Heizer om10 ch12-inventory

10/16/2010

Inventory
12 Management Global Company Profile:
Outline

Amazon.com
The Importance of Inventory
PowerPoint presentation to accompany Functions of Inventory
Heizer and Render
Operations Management, 10e Types of Inventory
Principles of Operations Management, 8e

PowerPoint slides by Jeff Heyl

© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 1 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 2

Outline – Continued Outline – Continued
Managing Inventory Inventory Models for Independent
ABC Analysis Demand
Record Accuracy The Basic Economic Order Quantity
Cycle Counting (EOQ) Model
Control of Service Inventories Minimizing Costs

Inventory Models Reorder Points
Production Order Quantity Model
Independent vs. Dependent Demand
Quantity Discount Models
Holding, Ordering, and Setup Costs


Outline – Continued Learning Objectives
When you complete this chapter you
Probabilistic Models and Safety should be able to:
Stock
Other Probabilistic Models 1. Conduct an ABC analysis
Single-Period Model 2. Explain and use cycle counting
3. Explain and use the EOQ model for
Fixed-Period (P) Systems independent inventory demand
4. Compute a reorder point and safety
stock


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10/16/2010

Learning Objectives Amazon.com
When you complete this chapter you
should be able to: Amazon.com started as a “virtual”
retailer – no inventory, no
5. Apply the production order quantity
warehouses, no overhead; just
model computers taking orders to be filled
by others
6. Explain and use the quantity
discount model Growth has forced Amazon.com to
7. Understand service levels and become a world leader in
probabilistic inventory models warehousing and inventory
management


Amazon.com Amazon.com
1. Each order is assigned by computer to
the closest distribution center that has 5. Crates arrive at central point where items
the product(s) are boxed and labeled with new bar code
2. A “flow meister” at each distribution 6. Gift wrapping is done by hand at 30
center assigns work crews packages per hour
3. Lights indicate products that are to be 7. Completed boxes are packed, taped,
picked and the light is reset weighed and labeled before leaving
4. Items are placed in crates on a conveyor, warehouse in a truck
bar code scanners scan each item 15 8. Order arrives at customer within 2 - 3
times to virtually eliminate errors days


Inventory Management Importance of Inventory

One of the most expensive assets
The objective of inventory of many companies representing as
management is to strike a balance much as 50% of total invested
between inventory investment and capital
it l
customer service
Operations managers must balance
inventory investment and customer
service


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10/16/2010

Functions of Inventory Types of Inventory
Raw material
1. To decouple or separate various
parts of the production process Purchased but not processed
Work-in-process
2. To decouple the firm from
Undergone some change but not completed
fluctuations in demand and
provide a stock of goods that will A function of cycle time for a product
provide a selection for customers Maintenance/repair/operating (MRO)
Necessary to keep machinery and
3. To take advantage of quantity processes productive
discounts
Finished goods
4. To hedge against inflation Completed product awaiting shipment

The Material Flow Cycle Managing Inventory

Cycle time 1. How inventory items can be
95% 5% classified

Input Wait for Wait to Move Wait in queue Setup Run Output
2.
2 How accurate inventory records
inspection be moved time for operator time time can be maintained

Figure 12.1


ABC Analysis ABC Analysis
Divides inventory into three classes
based on annual dollar volume Item
Percent of
Number of Annual Annual
Percent of
Annual
Stock Items Volume Unit Dollar Dollar
Class A - high annual dollar volume Number Stocked (units) x Cost = Volume Volume Class

#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A
Class B - medium annual dollar #11526 500 154.00 77,000 33.2%
72%
A
volume #12760 1,550 17.00 26,350 11.3% B

Class C - low annual dollar volume #10867 30% 350 42.86 15,001 6.4% 23% B

Used to establish policies that focus #10500 1,000 12.50 12,500 5.4% B

on the few critical parts and not the
many trivial ones

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10/16/2010


Percent of annua dollar usage
Percent of Percent of A Items
Item Number of Annual Annual Annual 80 –
Stock Items Volume Unit Dollar Dollar
Number Stocked (units) x Cost = Volume Volume Class
70 –
#12572 600 $ 14.17 $ 8,502 3.7% C 60 –
50 –

al
#14075 2,000 .60 1,200 .5% C
40 –
#01036 50% 100 8.50 850 .4% 5% C
30 –
#01307 1,200 .42 504 .2% C 20 – B Items
#10572 250 .60 150 .1% C 10 – C Items
8,550 $232,057 100.0% 0 – | | | | | | | | | |

