Inventory Management Assignment PDF

12 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall
12 Inventory
Management
PowerPoint presentation to accompany
Heizer and Render
Operations Management, 8e

12 - 2© 2011 Pearson Education, Inc. publishing as Prentice Hall
Outline
 The Importance of Inventory
 Functions of Inventory
 Types of Inventory
 Managing Inventory
 ABC Analysis
 Record Accuracy
 Cycle Counting
 Control of Service Inventories
 Inventory Models
 Independent vs. Dependent Demand
 Holding, Ordering, and Setup Costs

12 - 3© 2011 Pearson Education, Inc. publishing as Prentice Hall
Outline – Continued
 Inventory Models for Independent Demand
 The Basic Economic Order Quantity (EOQ) Model
 Minimizing Costs
 Reorder Points
 Production Order Quantity Model
 Quantity Discount Models
 Probabilistic Models and Safety Stock
 Other Probabilistic Models
 Single-Period Model
 Fixed-Period (P) Systems

12 - 4© 2011 Pearson Education, Inc. publishing as Prentice Hall
Learning Objectives
When you complete this chapter you should be able
to:
1. Conduct an ABC analysis
2. Explain and use cycle counting
3. Explain and use the EOQ model for independent
inventory demand
4. Compute a reorder point and safety stock
5. Apply the production order quantity model
6. Explain and use the quantity discount model
7. Understand service levels and probabilistic
inventory models

12 - 5© 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory Management
The objective of inventory management is to
strike a balance between inventory
investment and customer service

12 - 6© 2011 Pearson Education, Inc. publishing as Prentice Hall
Importance of Inventory
 One of the most expensive assets of many
companies representing as much as 50% of
total invested capital
 Operations managers must balance inventory
investment and customer service

12 - 7© 2011 Pearson Education, Inc. publishing as Prentice Hall
Functions of Inventory
1. To decouple or separate various parts of the
production process
2. To decouple the firm from fluctuations in
demand and provide a stock of goods that will
provide a selection for customers
3. To take advantage of quantity discounts
4. To hedge against inflation

12 - 8© 2011 Pearson Education, Inc. publishing as Prentice Hall
Types of Inventory
 Raw material
 Purchased but not processed
 Work-in-process
 Undergone some change but not completed
 A function of cycle time for a product
 Maintenance/repair/operating (MRO)
 Necessary to keep machinery and processes
productive
 Finished goods
 Completed product awaiting shipment

12 - 9© 2011 Pearson Education, Inc. publishing as Prentice Hall
The Material Flow Cycle
Figure 12.1
Input Wait for Wait to Move Wait in queue Setup Run Output
inspection be moved time for operator time time
Cycle time
95% 5%

12 - 10© 2011 Pearson Education, Inc. publishing as Prentice Hall
Managing Inventory
1. How inventory items can be classified
2. How accurate inventory records can be
maintained

12 - 11© 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC Analysis
 Divides inventory into three classes based on
annual dollar volume
 Class A - high annual dollar volume
 Class B - medium annual dollar volume
 Class C - low annual dollar volume
 Idea to establish inventory policies that focus
resources on the few critical inventory parts and
not the many trivial ones

12 - 12© 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC Analysis
Item
Stock
Number
Percent
of
Number
of Items
Stocked
Annual
Volume
(units) x
Unit
Cost =
Annual
Dollar
Volume
Percent
of
Annual
Dollar
Volume Class
#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A
#11526 500 154.00 77,000 33.2% A
#12760 1,550 17.00 26,350 11.3% B
#10867 30% 350 42.86 15,001 6.4% B
#10500 1,000 12.50 12,500 5.4% B
72%
23%
#12572 600 $ 14.17 $ 8,502 3.7% C
#14075 2,000 .60 1,200 .5% C
#01036 50% 100 8.50 850 .4% C
#01307 1,200 .42 504 .2% C
#10572 250 .60 150 .1% C
8,550 $232,057 100.0%
5%

12 - 13© 2011 Pearson Education, Inc. publishing as Prentice Hall
C Items
ABC Analysis
A Items
B Items
Percent of annual dollar usage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 – | | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percent of inventory items
Figure 12.2
The breakdown into A, B, and C
categories is not hard and fast. The
objective is to separate the
“important” from the
“unimportant”

12 - 14© 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC Analysis
 Other criteria than annual dollar volume
may be used
 Anticipated engineering changes
 Delivery problems
 Quality problems
 High unit cost

