Transcript Capacity and Aggregate Planning

IES 303
Chapter 15: Inventory Management
Supplement E
Week 13
February 2, 2006
Learning Objectives:
Understand the practical aspects of various inventory systems
Identify the major factors affecting inventory system performance
Understand how to calculate the optimal order quantity in various
circumstance
1
Inventory Management
 Inventory : Stock of items held to meet future demand
 Determine the amount of inventory to keep in stock
 Inventory management answers two questions:
 _________________________
 ________________ or
 ________________ (EOQ)
 _________________________
2
Physical Types of
Inventory
Reasons to Hold
Inventory
Meet unexpected demand
 Raw materials
 Purchased parts and supplies Smooth seasonal or cyclical
demand
 Labor
Meet variations in customer
 In-process (partially
demand
completed) products
 Component parts
 Tools, machinery, and
equipment
Take advantage of
price discounts
Quantity discounts
3
Pressures for Low Inventories

When keeping inventory, there are
always some cost incurred ________
___________________________


The variable cost of keeping items on
hand

$/ unit-period
Inventory holding cost generally
includes:

_________________________

_________________________

_________________________
4
Pressures for High Inventories

Customer service

Ordering cost ($ / order)

Setup cost

Transportation cost

Payment to suppliers

Labor and equipment
utilization
5
Types of Inventory

Cycle Inventory

Safety stock inventory

Anticipation inventory

Pipeline inventory
6
Inventory Reduction Approach

Cycle Inventory

Safety stock inventory

Anticipation inventory

Pipeline inventory
7



ABC Analysis
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
8
ABC Analysis
100 —
Class C
Class B
Percentage of dollar value
90 —
80 —
Class A
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0—
Figure 15.2
10
20
30
40
50
60
70
Percentage of items
80
90 100
9
Economic Order Quantity (EOQ)

EOQ: the lot size or order size that minimizes total annual
inventory holding and ordering cost

Total inventory cost = Holding cost (HC) + ordering cost (OC)

Assumptions for Basic EOQ Model

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________
10
Basic EOQ Model
Cycle Inventory Levels
Inventory Level
Order quantity, Q
0
Order Order
placed receipt
Lead
time
Order Order
placed receipt
Time
11
Basic EOQ Model
Graphs of Annual Holding, Ordering, and Total
Costs
Annual cost (dollars)
Total cost = HC + OC
Figure 15.4
Holding cost (HC)
Ordering cost (OC)
Lot Size (Q)
12
Basic EOQ Model

Derivation of total annual inventory cost and economic order quantity order
quantity functions
Q
D
C  ( H )  (S )
2
Q
Q = order size (units)
D = annual demand (units/year)
S = ordering cost per order ($/order)
H = annual per unit carrying cost ($/unit)
EOQ 
2 DS
H
TBOEOQ
EOQ

(12 months/year)
D
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Basic EOQ Model
Ex 1:Carpet Sell
The I-75 Carpet store stocks carpet in its warehouse and sells it
through a showroom. The store keeps several brands and
styles of carpet in stock; however, its bigger seller is the BIG
C carpet. The store wants to determine the optimal order
size and total inventory cost for this brand of carpet given an
estimated annual demand of 10,000 yards of carpet, an
annual carrying cost of $0.75 per yard, and an ordering cost
of $150.
The store would like to know the number of orders that will be
made annually and the time between orders given that the
store is open every except Sunday, Thanksgiving Day and
Christmas Day.
14
EOQ Sensitivity Analysis

Use estimates of relevant costs

Ignore uncertainty in demand


What happen if the holding / ordering cost is off by 20%,
30%?
Consider 4 cases of variations of the model parameters.
1.
Both ordering and carrying costs are 10% less than the original
estimates
2.
Both are 10% higher
3.
Ordering cost is 10% higher and carrying cost is10% lower
4.
Ordering cost is 10% lower and carrying cost is 10% higher
Determine EOQ in each case. Remark on the sensitivity of Q on the
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estimated total cost.
Basic Types of Inventory Control System


Continuous review system

________________________

________________________

The ordering interval may not be consistent

Manager has direct control
Periodic review System (P)

