectiveness and
efficiency of any firm s suppl hai . Its sig ifi a e o ti ues to g o i toda s a ket as
customers and competition evolve. However, supply chain network design and modeling is a
complex process involving many variables including transportation, warehousing, and
numerous other more specific supply chain costs. When inventory is added to the mix,
decisions become even more complicated and therefore more difficult to quantify and
understand as well.
Most supply chain managers are accurately aware that transportation typically drives the
majority of costs in a supply chain. And, it is well known that there is a direct relationship
between the location of facilities and the transportation costs. In theory, the closer you are to
your customers, the lower your costs will be. Figure 1 shows that for most distribution
networks, transportation costs are the biggest contributor to a fi s total supply chain costs at
over 50%. Thus, many Supply Chain Managers focus their network design efforts on generating
reductions in transportation costs.
Although less than transportation, it is also important to note that inventory costs are also
significant cost drivers in a supply chain at about 22%. Ignoring costs that account for almost a
quarter of the total could prove to be an expensive mistake. Many supply chain managers are
unsure about how the number and location of facilities will impact inventory. It is also unclear
how to incorporate inventory considerations into their analysis.
The purpose of this paper is to provide a deeper understanding of how supply chain network
design decisions drive inventory variables and vice versa. We will identify when inventory
matters to network design and when it does not.
We think that you might be surprised by
the complex relationships. You may
conclude that you need to worry less
than you thought about the impact of
changing warehouses on inventory.
Figure 1: Supply Chain Cost Drivers

Square Root of N Law
Past attempts to provide an easy to understand explanation of the relationship between the
number of warehouses and inventory have resulted in various basic guidelines or rules of
thumb for evaluating network design decisions. The most popular is the Square root of N law
which attempts to explain the relationship between number of warehouses and system wide
safety stock. This rule states that: The system-wide total safety stock is directly related to the
square root of the number of warehouses.
The benefit of this rule is that it is very simple and gives us some nice insight. It also provides a
sound reason why we assume safety stock changes as the number of warehouses changes. The
problem is that it is based on simplistic assumptions. The “quare Root of N law assumes there
is no variability in replenishment lead time, territories assigned to different warehouses have
more or less equal demand, and that customer demand is independent of each other. However,
the further away a system gets from these assumptions, the less effective the law. Real supply
chain networks generally do not operate under many of these assumptions. In addition, this
rule only focuses on safety stock. It is imperative to understand cycle stock implications as well.
The general difficulty in understanding this topic may be due to the fact that the inherent link
between network design choices and inventory levels is not necessarily intuitive. This further
increases the complexity of any supply chain network design project as well. Most supply
chains currently face high service level requirements, lead time with variability, and varying
replenishment frequencies, making it difficult to effectively use simple rules to make accurate
predictions about inventory.
This paper will present a more in-depth look at the factors that drive inventory in a network
design study. It will help supply chain managers think through the implications of adding or not
adding inventory considerations to their modeling. And, it will provide supply chain managers
with ideas on how to add inventory to their analysis.
Problem
We will highlight some of the most significant inventory variables with a case study taken from
the text Supply Chain Network Design. In this case, Al s Athleti s is a major sporting equipment
and apparel retailer in the United States. For simplicity, we ill assu e that Al s p odu t p ofile
consists of 100 SKUs.