12 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC Analysis
 Policies employed may include
 More emphasis on supplier development for
Class A items
 Tighter physical inventory control for Class
A items
 More care in forecasting Class A items
ABC analysis guides the development of appropriate inventory
management policies for better forecasting, tighter control,
supplier reliability, and an ultimate reduction in safety stock

12 - 16© 2011 Pearson Education, Inc. publishing as Prentice Hall
Record Accuracy
 Accurate records are a critical ingredient in
production and inventory systems
 Allows organization to focus on what is
needed
 Necessary to make precise decisions about
ordering, scheduling, and shipping
 Incoming and outgoing record keeping must
be accurate
 Stockrooms should be secure

12 - 17© 2011 Pearson Education, Inc. publishing as Prentice Hall
Cycle Counting
 A continuing reconciliation of inventory with
inventory records
 A continuing audit to make sure that the
recorded inventory is accurate
 With cycle counting procedures, items are
counted, records are verified, and inaccuracies
are periodically documented

12 - 18© 2011 Pearson Education, Inc. publishing as Prentice Hall
Cycle Counting
 Items are counted and records updated on a
periodic basis
 Often used with ABC analysis
to determine cycle
 Has several advantages
1. Eliminates shutdowns and interruptions
2. Eliminates annual inventory adjustment
3. Trained personnel audit inventory accuracy
4. Allows causes of errors to be identified and corrected
5. Maintains accurate inventory records

12 - 19© 2011 Pearson Education, Inc. publishing as Prentice Hall
Cycle Counting Example
5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C
items
Policy is to count A items every month (20 working days), B
items every quarter (60 days), and C items every six months
(120 days)
Item
Class Quantity Cycle Counting Policy
Number of Items
Counted per Day
A 500 Each month 500/20 = 25/day
B 1,750 Each quarter 1,750/60 = 29/day
C 2,750 Every 6 months 2,750/120 = 23/day
77/day

12 - 20© 2011 Pearson Education, Inc. publishing as Prentice Hall
Control of Service Inventories
 Can be a critical component
of profitability
 Losses may come from
shrinkage or pilferage
 Applicable techniques include
1. Good personnel selection, training, and discipline
2. Tight control on incoming shipments
3. Effective control on all goods leaving facility

12 - 21© 2011 Pearson Education, Inc. publishing as Prentice Hall
Independent Versus
Dependent Demand
 Independent demand - the demand for
item is independent of the demand for any
other item in inventory
 Dependent demand - the demand for item
is dependent upon the demand for some
other item in the inventory

12 - 22© 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding, Ordering, and Setup
Costs
 Holding costs - the costs of holding or
“carrying” inventory over time
 Ordering costs - the costs of placing an order
and receiving goods
 Setup costs - cost to prepare a machine or
process for manufacturing an order

12 - 23© 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding Costs
Category
Cost (and range) as
a Percent of
Inventory Value
Housing costs (building rent or depreciation,
operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or
depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost 3% (3 - 5%)
Investment costs (borrowing costs, taxes, and
insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence 3% (2 - 5%)
Overall carrying cost 26%
Table 12.1

12 - 24© 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding Costs
Category
Cost (and range) as
a Percent of
Inventory Value
Housing costs (building rent or depreciation,
operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or
depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost 3% (3 - 5%)
Investment costs (borrowing costs, taxes, and
insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence 3% (2 - 5%)
Overall carrying cost 26%
Table 12.1

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Inventory Models for Independent
Demand
1. Basic economic order quantity
2. Production order quantity
3. Quantity discount model
Need to determine when and how much to order

12 - 26© 2011 Pearson Education, Inc. publishing as Prentice Hall
Basic EOQ Model
1. Demand is known, constant, and independent
2. Lead time is known and constant
3. Receipt of inventory is instantaneous and
complete
4. Quantity discounts are not possible
5. Only variable costs are setup and holding
6. Stockouts can be completely avoided
Important assumptions

12 - 27© 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory Usage Over Time
Figure 12.3
Order
quantity = Q
(maximum
inventory
level)
Usage rate Average
inventory
on hand
Q
2
Minimum
inventory
Inventory level
Time
0

12 - 28© 2011 Pearson Education, Inc. publishing as Prentice Hall
Minimizing Costs
Objective is to minimize total costs
Table 12.4(c)
Annual cost
Order quantity
Total cost of
holding and
setup (order)
Holding cost
Setup (or order)
cost
Minimum
total cost
Optimal order
quantity (Q*)