10 20 30 40 50 60 70 80 90 100

Percent of inventory items
Figure 12.2


Other criteria than annual dollar Policies employed may include
volume may be used More emphasis on supplier
Anticipated engineering changes development for A items
Delivery problems Tighter physical inventory control for
A items
Quality problems
More care in forecasting A items
High unit cost


Record Accuracy Cycle Counting
Accurate records are a critical Items are counted and records updated
ingredient in production and inventory on a periodic basis
systems Often used with ABC analysis
Allows organization to focus on what to determine cycle
is needed Has several advantages
Necessary to make precise decisions 1. Eliminates shutdowns and interruptions
about ordering, scheduling, and 2. Eliminates annual inventory adjustment
shipping
3. Trained personnel audit inventory accuracy
Incoming and outgoing record 4. Allows causes of errors to be identified and
keeping must be accurate corrected
Stockrooms should be secure 5. Maintains accurate inventory records

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10/16/2010

Cycle Counting Example Control of Service
Inventories
5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C
items Can be a critical component
Policy is to count A items every month (20 working days), B of profitability
items every quarter (60 days), and C items every six months
(120 days) Losses may come from
shrinkage or pilferage
Item Number of Items
Class Quantity Cycle Counting Policy Counted per Day Applicable techniques include
A 500 Each month 500/20 = 25/day 1. Good personnel selection, training, and
B 1,750 Each quarter 1,750/60 = 29/day discipline
C 2,750 Every 6 months 2,750/120 = 23/day 2. Tight control on incoming shipments
77/day 3. Effective control on all goods leaving
facility

Independent Versus Holding, Ordering, and
Dependent Demand Setup Costs
Independent demand - the Holding costs - the costs of holding
demand for item is independent or “carrying” inventory over time
o t e de a d o a y other
of the demand for any ot e Ordering costs - the costs of
item in inventory placing an order and receiving
Dependent demand - the goods
demand for item is dependent Setup costs - cost to prepare a
upon the demand for some machine or process for
other item in the inventory manufacturing an order

Holding Costs Holding Costs
Cost (and range) Cost (and range)
as a Percent of as a Percent of
Category Inventory Value Category Inventory Value
Housing costs (building rent or 6% (3 - 10%) Housing costs (building rent or 6% (3 - 10%)
depreciation, operating costs, taxes, depreciation, operating costs, taxes,
insurance) insurance)
Material handling costs (equipment lease or 3% (1 - 3.5%) Material handling costs (equipment lease or 3% (1 - 3.5%)
depreciation, power, operating cost) depreciation, power, operating cost)
Labor cost 3% (3 - 5%) Labor cost 3% (3 - 5%)
Investment costs (borrowing costs, taxes, 11% (6 - 24%) Investment costs (borrowing costs, taxes, 11% (6 - 24%)
and insurance on inventory) and insurance on inventory)
Pilferage, space, and obsolescence 3% (2 - 5%) Pilferage, space, and obsolescence 3% (2 - 5%)
Overall carrying cost 26% Overall carrying cost 26%

Table 12.1 Table 12.1

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10/16/2010

Inventory Models for Basic EOQ Model
Independent Demand Important assumptions
1. Demand is known, constant, and
Need to determine when and how independent
much to order
2. Lead time is known and constant
3. Receipt of inventory is instantaneous and
1. Basic economic order quantity complete
2. Production order quantity 4. Quantity discounts are not possible
3. Quantity discount model 5. Only variable costs are setup and holding
6. Stockouts can be completely avoided

Inventory Usage Over Time Minimizing Costs
Objective is to minimize total costs

Usage rate Average Total cost of
Order inventory holding and
quantity = Q setup (order)
Inventor level

on hand
(maximum
inventory Q Minimum
ry

level) 2 total
t t l cost
t
Annual cost

Holding cost
Minimum
inventory

Setup (or order)
0 cost
Time
Optimal order Order quantity
quantity (Q*)
Figure 12.3 Table 12.4(c)

The EOQ Model setup cost = Q S
Annual
D The EOQ Model setup cost = Q S
Annual
D

Q
Q = Number of pieces per order Q = Number of pieces per order Annual holding cost = H
2
Q* = Optimal number of pieces per order (EOQ) Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year H = Holding or carrying cost per unit per year

