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Supply Chain Management: Strategy, Planning, and Operation

Seventh Edition

Chapter 12

Managing Uncertainty in a Supply Chain Safety Inventory

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Learning Objectives (1 of 2)

12.1 Understand the role of safety inventory in a supply chain.

12.2 Identify factors that influence the required level of safety inventory.

12.3 Evaluate the appropriate level of safety inventory for a supply chain.

12.4 Discuss the impact of supply uncertainty on safety inventory.

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Learning Objectives (2 of 2)

12.5 Understand how aggregation helps reduce the required safety inventory in a supply chain.

12.6 Determine the impact of replenishment policies on safety inventory.

12.7 Improve the management of safety inventory in a multiechelon supply chain.

12.8 Identify managerial levers that lower safety inventory without hurting product availability.

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The Role of Safety Inventory (1 of 3)

Safety inventory is carried to satisfy demand that exceeds the amount forecasted

Raising the level of safety inventory increases product availability and thus the margin captured from customer purchases

Raising the level of safety inventory increases inventory holding costs

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The Role of Safety Inventory (2 of 3)

Figure 12-1 Inventory Profile with Safety Inventory

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The Role of Safety Inventory (3 of 3)

Three key questions

What is the appropriate level of product availability?

How much safety inventory is needed for the desired level of product availability?

What actions can be taken to reduce safety inventory without hurting product availability?

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Summary of Learning Objective 1

Safety inventory helps a supply chain provide customers with a high level of product availability in spite of supply and demand uncertainty. It is carried just in case demand exceeds the amount forecasted or supply arrives later than expected.

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Factors Affecting the Level of Safety Inventory

The desired level of product availability

The uncertainty of demand

The uncertainty of supply

Inventory replenishment policies

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Measuring Product Availability

Product fill rate (fr)

Fraction of product demand satisfied from
product in inventory

Order fill rate

Fraction of orders filled from available inventory

Cycle service level (C S L)

Fraction of replenishment cycles that end with
all customer demand being met

Replenishment cycle – the interval between two successive replenishment deliveries

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Measuring Demand Uncertainty

D = Average demand per period

σD = Standard deviation of demand (forecast error) per period

Lead time (L) is the gap between when an order is placed and when it is received

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Evaluating Demand Distribution over L Periods

The coefficient of variation

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Measuring Supply Uncertainty

Lead time (L) is normally distributed with

L = Average lead time

σL = Standard deviation of lead time

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Replenishment Policies

Continuous review

Inventory is continuously tracked

Order for a lot size Q is placed when the inventory declines to the reorder point (R O P)

Periodic review

Inventory status is checked at regular periodic intervals

Order is placed to raise the inventory level to a specified threshold

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Summary of Learning Objective 2

Safety inventory is influenced by the desired product availability, demand uncertainty, replenishment lead times, and lead time variability. Product availability is measured using the fill rate or cycle service level. Demand uncertainty is measured by the forecast error. For lead time one measures both the mean and the standard deviation. The required safety inventory is also influenced by the inventory policy implemented. Continuous review policies order a fixed quantity after variable replenishment intervals. Periodic review policies order variable quantities after fixed replenishment intervals.

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Determining the Appropriate Level of Safety Inventory (1 of 8)

Evaluating Safety Inventory Given a Reorder Point

Expected demand during lead time = D × L

Safety inventory, ss = R O P − D × L

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Determining the Appropriate Level of Safety Inventory (2 of 8)

Average demand per week, D = 2,500

Standard deviation of weekly demand, sD = 500

Average lead time for replenishment, L = 2 weeks

Reorder point, R O P = 6,000

Average lot size, Q = 10,000

Safety inventory, ss = R O P −D L = 6,000 −5,000 = 1,000

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Determining the Appropriate Level of Safety Inventory (3 of 8)

Average inventory = cycle inventory + safety inventory

= 5,000 + 1,000 = 6,000

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Determining the Appropriate Level of Safety Inventory (4 of 8)

Evaluating Cycle Service Level Given a Reorder Point

(ddlt = demand during lead time)

C S L = F(R O P, DL, σL) = NORMDIST(R O P, DL, σL, 1)

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Determining the Appropriate Level of Safety Inventory (5 of 8)

