Inventory management ch12

Chapter 12
Inventory Management

Operations Management -- 5th Edition
Operations Management 5th Edition

Roberta Russell & Bernard W. Taylor, III

Beni Asllani
Copyright 2006 John Wiley & Sons, Inc. University of Tennessee at Chattanooga

Lecture Outline

 Elements of Inventory Management
 Inventory Control Systems
 Economic Order Quantity Models
 Quantity Discounts
 Reorder Point
 Order Quantity for a Periodic Inventory
System

Copyright 2006 John Wiley & Sons, Inc. 12-2

What Is Inventory?

 Stock of items kept to meet future
demand
 Purpose of inventory management
 how many units to order
 when to order


Types of Inventory

 Raw materials
 Purchased parts and supplies
 Work-in-process (partially completed)
products (WIP)
 Items being transported
 Tools and equipment


Inventory and Supply Chain
Management
 Bullwhip effect
 demand information is distorted as it moves away
from the end-use customer
 higher safety stock inventories to are stored to
compensate
 Seasonal or cyclical demand
 Inventory provides independence from vendors
 Take advantage of price discounts
 Inventory provides independence between
stages and avoids work stop-pages


Two Forms of Demand
 Dependent
 Demand for items used to produce
final products
 Tires stored at a Goodyear plant are
an example of a dependent demand
item
 Independent
 Demand for items used by external
customers
 Cars, appliances, computers, and
houses are examples of independent
demand inventory


Inventory and Quality
Management

 Customers usually perceive quality
service as availability of goods they want
when they want them
 Inventory must be sufficient to provide
high-quality customer service in TQM


Inventory Costs

 Carrying cost
 cost of holding an item in inventory
 Ordering cost
 cost of replenishing inventory
 Shortage cost
 temporary or permanent loss of sales
when demand cannot be met


Inventory Control Systems

 Continuous system (fixed-
order-quantity)
 constant amount ordered
when inventory declines to
predetermined level
 Periodic system (fixed-time-
period)
 order placed for variable
amount after fixed passage of
time


ABC Classification
 Class A
 5 – 15 % of units
 70 – 80 % of value
 Class B
 30 % of units
 15 % of value
 Class C
 50 – 60 % of units
 5 – 10 % of value


ABC Classification: Example
PART UNIT COST ANNUAL USAGE
1 $ 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120


ABC Classification:
Example (cont.)
TOTAL % OF TOTAL % OF TOTAL
PART PART
VALUE UNIT COSTQUANTITY % CUMMULATIVE
VALUE ANNUAL USAGE
9 1
$30,600 $ 60
35.9 6.0 90 6.0
8 16,000
2 18.7
350 5.0 40 11.0
2 14,000 16.4 4.0
A 15.0
3 30 130
1 5,400 6.3 9.0 24.0
4 4
4,800 5.680 6.0 B60 30.0
3 5
3,900 4.630 10.0 100 40.0
% OF TOTAL % OF TOTAL
6 6
3,600
CLASS ITEMS
4.220 VALUE 18.0 180 58.0
QUANTITY
5 3,000
7 3.510 13.0 170 71.0
10 2,400
A 9, 8,2.8
2 12.0
71.0 C 83.0
8 320 50 15.0
7 1,700
B 1, 4,2.0
3 17.0
16.5 100.0
25.0
9
C 510
6, 5, 10, 7 12.5 60 60.0
$85,400
10 20 120
Example 10.1


Economic Order Quantity
(EOQ) Models

 EOQ
 optimal order quantity that will
minimize total inventory costs
 Basic EOQ model
 Production quantity model


Assumptions of Basic
EOQ Model

 Demand is known with certainty and
is constant over time
 No shortages are allowed
 Lead time for the receipt of orders is
constant
 Order quantity is received all at once


Inventory Order Cycle
Order quantity, Q
Demand
rate
Inventory Level

Reorder point, R

0 Lead Lead Time
time time
Order Order Order Order
placed receipt placed receipt


EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity

Co D
Annual ordering cost =
Q
CcQ
Annual carrying cost =
2
CoD CcQ
Total cost = +
Q 2


EOQ Cost Model

Deriving Qopt Proving equality of
costs at optimal point
Co D CcQ
TC = +
Q 2 Co D CcQ
=
∂TC CoD C Q 2
= + c
∂Q Q2 2 2CoD
Q = 2
C0 D Cc Cc
0= +
Q2 2
2CoD
2CoD Qopt =
Qopt = Cc
Cc


EOQ Cost Model (cont.)
Annual
cost ($) Total Cost
Slope = 0

CcQ
Minimum Carrying Cost =
2
total cost

CoD
Ordering Cost =
Q

Optimal order Order Quantity, Q
Qopt


EOQ Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards

2CoD CoD CcQ
Qopt = TCmin = +
Cc Q 2
2(150)(10,000) (150)(10,000) (0.75)(2,000)
Qopt = TCmin = +
(0.75) 2,000 2