Review of Al’s Athletics1
In the late 1960s, Al Alford, a young football coach in a small Texas town many miles away from
a ajo it , de ided that the kids i his to should t e held a k e ause the did t ha e
access to the right sporting equipment to practice with. Opening a store close to them to supply
the right equipment could be the first step for these kids to grow up to be the next Nolan Ryan,
Mean Joe Green, or Olympic gymnast Kim Zmeskal. Before Al knew it, his business was
booming. Al and his family quickly realized that they could repeat their success within similar
ities a oss the south, a d 50 ea s late Al s Athleti s has g o to e o e of the la gest etail
sporting-goods hai s i the U.“. Al s Athleti s o has ajo etail-store outlets in 41 U.S.
states.
Al s g a dso Al the thi d is o the CEO a d li es a d o ks ea the o igi al sto e i
Brownfield, Texas. He realizes that competition in the sporting-goods industry is high, and he
has al a s elie ed i the philosoph of his g a dfathe that p o i it to the usto e ea s
e e thi g i this usi ess. As a esult, Al a ts to look at addi g a d opti izi g a ehouse
locations across the country to lower costs and provide the best service of any sporting goods
chain in the US. At the o e t, Al s Athleti s has 200 “to es lo ated a oss the atio . This
case originally discusses a number of distribution strategies that involve redesigning their
supply chain network with up to 10 warehouses from a choice of 26 potential locations.
We will now extend the case by adding multiple SKUs to the analysis. This will allow us to
further explore the inventory implications. To keep it simple, we will use a sample of 100 SKUs
that fall into 4 different categories, namely: high value light weight, high value heavy weight,
low value light weight, and low value heavy weight.
1
Case Study Referenced from Supply Chain Network Design (www.networkdesignbook.com)
Figure 2 Al's Athletics Store Locations and Potential DC Locations

CASE STUDY SCENARIOS
No that e k o the a kg ou d fo ou ase, let s take a look at the following scenarios
which will provide us further insight into the complex link between network design and
inventory levels. Each scenario will highlight a different variable or assumption that impacts
inventory levels, and examine its effects based on both high and low demand variability.
Scenario 1 – Square Root of N Law Tested
For the first scenario, let s set up the problem with simplistic assumptions in an attempt to
replicate the Square Root of N law. We will use a
straight forward model of Al s Athleti s network
that has no variability in lead time, a fixed review
period, and equal order amounts no matter the
number of warehouses. This initial model has small
demand variability, but we will examine a higher
variability example later in the analysis. The
parameters and assumptions are shown in Table 1.
The results of Al s safet sto k ithi this MIP model, shown in Figure 3 on the left, validate the
Square Root of N law, with system wide safety stock almost exactly as the law estimated, and
directly proportional to the square root of the number of warehouses.
Figure 3: Simplistic Model: Safety Stock
Table 1: Baseline Assumptions

But what about Cycle Stock?
Any o pa s i e to ost is comprised of two components however, safety stock and cycle
stock. While the s ua e oot of N law accurately estimates the safety stock levels under the
said assumptions fo Al s Net o k, it does not provide insight into cycle stock, and thus total
inventory costs. Cycle stock is driven by demand and replenishment frequency. For the purpose
of this ase stud , let s assu e that Al s network is replenished on a weekly basis. Later on we
will explore what happens to cycle stock when their replenishment frequency changes.
Figure 4: Low Demand Variability - Inventory Cost Breakdown
When Al s supply chain managers saw the results from the square root of N law, they were
naturally concerned about the increase in the number of warehouses in their network causing
them to hold excess safety stock. However, in many companies, cycle stock can be orders of
magnitude higher than safety stock, thereby making increases to safety stock, and their
anxieties, insignificant. Figure 4 shows both safety stock costs and cycle stock costs for the
purposes of comparison. Here we can see that the total inventory cost is more or less constant,
following the path of cycle stock. In other words, while we see a 123% increase in safety stock
as we go from 2 to 10 warehouses in the network, the increase in total inventory is only 6%. Al s
team finds it apparent from this first analysis that their inventory costs remain relatively flat
regardless of network design decisions. They might, however, want to look at other analysis
besides the Square Root of N law to conclude the effects of inventory in general.

Is the Square Root of N rule to be avoided? Maybe not.
As mentioned previously, Al s Athleti s i itial model considered a demand profile with low
variability. With low standard deviation of demand, the initial safety stock required is very low,
and thus the square root of N law is not very effective in determining how overall inventory
levels will be affected by changing the network. However, if Al s experiences high standard
deviation of demand (or, in other words, a lot of demand variability), their initial safety stock
cost can be much higher relative to the cycle stock costs.
Figure 5: High Demand Variability - Inventory Cost Breakdown
In this high demand variation situation, Al s safety stock cost most definitely increases as they
add warehouses to the network, and the Square Root of N law is actually pretty effective at
estimating how total costs will change. Total inventory costs now track with changes in safety
stock costs in this situation. Figure 5 shows how safety stock costs can again be accurately
predicted by the square root of n law in the graph on the left, and the one on the right shows
how total inventory costs are now driven by safety stock costs.
Let s ot fo get that this a al sis elied on a number of additional assumptions that often do
not accurately represent real-world situations however. In the following scenarios of Al s
Athletics Network, we will see how inventory is affected when these assumptions are removed,
and the implications these affects will have on total costs and network design decisions
considering both high and low variability in demand.