Q = 10,000, R O P = 6,000, L = 2 weeks

D = 2,500/week, σD = 500

C S L = F(R O P, DL, σL) = NORMDIST(ROP, DL, σL, 1)

= NORMDIST(6,000, 5,000, 707, 1) = 0.92

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Determining the Appropriate Level of Safety Inventory (6 of 8)

Evaluating Required Safety Inventory Given a Desired Cycle Service Level

Desired cycle service level = C S L

Mean demand during lead time = DL

Standard deviation of demand during lead time = σL

Probability(demand during lead time

Identify safety inventory ss so that

F(DL + ss, DL, sL) = CSL

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Determining the Appropriate Level of Safety Inventory (7 of 8)

or

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Determining the Appropriate Level of Safety Inventory (8 of 8)

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Evaluating Fill Rate Given a Reorder Point (1 of 4)

Expected shortage per replenishment cycle (E S C) is the average units of demand that are not satisfied from inventory in stock per replenishment cycle

Product fill rate

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Evaluating Fill Rate Given a Reorder Point (2 of 4)

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Evaluating Fill Rate Given a Reorder Point (3 of 4)

Lot size, Q = 10,000

Average demand during lead time, DL =5,000

Standard deviation of demand during lead time,

Safety inventory, ss = R O P − DL = 6,000−5,000 = 1,000

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Evaluating Fill Rate Given a Reorder Point (4 of 4)

Figure 12-2 Excel Solution of Example 12-4

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Evaluating Safety Inventory Given Desired Fill Rate (1 of 4)

Expected shortage per replenishment cycle is

E S C = (1 − fr)Q

No equation for ss

Try values or use G O A L S E E K in Excel

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Evaluating Safety Inventory Given Desired Fill Rate (2 of 4)

Desired fill rate, fr = 0.975

Lot size, Q = 10,000 boxes

Standard deviation of ddlt,

ESC = (1−fr)Q = (1 − 0.975)10,000 = 250

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Evaluating Safety Inventory Given Desired Fill Rate (3 of 4)

Use G O A L S E E K to find safety inventory ss = 67 boxes

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Evaluating Safety Inventory Given Desired Fill Rate (4 of 4)

Figure 12-3 Spreadsheet to Solve for ss Using GOALSEEK

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Impact of Desired Product Availability, Lead Time, and Demand Uncertainty

As desired product availability goes up the required safety inventory increases

Table 12- Required Safety Inventory for Different Values of Fill Rate

Fill Rate Safety Inventory
97.5% 67
98.0% 183
98.5% 321
99.0% 499
99.5% 767

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Impact of Desired Product Availability and Uncertainty

Goal is to reduce the level of safety inventory required in a way that does not adversely affect product availability

Reduce the supplier lead time L

Reduce the underlying uncertainty of demand (represented by σD )

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Benefits of Reducing Lead Time and Demand Uncertainty

D = 2,500/week σD, CSL = 0.95

If lead time is reduced to one week

If standard deviation is reduced to 400

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Adjusting Safety Inventory for Demand Lumpiness and Seasonality

Orders typically in large lots

Demand at various stages in the supply chain tends to be lumpy

Raise safety inventory by half the average size of a customer order

Demand is often seasonal

Fixing a R O P may lead to stockouts

Keep R O P constant in terms of days of demand

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Summary of Learning Objective 3 (1 of 2)

Given a desired cycle service level C S L, a lead time L, and a standard deviation of periodic demand σD , the required safety inventory ss for a continuous review policy is given

by

Given a reorder point

R O P, a lead time L, a standard deviation of periodic demand σD, and periodic demand D, the resulting cycle service level is given by

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Summary of Learning Objective 3 (2 of 2)

Given a level of safety inventory, one can evaluate the resulting fill rate. Given a desired fill rate, one can evaluate the required safety inventory. The required safety inventory increases with an increase in desired product availability, lead time, and uncertainty of periodic demand. In practice, it is best to evaluate safety inventory in terms of days of demand to account for seasonality of demand.

