# Chapter 6 Inventory Control Models Part 2 (Pascual)

```Jeniel Z. Pascual
Chapter 6: Inventory Control Models (Part 2)
1
Time between placing an order and its receipt is called lead time (L)
Reorder Point Graphs
400
3 days
400
12 days
• When the EOQ assumptions
are met, it is possible to
schedule orders to arrive so
that stockouts are completely
avoided!
• If the demand or the lead
time is uncertain, the exact
(ROP in the EOQ situation)
will not be known with
certainty!
• Therefore,
to
prevent
stockouts, it is necessary to
called safety stock.
2
Use of Safety Stock (1 of 4)
• If demand or the lead time are uncertain, the exact
ROP will not be known with certainty!
• To prevent stockouts, it is necessary to carry additional
inventory called safety stock.
• Can be implemented by adjusting the Reorder Point
(ROP)
ROP = (Average demand during lead time) + Safety stock
ROP = (Average demand during lead time) + SS
where
SS = safety stock
3
Use of Safety Stock (2 of 4)
• When
demand
is
unusually high during
the lead time, you dip into
encountering a stockout!
• The main
safety stock
stockouts
demand is
expected.
purpose of
is to avoid
when
the
higher than
4
Use of Safety Stock (3 of 4)
• Objective is to choose a safety stock amount the
minimises total holding and stockout costs
• If variation in demand and holding and stockout costs
are known, payoff/cost tables could be used to
determine safety stock
• More general approach is to choose a desired service
level based on satisfying customer demand
5
Use of Safety Stock (4 of 4)
• Set safety stock to achieve a desired service level
Service level = 1 − Probability of a stockout
or
Probability of a stockout = 1 − Service level
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Safety Stock with the Normal Distribution
ROP = (Average demand during lead time) + ZσdLT
where
Z = number of standard deviations for a given service level
σdLT = standard deviation of demand during the lead time
Thus
Safety stock = ZσdLT
7
Sample Problem
The Hinsdale Company carries a variety of electronic
inventory items, and these are typically identified by
SKU. One particular item, SKU A3378, has a demand
that is normally distributed during the lead time, with
a mean of 350 units and a standard deviation of 10.
Hinsdale wants to follow a policy that results in
stockouts occurring only 5% of the time on any order.
How much safety stock should be maintained and
what is the reorder point?
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Hinsdale Company --- Safety Stock and the
Normal Distribution
• Item A3378 has normally distributed demand during
Mean = 350 units, standard deviation = 10
• Stockouts should occur only 5% of the time
μ = Mean demand = 350
σdLT = Standard deviation = 10
X= Mean demand + Safety stock
SS= Safety stock = X − μ = Zσ
Z
X 

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Finding Z:
10
Hinsdale Company
From Appendix A we find Z = 1.65 
X


SS

ROP = (Average demand during lead time) + ZdLT
= 350 + 1.65(10)
= 350 + 16.5 = 366.5 units (or about 367 units)
11
Service Levels, Safety Stock, and Holding
Costs
• As service levels increase
o Safety stock increases at an increasing
rate
• As safety stock increases
o Annual holding costs increase
12
Hinsdale Company
Safety Stock for SKU A3378 at Different Service Levels:
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Calculating Annual Holding Cost with Safety
Stock
Under standard assumptions of EOQ
o Average inventory = Q&divide;2
o Annual holding cost = (Q&divide;2)Ch
With safety stock
where
THC
= total annual holding cost
Q
Ch
= order quantity
= holding cost per unit per year
SS
= safety stock
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Hinsdale Company
Service Level Versus Annual Holding Costs:
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Single-Period Inventory Models
(News Vendor Problem)
Marginal Analysis
 Marginal profit (MP) is the additional profit
achieved if one additional unit is stocked and
sold.
 Marginal loss (ML) is the loss that occurs when
an additional unit is stocked but cannot be sold.
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Single-Period Inventory Models
(News Vendor Problem)
Marginal Analysis with Discrete Distribution
P = probability that demand will be greater than
or equal to a given supply (or the probability of
selling at least one additional unit)
1 - P = probability that demand will be less than
supply (or the probability that one additional
unit will not sell)
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Steps of Marginal Analysis with
Discrete Distributions
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Sample Problem
Caf&eacute; du Donut is a popular New Orleans dining spot
on the edge of the French Quarter. Its specialty is
coffee and doughnuts; it buys the doughnuts fresh
daily from a large industrial bakery. The caf&eacute; pays \$4
for each carton (containing two dozen doughnuts)
delivered each morning. Any cartons not sold at the
end of the day are thrown away, for they would not
be fresh enough to meet the caf&eacute;’s standards. If a
carton of doughnuts is sold, the total revenue is \$6.
Hence,
MP = Marginal profit = \$6 - \$4 = \$2
ML = Marginal loss = \$4
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Caf&eacute; du Donut Example
Probability Distribution for Caf&eacute; du Donut
20
Caf&eacute; du Donut Example
21
Caf&eacute; du Donut Example
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A prudent manager should spend more time managing those items representing
the greatest dollar inventory cost because this is where the greatest potential
savings are.
ABC Analysis (1 of 5)
• The purpose is to divide the inventory into three
groups (A, B, and C) based on the overall inventory
value of the items
• Group A items account for the major portion of
inventory costs (high price!)
o Typically 70% of the dollar value but only 10% of the
quantity of items
o Great care should be taken in forecasting the demand
and developing good inventory management policies for
this group!
o Mistakes can be expensive!
23
ABC Analysis (2 of 5)
• Group B items are more moderately priced
o Items represent about 20% of the company’s
inventory
o Not appropriate to spend as much time developing
optimal inventory policies for this group as with the A
group since inventory costs are much lower!
o Moderate levels of control!
24
ABC Analysis (3 of 5)
• Group C items are very low cost but high volume
o These items may constitute only 10% of the company’s
business in dollars, but they may consist of 70% of the
items in inventory.
o It is not cost effective to spend a lot of time managing
these items!
o For the group C items, the company should develop a
very simple inventory policy, and this may include a
relatively large safety stock.
o Since the items cost very little, the holding cost
associated with a large safety stock will also be very
low.
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ABC Analysis (4 of 5)
• More care should be taken in determining the safety
stock with the higher priced group B items.
• For the very expensive group A items, the cost of
carrying the inventory is so high, it is beneficial to
carefully analyse the demand for these so that safety
stock is at an appropriate level!
• Otherwise, the company may have exceedingly high
holding costs for the group A items.
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ABC Analysis (5 of 5)
Summary of ABC Analysis:
27
Material Requirements Planning
Dependent Demand
Material Structure Tree
The Bill of Materials (BOM) identifies the
components, their descriptions, and the number
required in the production of one unit of the final
product. From the BOM, we develop a material
structure tree.
28
Material Requirements Planning
29
Material Requirements Planning
Gross Materials Requirements Plan
30
MRP
Net Materials
Requirements
Plan
31
Material Requirements Planning
Two or More End Products
32
MRP
Two or More
End Products
33
Just-In-Time Inventory Control
With this approach, inventory arrives just in
time to be used during the manufacturing
process to produce subparts, assemblies, or
finished goods.
34
Enterprise Resource Planning
A computerized information system
that integrates and coordinates the
operations of a firm.
The benefits of a well-developed ERP
system are reduced transaction costs and
increased speed and accuracy of
information.
However,
there
are
drawbacks as well. The software is
expensive to buy and costly to customize.
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Thank You!
36
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