Scenario 2 – When does inventory really matter?
As mentioned previously, it is often seen that inventory costs are significantly lower compared
to transportation costs. In this e sio of Al s et o k, even as the number of warehouses
rises, the penalty associated with increased inventory costs is irrelevant. Since transportation
costs are always higher i Al s et ork, the transportation savings realized with more
warehouses trumps the additional inventory costs that are accrued, seen in the graph on the
left in Figure 6. This makes transportation, and therefore site location, the primary driver of
Al s distribution strategy. On the other hand, if inventory holding costs are high, inventory may
actually play an important role in determining the optimal number of warehouses to have in
the system. With that said, let s take a look at the two scenarios to demonstrate this tradeoff:
1. A typical scenario where Al s Athleti s inventory costs are less than transportation costs
2. A scenario where Al s Athleti s inventory is expensive to hold and drives the decision.
Figure 6: Inventory vs. Transportation Costs
We find that typically, a o pa s inventory costs never approach the transportation costs,
regardless of the number of warehouses. In fact, in the scenario portrayed by the graph on the
left in Figure 6, we validate the ratio between inventory costs and transportation costs shown
previously in Figure 1. Thus, in terms of network design, despite a slight increase in inventory
costs by increasing the number of warehouses, the lower transportation costs drive the
decision for the network strategy.
The graph on the right exhibits a e sio of Al s Athleti s ith highe inventory costs (about 5
times the industry standard). In this case, we highlight that there are scenarios where inventory
costs outweigh the transportation costs, and thus the total cost line shows a more complicated
decision process, with the 5 warehouse scenario being optimal.
While the graph on the right shows that expensive inventory costs can have an impact on the
network design decisions, the graph on the left demonstrates that typically companies only
need consider transportation costs, confirming why most supply chain managers may leave

inventory out of their decision process altogether. Let s be sure to understand what drives the
impact of safety stock however.
Demand variability greatly affects safety stock and therefore total inventory. In most networks
with relatively low demand variability, safety stock levels and thus total inventory costs are low.
As a result, a larger gap between warehouse holding costs and transportation costs occurs. In
this way, transportation will always be the overbearing costs and any savings afforded on the
a ehouse holdi g ost f o t o t e e ough to tip the s ale in terms of network design
decisions. The exception to this occurs with companies carrying high value product
(pharmaceuticals, electronics, etc.) or large bulky product which may be expensive to store. For
these companies, inventory holding costs are typically high even though demand variability may
be low. In this instance the overall cost trends would be along the lines of the graph on the right
in Figure 6. Our next scenario takes a closer look at the underlying drivers of inventory in a
system.
Scenario 3 – Lead Time Variability
Risk pooling is a term that suggests downstream demand variability is reduced if one
aggregates demand across locations to the warehouse. The reasoning here says that if demand
is aggregated across different locations, it becomes more likely that high demand from one
customer will be offset by low demand from another. This reduction in overall variability allows
a decrease in safety stock and therefore reduces average inventory. Knowing this, analysts infer
that having fewer warehouses aggregates more demand locations to each warehouse, resulting
i the pooli g of the isk f o a ia ilit .
When evaluating network design decisions and optimizing for transportation, many companies
focus on the downstream demand
variability and are encouraged by the
benefits from risk pooling. However, if
we introduce variability in lead times
associated with procurement of
product from the vendor (which we
feel is a realistic expectation), the
benefits of risk pooling are dampened
while the total system wide safety
stock increases. In Figure 7, the
percent increase in safety stock is
124% (starting at a significantly lowerFigure 7: Safety Stock Costs Under Lead Time Variability