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Impact of Supply Uncertainty on Safety Inventory

We incorporate supply uncertainty by assuming that lead time is uncertain

D : Average demand per period

σL : Standard deviation of demand per period

L : Average lead time for replenishment

sL : Standard deviation of lead time

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Impact of Lead Time Uncertainty on Safety Inventory (1 of 3)

Average demand per period, D = 2,500

Standard deviation of demand per period, σD = 500

Average lead time for replenishment, L = 7 days

Standard deviation of lead time, sL = 7 days

Mean ddlt, DL = DL = 2,500 × 7 = 17,500

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Impact of Lead Time Uncertainty on Safety Inventory (2 of 3)

Required safety inventory

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Impact of Lead Time Uncertainty on Safety Inventory (3 of 3)

Table 12-2 Required Safety Inventory as a Function of Lead Time Uncertainty

sL σL ss (units) ss (days)
6 15,058 19,298 7.72
5 12,570 16,109 6.44
4 10,087 12,927 5.17
3 7,616 9,760 3.90
2 5,172 6,628 2.65
1 2,828 3,625 1.45
0 1,323 1,695 0.68

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Summary of Learning Objective 4

An increase in supply uncertainty significantly increases the amount of safety inventory required for a given level of product availability. Lead time uncertainty has a more significant impact on the required safety inventory than lead time itself. A reduction in supply uncertainty can help to dramatically reduce the required safety inventory without hurting product availability.

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Impact of Aggregation on Safety Inventory (1 of 5)

How does aggregation affect forecast accuracy and safety inventories

Di: Mean periodic demand in region i, i = 1, …, k

σi : Standard deviation of periodic demand in region i, i =, …, k

ρij: Correlation of periodic demand for regions i, j,

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Impact of Aggregation on Safety Inventory (2 of 5)

Total safety inventory in decentralized option

Simplified to

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Impact of Aggregation on Safety Inventory (3 of 5)

Require safety inventory on aggregation

Holding – cost savings on aggregation per unit sold

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Impact of Aggregation on Safety Inventory (4 of 5)

The safety inventory savings on aggregation increase with the desired cycle service level C S L

The safety inventory savings on aggregation increase with the replenishment lead time L

The safety inventory savings on aggregation increase with the holding cost H

The safety inventory savings on aggregation increase with the coefficient of variation of demand

The safety inventory savings on aggregation decrease as the correlation coefficients increase

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Impact of Correlation on Value of Aggregation (1 of 3)

Standard deviation of weekly demand, σD =5

Replenishment, L = 2 weeks; Decentralized C S L = 0.9

Total required safety inventory,

Aggregate ρ = 0

Standard deviation of weekly demand at central outlet,

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Impact of Correlation on Value of Aggregation (2 of 3)

Table 12-3 Safety Inventory in the Disaggregate and Aggregate Options

Rho Disaggregate
Safety Inventory
Aggregate
Safety Inventory
0 36.25 18.12
0.2 36.25 22.93
0.4 36.25 26.88
0.6 36.25 30.33
0.8 36.25 33.42
1.0 36.25 36.25

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Impact of Aggregation on Safety Inventory (5 of 5)

Figure 12-4 Square-Root Law

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Impact of Correlation on Value of Aggregation (3 of 3)

Two possible disadvantages to aggregation

Increase in response time to customer order

Increase in transportation cost to customer

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Trade-Offs of Physical Centralization (1 of 2)

Use four regional or one national distribution center

Four regional centers

Total required safety inventory,

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Trade-Offs of Physical Centralization (2 of 2)

One national distribution center,  = 0

Standard deviation of weekly demand,

Decrease in holding costs

Decrease in facility costs

Increase in transportation

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Information Centralization

Online systems that allow customers or stores to locate stock

Improves product availability without adding to inventories

Reduces the amount of safety inventory

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Specialization (1 of 2)

Inventory is carried at multiple locations

Should all products should be stocked at every location?

Required level of safety inventory

Affected by coefficient of variation of demand

Low demand, slow-moving items, typically have a high coefficient of variation

High demand, fast-moving items, typically have a low coefficient of variation

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Impact of Coefficient of Variation on Value of Aggregation (1 of 2)

Table 12-4 Value of Aggregation at W.W. Grainger

Blank Motors Cleaner
Inventory is stocked in each store Blank Blank
Mean weekly demand per store 20 1,000
Standard deviation 40 100
Coefficient of variation 2.0 0.1
Safety inventory per store 132 329
Total safety inventory 211,200 526,400
Value of safety inventory $105,600,000 $15,792,000
Inventory is aggregated at the DC Blank Blank
Mean weekly aggregate demand 32,000 1,600,000
Standard deviation of aggregate demand 1,600 4,000
Coefficient of variation 0.05 0.0025
Aggregate safety inventory 5,264 13,159
Value of safety inventory $2,632,000 $394,770