Annual setup cost = (Number of orders placed per year) Annual holding cost = (Average inventory level)
x (Setup or order cost per order) x (Holding cost per unit per year)

Annual demand Setup or order Order quantity
= = (Holding cost per unit per year)
Number of units in each order cost per order 2

D (S) Q (H)
= =
Q 2


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10/16/2010

The EOQ Model setup cost = Q S
Annual
D An EOQ Example
Q
Q = Number of pieces per order Annual holding cost = H
2
Q* = Optimal number of pieces per order (EOQ) Determine optimal number of needles to order
D = Annual demand in units for the inventory item D = 1,000 units
S = Setup or ordering cost for each order S = $10 per order
H = Holding or carrying cost per unit per year H = $.50 per unit per year
Optimal d
O ti l order quantity is found when annual setup cost
tit i f d h l t t
equals annual holding cost 2DS
Q* =
D
S =
Q
H
H
Q 2
Solving for Q* 2(1,000)(10)
2DS = Q2H Q* = = 40,000 = 200 units
Q2 = 2DS/H 0.50
Q* = 2DS/H

An EOQ Example An EOQ Example
Determine optimal number of needles to order Determine optimal number of needles to order
D = 1,000 units Q* = 200 units D = 1,000 units Q* = 200 units
S = $10 per order S = $10 per order N = 5 orders per year
H = $.50 per unit per year H = $.50 per unit per year

Expected Number of working
Demand D Expected days per year
number of = N = = time between = T =
orders Order quantity Q*
orders N
1,000 250
N= = 5 orders per year
200 T= = 50 days between orders
5


An EOQ Example Robust Model
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year The EOQ model is robust
H = $.50 per unit per year T = 50 days
It works even if all parameters
Total annual cost = Setup cost + Holding cost and assumptions are not met
TC =
D
S +
Q
H The total cost curve is relatively
Q 2
flat in the area of the EOQ
1,000 200
TC = ($10) + ($.50)
200 2

TC = (5)($10) + (100)($.50) = $50 + $50 = $100


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10/16/2010

An EOQ Example An EOQ Example
Management underestimated demand by 50% Actual EOQ for new demand is 244.9 units
D = 1,000 units 1,500 units Q* = 200 units D = 1,000 units 1,500 units Q* = 244.9 units
S = $10 per order N = 5 orders per year S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days H = $.50 per unit per year T = 50 days

D Q D Q
TC = S + H TC = S + H
Q 2 Q 2 Only 2% less
1,500 200 1,500 244.9 than the total
TC = ($10) + ($.50) = $75 + $50 = $125 TC = ($10) + ($.50) cost of $125
200 2 244.9 2
when the
TC = $61.24 + $61.24 = $122.48 order quantity
Total annual cost increases by only 25% was 200

Reorder Points Reorder Point Curve
EOQ answers the “how much” question Q*
Inventory level (units) Resupply takes place as order arrives
The reorder point (ROP) tells “when” to
order Slope = units/day = d

Demand Lead time for a
ROP = per day new order in days ROP
(units)
=dxL
D
d = Number of working days in a year
Time (days)
Lead time = L
Figure 12.5

Reorder Point Example Production Order Quantity
Model
Demand = 8,000 iPods per year
250 working day year Used when inventory builds up
Lead time for orders is 3 working days
over a period of time after an
d=
D order is placed
Number of working days in a year
Used when units are produced
= 8,000/250 = 32 units and sold simultaneously
ROP = d x L
= 32 units per day x 3 days = 96 units


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10/16/2010

Production Order Quantity Production Order Quantity
Model Model
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
Part of inventory cycle during
which production (and usage) t = Length of the production run in days
is taking place
Inventory level

Annual inventory Holding cost
holding cost = (Average inventory level) x per unit per year
l

Demand part of cycle
with no production
Maximum
inventory Annual inventory
= (Maximum inventory level)/2
level

Maximum Total produced during Total used during
= –
t inventory level the production run the production run
Time
= pt – dt
Figure 12.6


Model Model
Q = Number of pieces per order p = Daily production rate Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days D = Annual demand

Maximum
=
Total produced during
–
Total used during Setup cost = (D/Q)S
inventory level
i t l l the
th production run
d ti the
th production run
d ti
Holding cost = 1 HQ[1 - (d/p)]
= pt – dt 2
However, Q = total produced = pt ; thus t = Q/p 1
(D/Q)S = 2 HQ[1 - (d/p)]
Maximum Q Q d 2DS
inventory level = p p –d
p
=Q 1–
p Q2 =
H[1 - (d/p)]
Maximum inventory level Q d 2DS
Holding cost = (H) = 1– H
2 2 p Q* =
p H[1 - (d/p)]