cost of course) with no lead time variability, while with constant lead time variability safety
stock costs only increase by 2%. The important thing to note is not the large differences in
increases but whether significant increases actually take place. When LT Variability in a
network is high, you might not need to worry that extra warehouses will drive up inventory—
you may want to work on reducing LT variability instead.
In essence, in cases where lead time variability is high and demand variability is low variability,
the benefits of risk pooling exemplified by the Square Root of N Law no longer apply. We often
see this in practice, lead time variability has a dramatic impact on inventory while the change in
the number of warehouses does not.
Figure 8 shows how much more safety stock you need when you have lead time variability (this
o pa iso is f o the ase of 5 a ehouses i Al s odel .
Increasing Lead Time Variability
Before Al s a al st u s to tell the manager that the number of warehouses in their supply
chain would not affect safety stock due to lead time variability, it is important to note what
happens when lead time variability increases as the number of warehouses increases. This has a
profound impact on total costs and the network design decision process as well. Figure 9 shows
that Al s may once again realize the benefits of risk pooling if lead time variability increases as
the number of warehouses increases.
Figure 8: Inventory Cost Breakdown (Under Lead Time Variability)

Figure 9: Effect of Increasing Lead Time Variability on Safety Stock
Lead Time and demand variability
Again, it is important to pay attention to all the assumptions involved in the model. We just saw
that adding lead time variability will greatly increase safety stock costs and eliminate the
benefits of risk pooling, but if the variability is increasing with the number of warehouses, risk
pooling is a factor. This effect is compounded due to our low standard deviation of demand
assumption as well. Because there was little variability to begin with, and thus a very low initial
amount of safety stock, any change in LT variability will lead to a huge increase in safety stock
costs. However, as we have done in previous scenarios, let s e a i e lead ti e a ia ilit he
safety stock costs are already large due to a high standard deviation of demand.
Figure 10: Effect of Lead Time Variability on Different Types of Demand

Figure 10 shows that if safety stock is already in place to protect against a high variability of
demand (graph on the left), adding lead time variability to the situation will have a much
smaller effect on safety stock, and thus total inventory costs.
Closing Notes on Lead Time Variability
There is nothing mathematical that suggests that lead time variability will increase or decrease
as you change the number of warehouses—this is in contrast with the theory of risk pooling
that states that demand variability will change with the number of warehouse. You will have to
investigate this on each project to see how the change in the number of warehouses will impact
your lead time variability.
Scenario 4 – The Effect of Replenishment Frequency
For this e sio of Al s Net o k, consider similar parameter setting as in the previous scenarios.
Now we will investigate the e do s a ilit to keep up ith Al s o de e ui e e ts as the
number of warehouses in the network increases, and the resulting effect on cycle stock.
We will focus specifically on how frequently each warehouse can be replenished.
Replenishment frequency drives how much product Al s must request in each order, and thus is
a primary factor in system wide cycle stock. In addition, as shown in the first scenario, cycle
stock generally represents a larger portion of inventory costs in industries with low demand
variability, so this is an area where companies must pay special attention.
As the number of warehouses in Al s network increases, it is likely that it is going to take their
vendors more time to fill a full truck with product for each facility, resulting in less frequent
replenishments. This is not a natural mathematical function, so the supply chain manager at
Al s Athleti s will need to use judgment in determining how replenishment frequency will
change in the new network.
In this scenario we assume that for every additional warehouse added to the network, the
replenishment frequency decreases by 15%. In effect, if the vendor replenishes two
warehouses every seven days, with three warehouses it will be just over 8 days between
replenishments. As the replenishment frequency decreases, the system wide cycle stock begins
to increase.

Figure 11: Cycle Stock Costs Under Decreasing Replenishment Frequencies
Because this might not be intuitive to many managers, the resulting underestimation of cycle
stock could lead them to make a costly decision. Figure 11 shows the effects on system wide
cycle stock costs using the first of
Al s scenarios described above
(with high demand variability).
Previously (with low demand
variability), transportation was
the primary driver of cost and
therefore the network design
decision, this increase in cycle
stock due to decreasing
replenishment frequency gives
the inventory costs greater
weight in the decision process as seen in Figure 12 below. At some point, the inventory holding
costs become too high and Al s Athleti s must consider balancing this by taking a penalty on the
transportation costs utilizing LTL, Multi-Stop Truck Load or other more expensive but more
efficient mode of transport.
Figure 12: Effect of Decreasing Replenishment Frequencies on Total Costs.
Decreasing Replenishment Frequency and demand variability.
While changing replenishment frequency o t have a noticeable impact on safety stock when
demand variability is low, it is still important to examine how the change in cycle stock will
impact total inventory costs when Al s faces a high standard deviation of demand. As we have
seen before, cycle stock is not as important in this case. Therefore, the optimal number of
warehouses is not impacted as much by decreasing replenishment frequency.