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Impact of Coefficient of Variation on Value of Aggregation (2 of 2)

Table 12-4 [Continued]

Blank Motors Cleaner
Savings Blank Blank
Total inventory saving on aggregation $102,968,000 $15,397,230
Total holding cost saving on aggregation $25,742,000 $3,849,308
Holding cost saving per unit sold $15.47 $0.046
Savings as a percentage of product cost 3.09% 0.15%

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Specialization (2 of 2)

Item Type Centralized Inventories Decentralized Inventories
Fast Moving Predictable {Low Value} Customer willing to pay premium? Low cost
Slow Moving Unpredictable {High Value} Low cost Customer willing to pay premium?

Figure 12-5 Specialization of Inventory Based on Product Type

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Product Substitution

The use of one product to satisfy demand for a different product

Manufacturer-driven substitution

Allows aggregation of demand

Reduce safety inventories

Influenced by the cost differential, correlation of demand

Customer-driven substitution

Allows aggregation of safety inventory

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Component Commonality

Without common components

Uncertainty of demand for a component is the same as for the finished product

Results in high levels of safety inventory

With common components

Demand for a component is an aggregation of the demand for the finished products

Component demand is more predictable

Component inventories are reduced

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Value of Component Commonality (1 of 3)

27 servers, 3 components, 3 × 27 = 81 distinct components

Monthly demand = 5,000

Standard deviation = 3,000

Replenishment lead time = 1 month

C S L = 0.95

Total safety inventory required

Safety inventory per common component

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Value of Component Commonality (2 of 3)

With component commonality

Nine distinct components

Total safety inventory required

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Value of Component Commonality (3 of 3)

Table 12-5 Marginal Benefit of Component Commonality

Number of Finished Products per Component Safety Inventory Marginal Reduction in Safety Inventory Total Reduction in Safety Inventory
1 399,699 Blank Blank
2 282,630 117,069 117,069
3 230,766 51,864 168,933
4 199,849 30,917 199,850
5 178,751 21,098 220,948
6 163,176 15,575 236,523
7 151,072 12,104 248,627
8 141,315 9,757 258,384
9 133,233 8,082 266,466

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Postponement (1 of 2)

Delay product differentiation or customization until closer to the time the product is sold

Have common components in the supply chain for most of the push phase

Move product differentiation as close to the pull phase of the supply chain as possible

Inventories in the supply chain are mostly aggregate

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Postponement (2 of 2)

Figure 12-6 Supply Chain Flows without and with Postponement

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Value of Postponement

100 different paint colors, D = 30/week, D = 10, L = 2 weeks, CSL = 0.95

Total required safety inventory,

Standard deviation of base paint weekly demand,

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Summary of Learning Objective 5

Aggregation reduces the required safety inventory as long as the demand across the aggregated regions is not perfectly, positively correlated. The safety inventory savings on aggregation increase with the desired C S L, the replenishment lead time, the product holding cost, and the coefficient of variation of demand. The safety inventory savings on aggregation decrease as the correlation of demand across regions increases. Firms can aggregate inventories through physical aggregation, information centralization, product substitution, component commonality, and postponement.

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Impact of Replenishment Policies on Safety Inventory (1 of 4)

Continuous Review Policies

D : Average demand per period

σD : Standard deviation of demand per period

L : Average lead time for replenishment

Mean demand during lead time, DL = D×L

Standard deviation of demand during lead time,

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Impact of Replenishment Policies on Safety Inventory (2 of 4)

Periodic Review Policies

Lot size determined by prespecified order-up-to level (O U L)

D : Average demand per period

σD : Standard deviation of demand per period

L : Average lead time for replenishment

T : Review interval

C S L : Desired cycle service level

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Impact of Replenishment Policies on Safety Inventory (3 of 4)

Probability

Mean demand during T+L periods,

Std dev demand during T+L periods,

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Impact of Replenishment Policies on Safety Inventory (4 of 4)

Figure 12-7 Inventory Profile for Periodic Review Policy with L = 4, T = 7

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Evaluation Safety Inventory for a Periodic Review Policy

D = 2,500, σD= 500, L = 2 weeks, T = 4 weeks

Mean demand during T + L periods,

Std dev demand during T + L periods,

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Summary of Learning Objective 6

Whereas the required safety inventory is proportional to for a continuous review policy, the required safety inventory for a periodic review replenishment policy is proportional to

where T is the reorder interval. As a result, periodic

review replenishment policies require more safety inventory than continuous review policies for the same lead time and level of product availability.