12 - 29© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual setup cost = (Number of orders placed per year)
x (Setup or order cost per order)
Annual demand
Number of units in each order
Setup or order
cost per order
=
Annual setup cost = S
D
Q
= (S)D
Q

12 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual holding cost = (Average inventory level)
x (Holding cost per unit per year)
Order quantity
2
= (Holding cost per unit per year)
= (H)Q
2
Annual setup cost = S
D
Q
Annual holding cost = H
Q
2

12 - 31© 2011 Pearson Education, Inc. publishing as Prentice Hall
The EOQ Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost
equals annual holding cost
Annual setup cost = S
D
Q
Annual holding cost = H
Q
2
D
Q S = H
Q
2
Solving for Q* 2DS = Q2H
Q2 = 2DS/H
Q* = 2DS/H

12 - 32© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
Q* = 2DS
H
Q* = 2(1,000)(10)
0.50 = 40,000 = 200 units

12 - 33© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order
H = $.50 per unit per year
= N = =
Expected
number of
orders
Demand
Order quantity
D
Q*
N = = 5 orders per year
1,000
200

12 - 34© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year
= T =
Expected
time between
orders
Number of working
days per year
N
T = = 50 days between orders
250
5

12 - 35© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
TC = S + H
D
Q
Q
2
TC = ($10) + ($.50)
1,000
200
200
2
TC = (5)($10) + (100)($.50) = $50 + $50 = $100

12 - 36© 2011 Pearson Education, Inc. publishing as Prentice Hall
Robust Model
 The EOQ model is robust
 It works even if all parameters and
assumptions are not met
 The total cost curve is relatively flat in the
area of the EOQ

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An EOQ Example
Management underestimated demand by 50%
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
TC = S + H
D
Q
Q
2
TC = ($10) + ($.50) = $75 + $50 = $125
1,500
200
200
2
1,500 units
Total annual cost increases by only 25%

12 - 38© 2011 Pearson Education, Inc. publishing as Prentice Hall
An EOQ Example
Actual EOQ for new demand is 244.9 units
D = 1,000 units Q* = 244.9 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
TC = S + H
D
Q
Q
2
TC = ($10) + ($.50)
1,500
244.9
244.9
2
1,500 units
TC = $61.24 + $61.24 = $122.48
Only 2% less
than the total
cost of $125
when the
order quantity
was 200

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Reorder Points
 EOQ answers the “how much” question
 The reorder point (ROP) tells “when” to order
ROP = Lead time for a new
order in days
Demand
per day
= d x L
d = D
Number of working days in a year

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Reorder Point Curve
Q*
ROP
(units)
Inventory level (units)
Time (days)
Figure 12.5 Lead time = L
Slope = units/day = d
Resupply takes place as order arrives

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Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days
ROP = d x L
d = D
Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units

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Production Order Quantity Model
 Used when inventory builds up over a
period of time after an order is placed
 Used when units are produced and sold
simultaneously

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Production Order Quantity Model
Inventory level
Time
Demand part of cycle
with no production
Part of inventory cycle during
which production (and usage)
is taking place
t
Maximum
inventory
Figure 12.6

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Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days
= (Average inventory level) x
Annual inventory
holding cost
Holding cost
per unit per year
= (Maximum inventory level)/2
Annual inventory
level
= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt – dt

12 - 45© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days
= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt – dt
However, Q = total produced = pt ; thus t = Q/p
Maximum
inventory level = p – d = Q 1 –
Q
p
Q
p
d
p
Holding cost = (H) = 1 – H
d
p
Q
2
Maximum inventory level
2

12 - 46© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
D = Annual demand
Q2 = 2DS
H[1 - (d/p)]
Q* = 2DS
H[1 - (d/p)]p
Setup cost = (D/Q)S
Holding cost = HQ[1 - (d/p)]1
2
(D/Q)S = HQ[1 - (d/p)]
1
2

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Production Order Quantity
Example
D = 1,000 units p = 8 units per day
S = $10 d = 4 units per day
H = $0.50 per unit per year
Q* = 2DS
H[1 - (d/p)]
= 282.8 or 283 units
Q* = = 80,000
2(1,000)(10)
0.50[1 - (4/8)]

12 - 48© 2011 Pearson Education, Inc. publishing as Prentice Hall
Production Order Quantity Model
When annual data are used the equation becomes
Q* = 2DS
annual demand rate
annual production rate
H 1 –
Note:
d = 4 = =
D
Number of days the plant is in operation
1,000
250