Low Demand Variability, Expensive Inventory
SUMMARY
*I o pa i g, oti e that g aph s ithi the su a a ot al a s follo the sa e -axis scale.
Baseline Scenarios
We started with the most assumptions in order to validate the Square Root of N Model.
With Low Demand Variability we see transportation typically dominates in terms of driving the
network decisions based on the relatively low inventory costs (although Expensive Inventory
increases our holding cost significantly, it’s still irrelevant in relation to transportation costs). In
this situation, it is easy for managers to ignore inventory considerations when making changes
to their Supply Chain network.
With High Demand Variability however, Inventory costs take on a much greater role in the
network design decision making process. In the case of inexpensive inventory the network
design decision remains tight but ten warehouses still remains optimal. Whereas with expensive
inventory the holding costs outweigh transportation costs with nine warehouses. Supply chain
managers should be aware of this trade-off and explore inventory further within their mode
Low Demand Variability, Inexpensive Inventory
High Demand Variability, Expensive InventoryHigh Demand Variability, Inexpensive Inventory

Constant LT Variability Scenarios
In situations with low demand variability, considering constant replenishment frequency and
lead time variability, the impact on safety stock and thus inventory costs is significant. However,
transportation still drives the optimal number of warehouses in the network.
In this situation, managers may still be content to ignore inventory considerations when making
changes to their Supply Chain network.
With High Demand Variability, Inventory costs continue to take on a much greater role, as seen
in the baseline. However, safety stock has already been high in order to cover for high demand
variability and therefore the addition of a constant LT variability does not have much additional
effect on stocking levels. When LT Variability in a network is constant and high, concern for an
increase of safety stock as a result of additional warehouses should reduce dramatically.
High Demand Variability, Inexpensive Inventory High Demand Variability, Expensive Inventory

Increasing LT Variability Scenarios
When considering a lead time variability that increases with each additional warehouse in the
network, we start to see the impact inventory can have on the network design decision process.
With Low Demand Variability and Inexpensive Inventory transportation still overwhelms. But
with Expensive Inventory we see the trough of the total cost curve now sits at 8 warehouses.
Supply Chain managers must now be aware of the inventory costs when selecting their final
design decisions.
With High Demand Variability however, Inventory costs take on a much greater role in the
network design decision making process. In the case of inexpensive inventory the network
design decision remains the same. Whereas with expensive inventory the holding costs begin to
outweigh transportation costs with just six warehouses. In these situations, Supply chain
managers should be sure to accurately measure the Lead Time and the associated variability in
order to incorporate into their network design decision process.

Decreasing Replenishment Frequency Scenarios
Here we assume that with more warehouses your vendor will take longer to fill up a truck for
each warehouse, and replenishment frequency will decrease.
With Low Demand Variability we again see the transportation dominating in terms of driving
the network design.
With High Demand Variability however, as replenishment frequency is a key driver of cycle
stock, and cycle stock a key driver of inventory costs, the number of warehouses in both of the
below scenarios shifts left. As the decrease in frequency is not a natural mathematical function,
supply chain managers need to use judgment in determining how replenishment frequency will
change in the new network in order to appropriately include the factor in their network design
model

18 | Page
Closing Comments
The interaction between network design and inventory is quite complex and a number of
different variables play a key role towards making an informed decision. The white paper
details some of the tipping points to look out for while considering network re-design projects
and hopefully gives the reader enough insight to know when to consider a detailed inventory
analysis as a supplement to the re-design effort.

White_Paper_on_the_Impact_of_Inventory_on_Network_Design_v2

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