Qopt = 2,000 yards TCmin = $750 + $750 = $1,500

Orders per year = D/Qopt Order cycle time = 311 days/(D/Qopt)
= 10,000/2,000 = 311/5
= 5 orders/year = 62.2 store days

Production Quantity
Model
 An inventory system in which an order is
received gradually, as inventory is
simultaneously being depleted
 AKA non-instantaneous receipt model
 assumption that Q is received all at once is relaxed
 p - daily rate at which an order is received over
time, a.k.a. production rate
 d - daily rate at which inventory is demanded


Production Quantity Model
(cont.)
Inventory
level

Maximum
Q(1-d/p) inventory
level

Average
Q
(1-d/p) inventory
2 level

0
Begin End Time
order order
Order
receipt receipt
receipt period


Production Quantity Model
(cont.)
p = production rate d = demand rate

Q
Maximum inventory level = Q - d
p
d
=Q1-
p 2CoD
Qopt = d
Q d Cc 1 - p
Average inventory level = 1-
2 p

CoD CcQ d
TC = + 1- p
Q 2


Production Quantity Model:
Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day

2CoD 2(150)(10,000)
Qopt = = = 2,256.8 yards
32.2
Cc 1 - d 0.75 1 -
p 150

Co D CcQ d
TC = + 1- p = $1,329
Q 2

Q 2,256.8
Production run = = = 15.05 days per order
p 150


Production Quantity Model:
Example (cont.)

D 10,000
Number of production runs = = = 4.43 runs/year
Q 2,256.8

d 32.2
Maximum inventory level = Q 1 - = 2,256.8 1 -
p 150
= 1,772 yards


Quantity Discounts

Price per unit decreases as order
quantity increases

CoD CcQ
TC = + + PD
Q 2
where

P = per unit price of the item
D = annual demand


Quantity Discount Model (cont.)
ORDER SIZE PRICE
0 - 99 $10 TC = ($10 )
100 – 199 8 (d1)
200+ 6 (d2)
TC (d1 = $8 )

TC (d2 = $6 )
Inventory cost ($)

Carrying cost

Ordering cost

Q(d1 ) = 100 Qopt Q(d2 ) = 200

Quantity Discount: Example
QUANTITY PRICE
Co = $2,500
1 - 49 $1,400
Cc = $190 per computer
50 - 89 1,100
D = 200
90+ 900

2 Co D 2(2500)(200)
Qopt = = = 72.5 PCs
Cc 190

For Q = 72.5
CoD CcQopt
TC = + + PD = $233,784
Qopt 2

For Q = 90
Co D CcQ
TC = + + PD = $194,105
Q 2

Reorder Point
Level of inventory at which a new order
is placed

R = dL
where
d = demand rate per period
L = lead time


Reorder Point: Example

Demand = 10,000 yards/year
Store open 311 days/year
Daily demand = 10,000 / 311 = 32.154
yards/day
Lead time = L = 10 days

R = dL = (32.154)(10) = 321.54 yards


Safety Stocks
 Safety stock
 buffer added to on hand inventory during lead
time
 Stockout
 an inventory shortage
 Service level
 probability that the inventory available during
lead time will meet demand


Variable Demand with
a Reorder Point
Q
Inventory level

Reorder
point, R

0
LT LT
Time


Reorder Point with
a Safety Stock
Inventory level

Q
Reorder
point, R

Safety Stock
0
LT LT
Time

Reorder Point With
Variable Demand

R = dL + zσ d L
where
d = average daily demand
L = lead time
σd = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
zσd L = safety stock


Reorder Point for
a Service Level
Probability of
meeting demand during
lead time = service level

Probability of
a stockout

Safety stock
zσ d L

dL R
Demand

Reorder Point for
Variable Demand
The carpet store wants a reorder point with a 95%
service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
σd = 5 yards per day

For a 95% service level, z = 1.65

R = dL + z σd L Safety stock = z σd L
= 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10)
= 326.1 yards = 26.1 yards


Order Quantity for a
Periodic Inventory System

Q = d(tb + L) + zσ d tb + L - I

where
d = average demand rate
tb = the fixed time between orders
L = lead time
σd = standard deviation of demand

zσ d tb + L = safety stock
I = inventory level

Fixed-Period Model with
Variable Demand
d = 6 bottles per day
σ d = 1.2 bottles
tb = 60 days
L = 5 days
I = 8 bottles
z = 1.65 (for a 95% service level)

Q = d(tb + L) + zσ d tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 bottles

Copyright 2006 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of this work beyond that
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use of the information herein.


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