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Quantity Discount Models
 Reduced prices are often available when larger
quantities are purchased
 Trade-off is between reduced product cost and
increased holding cost
Total cost = Setup cost + Holding cost + Product cost
TC = S + H + PD
D
Q
Q
2

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Quantity Discount Models
Discount
Number Discount Quantity Discount (%)
Discount
Price (P)
1 0 to 999 no discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75
Table 12.2
A typical quantity discount schedule

12 - 51© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Models
1. For each discount, calculate Q*
2. If Q* for a discount doesn’t qualify, choose the
smallest possible order size to get the discount
3. Compute the total cost for each Q* or adjusted
value from Step 2
4. Select the Q* that gives the lowest total cost
Steps in analyzing a quantity discount

12 - 52© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Models
1,000 2,000
Total cost $
0
Order quantity
Q* for discount 2 is below the allowable range at point a
and must be adjusted upward to 1,000 units at point b
a
b
1st price
break
2nd price
break
Total cost
curve for
discount 1
Total cost curve for discount 2
Total cost curve for discount 3
Figure 12.7

12 - 53© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Calculate Q* for every discount Q* = 2DS
IP
Q1* = = 700 cars/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 cars/order
2(5,000)(49)
(.2)(4.80)
Q3* = = 718 cars/order
2(5,000)(49)
(.2)(4.75)

12 - 54© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Calculate Q* for every discount Q* = 2DS
IP
Q1* = = 700 cars/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 cars/order
2(5,000)(49)
(.2)(4.80)
Q3* = = 718 cars/order
2(5,000)(49)
(.2)(4.75)
1,000 — adjusted
2,000 — adjusted

12 - 55© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quantity Discount Example
Discount
Number
Unit
Price
Order
Quantity
(Q)
Annual
Product
Cost
Annual
Ordering
Cost
Annual
Holding
Cost
Total
Cost
1 $5.00 700 $25,000 $350 $350 $25,700
2 $4.80 1,000 $24,000 $245 $480 $24,725
3 $4.75 2,000 $23,750 $122.50 $950 $24,822.50
Table 12.3
Choose the price and quantity that gives
the lowest total cost
Buy 1,000 units at $4.80 per unit
(S)D
Q (IP)Q
2
D = 5000 units S = $49
H = 20% of product cost

12 - 56© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Models and Safety
Stock
 Used when demand is not constant or
certain
 Use safety stock to achieve a desired
service level and avoid stockouts
ROP = d x L + ss
Annual stockout costs = the sum of [the units short
x the probability x the stockout cost/unit
x the number of orders per year]

12 - 57© 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety Stock Example
Number of Units Probability
30 .2
40 .2
ROP  50 .3
60 .2
70 .1
1.0
ROP = 50 units Stockout cost = $40 per unit
Orders per year = 6 Carrying cost = $5 per unit per year

12 - 58© 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety Stock Example
ROP = 50 units Stockout cost = $40 per unit
Orders per year = 6 Carrying cost = $5 per unit per year
Safety
Stock
Additional
Holding Cost Stockout Cost
Total
Cost
20 (20)($5) = $100 $0 $100
10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290
0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960
A safety stock of 20 frames gives the lowest total cost
ROP = 50 + 20 = 70 frames

12 - 59© 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety stock 16.5 units
ROP 
Place
order
Probabilistic Demand
Inventory level
Time
0
Minimum demand during lead time
Maximum demand during lead time
Mean demand during lead time
Normal distribution probability of
demand during lead time
Expected demand during lead time (350 kits)
ROP = 350 + safety stock of 16.5 = 366.5
Receive
order
Lead
time
Figure 12.8

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Probabilistic Demand
Use prescribed service levels to set safety stock
when the cost of stockouts cannot be determined
ROP = demand during lead time + ZsdLT
where Z = number of standard deviations
sdLT = standard deviation of demand
during lead time

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Probabilistic Demand
Safety
stock
Probability of
no stockout
95% of the time
Mean
demand
350
ROP = ? kits Quantity
Number of
standard deviations
0 z
Risk of a stockout
(5% of area of
normal curve)

12 - 62© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Example
Average demand = m = 350 kits
Standard deviation of demand during lead time = sdLT = 10 kits
5% stockout policy (service level = 95%)
Using Appendix I, for an area under the curve
of 95%, the Z = 1.65
Safety stock = ZsdLT = 1.65(10) = 16.5 kits
Reorder point = expected demand during lead time
+ safety stock
= 350 kits + 16.5 kits of safety stock
= 366.5 or 367 kits