________________________

________________________

No direct control

Tend to have higher inventory to prevent stockout
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Continuous review system
IP
On-hand inventory
IP
Order
received
Order
received
Q
Order
received
Order
received
Q
OH
OH
IP
Q
OH
R
Order
placed
Order
placed
L
TBO
Order
placed
L
TBO
L
TBO
Time
17
Continuous review system
Selecting Reorder Point

When demand is certain


Reorder point (R) = demand during lead time
When demand is uncertain

Reorder point (R) = Avg demand during lead time + Safety stock
18
Variable Demand
Safety Stocks

________________
________________
Stockout

an inventory shortage
Service level
• ________________
________________
Inventory level
Safety stock
Q
Reorder
point, R
0
LT
LT
Time
Variable Demand with Reorder Point
19
Variable Demand
Safety Stocks
Inventory level

Prevent stockout under uncertain demand
Q
Reorder
point, R
Safety Stock
0
LT
LT
Time
20
Reorder Point for a Service Level
Probability of
meeting demand during
lead time = service level
Average demand
during lead time
Probability of
a stockout
Safety stock
zt L
Demand
R
21
Reorder Point with Variable Demand

Reorder point with safety stock

Service level = probability of NO stockout
R  dL  z t L
d  average demand
L  lead time
σ t  standard deviation of demand
z  number of standard deviations corresponding to
the service level probability
z t
L  safety stock
22
Variable Demand
Ex 2: PM computer
PM Computers assembles microcomputers from generic
components. It purchases its color monitors from a
manufacturer in Taiwan. There is a long lead time of 25
days. Daily demand is normally distributed with a mean of
2.5 monitors and a standard deviation of 1.2 monitors.
Determine the safety stock and reorder point corresponding
to a 90% service level
23
Periodic Review System (P system)
On-hand inventory
T
IP
IP
Order
received
IP
Order
received
Order
received
Q3
Q1
OH
OH
Q2
IP1
IP3
IP2
Order
placed
Order
placed
L
L
P
Figure 15.12
Protection interval
L
P
Time
24
On-hand inventory
Special Inventory Model
Noninstantaneous
Replenishment
Production quantity
Q
Demand during
production interval
Imax
Maximum inventory
p–d
Time
Production
and demand
Demand
only
TBO
25
Figure E.1
Special Inventory Model
Noninstantaneous Replenishment
p–d
Q
Imax =
(p – d) = Q p
p
(
Imax
D
C = 2 (H) +
(S)
Q
ELS =
2DS
H
)
Q p–d
C =2
p
(
)
D
+
(S)
Q
p
p–d
26
Noninstantaneous Replenishment
Ex 3: Cheese Maker
The Wood Valley Dairy makes cheese to supply to stores in its
area. The dairy can make 250 lbs of cheese per day, and
the demand at area stores is 180 lbs per day. Each time the
dairy makes cheeses, it costs $125 to set up the production
process. The annual cost of carrying a pound of cheese is
$12.
Determine the followings:
-
The optimal order size and the minimum total annual
inventory cost
-
Length of time to receive an order, production run
-
Number of orders per year
-
Maximum inventory level
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Special Inventory Model
Quantity Discount

Price discount for higher quantity orders

Include the purchase price in EOQ model

P = Unit price of item
Q
D
C  H  S  PD
2
Q
TC = ($10 )
Inventory cost ($)
TC (P1 = $8 )
TC (P2 = $6 )
Carrying cost
Ordering cost
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Q(P1 ) = 100 Qopt Q(P2 ) = 200
Quantity Discount
Ex 4: Sweatshirt in bookstore
The UW bookstore purchases sweatshirts with school logo from a
vendor. The vendor sells the sweatshirts to the store for $38 a
piece. The cost to bookstore for placing an order is $120, and the
annual carrying cost is 25% of the cost of sweatshirt. 1700
sweatshirts are estimated to be sold during the year. The vendor
has offered the bookstore the following volume discount:
Order Size
Discount
1-299
0%
300-499
2%
500-799
4%
800 and up
5%
29
What is an optimal order quantity?