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Managing Safety Inventory in a Multiechelon Supply Chain

In multiechelon supply chains, stages often do not know demand and supply distributions

Inventory between a stage and the final customer is called the echelon inventory

Reorder points and order-up-to levels at any stage should be based on echelon inventory

Decisions must be made about the level of safety inventory carried at different stages

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Summary of Learning Objective 7

In a multiechelon supply chain, it is important to manage safety inventory across stages in a coordinated manner. Increasing safety inventory at upstream stages allows downstream stages to decrease the amount of safety inventory they carry.

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Managerial Levers to Reduce Safety Inventory

Reduction of supply uncertainty

Sharing information

Coordinated demand

Reduction of lead times

Delays contribute more to lead time than production and transportation time

Reduction of demand uncertainty

Reduce information distortion through sharing

Aggregate demand

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Summary of Learning Objective 8

The required level of safety inventory may be reduced and product availability may be improved if a supply chain can reduce demand uncertainty, replenishment lead times, and the variability of lead times. A switch from periodic monitoring to continuous monitoring can also help reduce inventories. Another key managerial lever to reduce the required safety inventories is to exploit aggregation. This may be achieved by physically aggregating inventories, virtually aggregating inventories using information centralization, specializing inventories based on demand volume, exploiting substitution, using component commonality, and postponing product differentiation.

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Copyright

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315

However, given demand fluctuations and forecast errors, actual demand over the three
weeks may be higher or lower than the 300 purses that were forecast. If the actual demand at
Bloomingdale’s is higher than 300, some customers will be unable to purchase purses, resulting
in a potential loss of margin for Bloomingdale’s. The store manager thus decides to place an
order with Gucci when the store still has 400 purses. This policy improves product availability
for the customer because the store now runs out of purses only if the demand over the three
weeks exceeds 400. Given an average weekly demand of 100 purses, the store will have an aver-
age of 100 purses remaining when the replenishment lot arrives. Safety inventory is the average
inventory remaining when the replenishment lot arrives. Thus, Bloomingdale’s carries a safety
inventory of 100 purses.

Given a lot size of Q = 600 purses, the cycle inventory, the focus of the previous chapter,
is Q>2 = 300 purses. The inventory profile at Bloomingdale’s in the presence of safety inven-
tory is shown in Figure 12-1, which illustrates that the average inventory at Bloomingdale’s is the
sum of the cycle and safety inventories.

This example illustrates a trade-off that a supply chain manager must consider when plan-
ning safety inventory. On one hand, raising the level of safety inventory increases product avail-
ability, and thus the margin captured from customer purchases. On the other hand, raising the level
of safety inventory increases inventory holding costs. This issue is particularly significant in
industries in which product life cycles are short and demand is volatile. Carrying excessive inven-
tory can help counter demand volatility but can really hurt if new products come onto the market
and demand for the product in inventory dries up. The inventory on hand then becomes worthless.

In today’s business environment, it has become easier for customers to search across stores
for product availability. If Amazon is out of a book, for example, a customer can easily check to
see whether barnesandnoble.com has the title available. The increased ease of searching puts
pressure on firms to improve product availability. Simultaneously, product variety has grown
with increased customization. As a result, markets have become increasingly heterogeneous and
demand for individual products is unstable and difficult to forecast. Both the increased variety
and the greater pressure for availability push firms to raise the level of safety inventory they hold.
Given the product variety and high demand uncertainty in most high-tech supply chains, a sig-
nificant fraction of the inventory carried is safety inventory.

As product variety has grown, however, product life cycles have shrunk. Thus, it is more
likely that a product that is “hot” today will be obsolete tomorrow, which increases the cost to
firms of carrying too much inventory. Thus, a key to the success of any supply chain is to figure
out ways to decrease the level of safety inventory carried without hurting the level of product
availability.

The importance of reduced safety inventories is emphasized by the experience of Nord-

Average
Inventory

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