Example Model
D = 1,000 units p = 8 units per day Note:
S = $10 d = 4 units per day
D 1,000
H = $0.50 per unit per year d = 4 = Number of days the plant is in operation = 250

2DS
Q* =
H[1 - (d/p)] When annual data are used the equation becomes

2(1,000)(10) 2DS
Q* = = 80,000 Q* =
0.50[1 - (4/8)] annual demand rate
H 1–
annual production rate
= 282.8 or 283 hubcaps

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10/16/2010

Quantity Discount Models Quantity Discount Models
Reduced prices are often available when A typical quantity discount schedule
larger quantities are purchased
Trade-off is between reduced product cost Discount Discount
and increased holding cost Number Discount Quantity Discount (%) Price (P)
1 0 to 999 no discount $5.00
Total cost = Setup cost + Holding cost + Product cost 2 1,000 to 1,999 4 $4.80

3 2,000 and over 5 $4.75
D Q
TC = S+ H + PD
Q 2 Table 12.2


Quantity Discount Models Quantity Discount Models
Steps in analyzing a quantity discount Total cost curve for discount 2
Total cost
curve for
1. For each discount, calculate Q* discount 1

2. If Q* for a discount doesn’t qualify,
y
Total cost $
t

choose the smallest possible order size
to get the discount Total cost curve for discount 3
b
3. Compute the total cost for each Q* or a Q* for discount 2 is below the allowable range at point a
and must be adjusted upward to 1,000 units at point b
adjusted value from Step 2
1st price 2nd price
4. Select the Q* that gives the lowest total break break
cost 0 1,000 2,000
Figure 12.7
Order quantity

Quantity Discount Example Quantity Discount Example
Calculate Q* for every discount 2DS Calculate Q* for every discount 2DS
Q* = Q* =
IP IP
2(5,000)(49) 2(5,000)(49)
Q1* = = 700 cars/order Q1* = = 700 cars/order
(.2)(5.00)
( 2)(5 00) (.2)(5.00)
( 2)(5 00)

2(5,000)(49) 2(5,000)(49)
(.2)(4.80) (.2)(4.80) 1,000 — adjusted
2(5,000)(49) 2(5,000)(49)
(.2)(4.75) (.2)(4.75) 2,000 — adjusted

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10/16/2010

Quantity Discount Example Probabilistic Models and
Safety Stock
Discount Unit Order
Annual
Product
Annual
Ordering
Annual
Holding
Used when demand is not constant
Number Price Quantity Cost Cost Cost Total or certain
1 $5.00 700 $25,000 $350 $350 $25,700 Use safety stock to achieve a desired
2 $4.80 1,000 $24,000 $245 $480 $24,725 service level and avoid stockouts
3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50
ROP = d x L + ss
Table 12.3
Choose the price and quantity that gives
Annual stockout costs = the sum of the units short
the lowest total cost
x the probability x the stockout cost/unit
Buy 1,000 units at $4.80 per unit x the number of orders per year


Safety Stock Example Safety Stock Example
ROP = 50 units Stockout cost = $40 per frame ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year Orders per year = 6 Carrying cost = $5 per frame per year

Safety Additional Total
Number of Units Probability Stock Holding Cost Stockout Cost Cost

30 .2 20 (20)($5) = $100 $0 $100

40 .2 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290

ROP 50 .3 0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960
60 .2
70 .1 A safety stock of 20 frames gives the lowest total cost
1.0 ROP = 50 + 20 = 70 frames

Probabilistic Demand Probabilistic Demand
Use prescribed service levels to set safety
stock when the cost of stockouts cannot be
Minimum demand during lead time
determined
Inventory level

Maximum demand during lead time
y

Mean demand during lead time
ROP = 350 + safety stock of 16.5 = 366.5
ROP = demand during lead time + ZσdLT
ROP
Normal distribution probability of
demand during lead time
Expected demand during lead time (350 kits)
where Z = number of standard deviations
Safety stock 16.5 units σdLT = standard deviation of demand
0 Lead
during lead time
time Time
Figure 12.8 Place Receive
order order

