Inventory Control: Part 3 –
Independent Demand Inventories
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Types of Inventories

By Function
- Lot-Size (Cycle or Replenishment)
- Instantaneous (Purchase)
- Non-Instantaneous (Produce)
- Safety (Fluctuation or Buffer)
- Anticipation (Seasonal)
- Transportation (Pipeline)
- Hedge (Beyond Scope of Class)
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Safety Stocks





Used for Emergencies
Finished Goods: Unexpected Demand (Level
Related to Customer Service)
Raw Materials: Orders Not Received
Work-in-Process (WIP): Worker Unavailable or
Machine Breakdown - Decoupling Inventory
Also Known as Buffer or Fluctuation Inventory
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Quantity
Finished Goods Safety Stocks:
Stored with Lot-Size Stocks
Maximum probable demand
during lead time
Expected demand
during lead time (DDLT)
OP
Safety stock (SS)
LT
Time
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Safety Stocks

From Graph:
OP = DDLT + SS where
OP = Order Point
DD = Forecast Demand
LT = Lead Time
SS = Safety Stock

So: SS = OP – DDLT by Algebra

OP Set from Customer Service Level (SL)
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Safety Stocks Example 1
The Frigid Corporation manufactures refrigerators. The
probability distribution of demand during lead time is:
Demand
Probability
10
.20
20
.20
30
.30
40
.20
50
.10
Suppose the customer service level is 70%. Determine
the reorder point (consider only 10, 20, 30, 40, 50).
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Safety Stocks Example 1


Let SL = .7 (70%)
Demand
Probability
10
.2
20
.2
30
.3
40
.2
50
.1
CDF
.2
.4
.7 
.9
1.0
OP = 30 (Meets Demand 70% of Time)
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Safety Stocks Example1

SS = OP – DDLT
DDLT= Expected Value of Demand
DDLT= .2(10)+.2(20)+.3(30)+.2(40)+.1(50)
DDLT= 28
SS = 30 – 28 = 2


If SL is 80%, What is OP and SS?
If SL is 90%, What is OP and SS?
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Safety Stocks:
Normal Demand
Risk of
a Stock Out
Probability of
No Stock Out
(Service Level)
Quantity
Safety
Stock
Mean
OP
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Safety Stocks Example 2
The Inandout Production Company
requires steel rods at the mean rate of 35
rods per day. This rate follows a normal
distribution with a standard deviation of 3
per day. The service level has been set at
90%. If lead time for reordering is one
day, what is the optimum safety stock?
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Safety Stocks:
Example 2

Given: SL = .9 (90%), DDLT = 35, DDLT = 3
Z from Normal Table (text page 314) = 1.28
( Z is also known as safety factor)
Z = (OP – DDLT) / DDLT or
OP = DDLT + Z DDLT = 35 + (1.28)(3)  39
SS = OP – DDLT = 39 – 35 = 4
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Types of Inventories
Type
1. Lot-Size
a. Instantaneous
b. Non-Instantaneous
2. Safety
3. Anticipation
4. Transportation
5. Hedge
Best Size
Q*/2
IMAX*/2
OP - DDLT
Guesstimate
(Usage) (Time)
Guesstimate
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Implementation of
Inventory Control

Q* and N* Cannot Both be Fixed
(E.g. Q* = 10, A= 100, N* = A/Q* = 100/10 = 10)

N Varies and Q* Fixed: Order Point System
(AKA Fixed Order Quantity). Requires Two-Bin
System, Kanban, or Perpetual Inventory. Order
say Q* when Actual Inventory ≤ OP.

Q Varies and N* Fixed: Periodic Review System
(AKA Fixed Order Cycle System)
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Periodic Review System



Let T = D (R + LT) + SS Where
T = Target Inventory Level
D = Demand per Unit of Time
LT = Lead Time
R = Review Period (Fixed at 1/N*)
SS = Safety Stock
Order Q = T – I Where
I = Inventory on Hand.
See Example on Page 321 of Text.
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