12 - 63© 2011 Pearson Education, Inc. publishing as Prentice Hall
Other Probabilistic Models
1. When demand is variable and lead time is
constant
2. When lead time is variable and demand is
constant
3. When both demand and lead time are
variable
When data on demand during lead time is not
available, there are other models available

12 - 64© 2011 Pearson Education, Inc. publishing as Prentice Hall
Other Probabilistic Models
Demand is variable and lead time is constant
ROP = (average daily demand
x lead time in days) + ZsdLT
where sd = standard deviation of demand per day
sdLT = sd lead time

12 - 65© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Example
Average daily demand (normally distributed) = 15
Standard deviation = 5
Lead time is constant at 2 days
90% service level desired
Z for 90% = 1.28
From Appendix I
ROP = (15 units x 2 days) + Z sdLT
= 30 + 1.28(5)( 2)
= 30 + 9.02 = 39.02 ≈ 39
Safety stock is about 9 units

12 - 66© 2011 Pearson Education, Inc. publishing as Prentice Hall
Other Probabilistic Models
Lead time is variable and demand is constant
ROP = (daily demand x average lead
time in days)
+ Z x (daily demand) x sLT
where sLT = standard deviation of lead time in days

12 - 67© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Example
Daily demand (constant) = 10
Average lead time = 6 days
Standard deviation of lead time = sLT = 3
98% service level desired
Z for 98% = 2.055
From Appendix I
ROP = (10 units x 6 days) + 2.055(10 units)(3)
= 60 + 61.65 = 121.65
Reorder point is about 122 units

12 - 68© 2011 Pearson Education, Inc. publishing as Prentice Hall
Other Probabilistic Models
Both demand and lead time are variable
ROP = (average daily demand
x average lead time) + ZsdLT
where sd = standard deviation of demand per day
sLT = standard deviation of lead time in days
sdLT = (average lead time x sd2)
+ (average daily demand2 x sLT2)

12 - 69© 2011 Pearson Education, Inc. publishing as Prentice Hall
Probabilistic Example
Average daily demand (normally distributed) = 150
Standard deviation = sd = 16
Average lead time 5 days (normally distributed)
Standard deviation = sLT = 1 day
95% service level desired Z for 95% = 1.65
From Appendix I
ROP = (150 packs x 5 days) + 1.65sdLT
= (150 x 5) + 1.65 (5 days x 162) + (1502 x 12)
= 750 + 1.65(154) = 1,004 units

12 - 70© 2011 Pearson Education, Inc. publishing as Prentice Hall
Single Period Model
 Only one order is placed for a product
 Units have little or no value at the end of the
sales period
Cs = Cost of shortage = Sales price/unit – Cost/unit
Co = Cost of overage = Cost/unit – Salvage value/unit
Service level = Cs
Cs + Co

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Single Period Example
Average demand = m = 120 papers/day
Standard deviation = s = 15 papers
Cs = cost of shortage = $1.25 - $.70 = $.55
Co = cost of overage = $.70 - $.30 = $.40
Service level = Cs
Cs + Co
.55
.55 + .40
.55
.95
=
= = .578
Service
level
57.8%
Optimal stocking level
m = 120

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Single Period Example
From Appendix I, for the area .578, Z .20
The optimal stocking level
= 120 copies + (.20)(s)
= 120 + (.20)(15) = 120 + 3 = 123 papers
The stockout risk = 1 – service level
= 1 – .578 = .422 = 42.2%

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Fixed-Period (P) Systems
 Orders placed at the end of a fixed period
 Inventory counted only at end of period
 Order brings inventory up to target level
 Only relevant costs are ordering and holding
 Lead times are known and constant
 Items are independent from one another

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Fixed-Period (P) Systems
On-hand inventory
Time
Q1
Q2
Target quantity (T)
P
Q3
Q4
P
P
Figure 12.9

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Fixed-Period (P) Example
Order amount (Q) = Target (T) - On-
hand inventory - Earlier orders not yet
received + Back orders
Q = 50 - 0 - 0 + 3 = 53 jackets
3 jackets are back ordered No jackets are in stock
It is time to place an order Target value = 50

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Fixed-Period Systems
 Inventory is only counted at each review
period
 May be scheduled at convenient times
 Appropriate in routine situations
 May result in stockouts between periods
 May require increased safety stock