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10/16/2010

Probabilistic Demand Probabilistic Example
Average demand = μ = 350 kits
Standard deviation of demand during lead time = σdLT = 10 kits
5% stockout policy (service level = 95%)
Probability of Risk of a stockout
no stockout (5% of area of
95% of the time normal curve)) Using Appendix I, for an area under the curve
of 95%, the Z = 1.65

Safety stock = ZσdLT = 1.65(10) = 16.5 kits
Mean ROP = ? kits Quantity
demand Reorder point = expected demand during lead time
350
Safety + safety stock
stock
= 350 kits + 16.5 kits of safety stock
0 z
Number of = 366.5 or 367 kits
standard deviations

Other Probabilistic Models Other Probabilistic Models
When data on demand during lead time is Demand is variable and lead time is constant
not available, there are other models
available
ROP = (average daily demand
1.
1 When demand is variable and lead x lead time in days) + ZσdLT
time is constant
where σd = standard deviation of demand per day
2. When lead time is variable and
σdLT = σd lead time
demand is constant
3. When both demand and lead time
are variable


Probabilistic Example Other Probabilistic Models
Average daily demand (normally distributed) = 15 Lead time is variable and demand is constant
Standard deviation = 5
Lead time is constant at 2 days Z for 90% = 1.28
90% service level desired From Appendix I ROP = (daily demand x average lead
time in days)
ROP = (15 units x 2 days) + ZσdLT = Z x (daily demand) x σLT

= 30 + 1.28(5)( 2) where σLT = standard deviation of lead time in days
= 30 + 9.02 = 39.02 ≈ 39

Safety stock is about 9 iPods


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10/16/2010

Probabilistic Example Other Probabilistic Models
Z for 98% = 2.055 Both demand and lead time are variable
Daily demand (constant) = 10 From Appendix I
Average lead time = 6 days
Standard deviation of lead time = σLT = 3
ROP = (average daily demand
98% service level desired
x average lead time) + ZσdLT
ROP = (10 units x 6 days) + 2.055(10 units)(3)
where σd = standard deviation of demand per day
= 60 + 61.65 = 121.65 σLT = standard deviation of lead time in days
σdLT = (average lead time x σd2)
Reorder point is about 122 cameras + (average daily demand)2 x σLT2


Probabilistic Example Single Period Model
Average daily demand (normally distributed) = 150 Only one order is placed for a product
Standard deviation = σd = 16
Average lead time 5 days (normally distributed) Units have little or no value at the end of
Standard deviation = σLT = 1 day the sales period
95% service level desired Z for 95% = 1.65
1 65
From Appendix I Cs = Cost of shortage = Sales price/unit – Cost/unit
Co = Cost of overage = Cost/unit – Salvage value
ROP = (150 packs x 5 days) + 1.65σdLT
= (150 x 5) + 1.65 (5 days x + 162) (1502 x 1 2) Cs
= 750 + 1.65(154) = 1,004 packs Service level =
Cs + Co


Single Period Example Single Period Example
Average demand = μ = 120 papers/day
Standard deviation = σ = 15 papers From Appendix I, for the area .578, Z ≅ .20
Cs = cost of shortage = $1.25 - $.70 = $.55
The optimal stocking level
Co = cost of overage = $.70 - $.30 = $.40
= 120 copies + (.20)(σ)
Cs
Service level = = 120 + (.20)(15) = 120 + 3 = 123 papers
Cs + Co
Service
.55 level
= 57.8% The stockout risk = 1 – service level
.55 + .40
.55 = 1 – .578 = .422 = 42.2%
= = .578 μ = 120
.95
Optimal stocking level


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10/16/2010

Fixed-
Fixed-Period (P) Systems Fixed-
Fixed-Period (P) Systems
Target quantity (T)
Orders placed at the end of a fixed period
Inventory counted only at end of period Q2
Q4

On-hand inventory
Order brings inventory up to target level
g y p g
Q1 P
Q3
Only relevant costs are ordering and holding
P
Lead times are known and constant
Items are independent from one another
P

Time Figure 12.9

Fixed-
Fixed-Period (P) Example Fixed-
Fixed-Period Systems
3 jackets are back ordered No jackets are in stock
It is time to place an order Target value = 50 Inventory is only counted at each
review period

Order amount (Q) = Target (T) - On
On- May be scheduled at convenient times
y
hand inventory - Earlier orders not yet Appropriate in routine situations
received + Back orders May result in stockouts between
Q = 50 - 0 - 0 + 3 = 53 jackets periods
May require increased safety stock


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Printed in the United States of America.

© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 83

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