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Chapter. 8 Independent Demand -Inventory
Prepared by :
Arya Wirabhuana, ST, M.Sc
Inventory System
Defined
Inventory is the stock of any item or resource used
in an organization. These items or resources can
include: raw materials, finished products,
component parts, supplies, and work-in-process.
An inventory system is the set of policies and
controls that monitor levels of inventory and
determines what levels should be maintained,
when stock should be replenished, and how large
orders should be.
A Water Tank Analogy for Inventory
Supply Rate
Inventory Level
Demand Rate
Inventory Level
Inventory Cost Structures
Item cost
Ordering (or setup) cost
Carrying (or holding) cost:
– Cost of capital
– Cost of storage
– Cost of obsolescence, deterioration, and loss
Stock out cost
7
Classifying Inventory Models
Fixed-Order Quantity Models
– Event triggered
Fixed-Time Period Models
– Time triggered
Economic Order Quantity (EOQ)
Assumptions
Demand rate is constant, recurring, and known.
Lead time is constant and known.
No stockouts allowed.
Material is ordered or produced in a lot or batch and
the lot is received all at once
Unit cost is constant (no quantity discounts)
Carrying cost depends linearly on the average level of
inventory
Ordering (setup) cost per order is fixed
The item is a single product
EOQ Inventory Levels
Time
Lot size = Q
Order
Interval
Average Inventory
Level = Q/2
Total Cost of Inventory
Basic Fixed-Order Quantity (EOQ) Model Formula
TC = DC + D
Q S +
Q
2 H
Total Annual Cost =
Annual
Purchase
Cost
Annual
Ordering
Cost
Annual
Holding
Cost + +
TC = Total annual cost
D = Demand
C = Cost per unit
Q = Order quantity
S = Cost of placing an order
or setup cost
R = Reorder point
L = Lead time
H = Annual holding and storage
cost per unit of inventory
Continuous Review System
Assumption of “constant demand” is relaxed.
Monitoring of “on hand” stock position in a
continuous system
Q system (another name for continuous
review system)
A Continuous Review (Q) System
R = Reorder Point
Q = Order Quantity
L = Lead time
Periodic Review System
All assumption of EOQ (except that demand
is constant and “no stockout”) remains in
effect.
Also known as “P System” or “Fixed-order-
Interval System”
A Periodic Review (P) System
“Time Between Orders (P) and
Target Level (T) Calculation
DCi
SP
2
'' smT Where:
m’ = average demand over P+L
s’ = safety stock
Using P and Q System in Practice
Use P system when orders must be placed
at specified intervals.
Use P systems when multiple items are
ordered from the same supplier (joint-
replenishment).
Use P system for inexpensive items.
Special Purpose Model: Price-Break
Model Formula
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
iC
2DS = QOPT
Based on the same assumptions as the EOQ model,
the price-break model has a similar Qopt formula:
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula above will
have to be used with each price-break cost value.
Price-Break Example Problem Data
(Part 1)
A company has a chance to reduce their inventory
ordering costs by placing larger quantity orders using the
price-break order quantity schedule below. What should
their optimal order quantity be if this company purchases
this single inventory item with an e-mail ordering cost of
$4, a carrying cost rate of 2% of the inventory cost of the
item, and an annual demand of 10,000 units?
Order Quantity(units) Price/unit($)
0 to 2,499 $1.20
2,500 to 3,999 1.00
4,000 or more .98
Price-Break Example Solution (Part 2)
units 1,826 = 0.02(1.20)
4)2(10,000)( =
iC
2DS = QOPT
Annual Demand (D)= 10,000 units
Cost to place an order (S)= $4
First, plug data into formula for each price-break value of “C”.
units 2,000 = 0.02(1.00)
4)2(10,000)( =
iC
2DS = QOPT
units 2,020 = 0.02(0.98)
4)2(10,000)( =
iC
2DS = QOPT
Carrying cost % of total cost (i)= 2%
Cost per unit (C) = $1.20, $1.00, $0.98
Interval from 0 to 2499, the
Qopt value is feasible.
Interval from 2500-3999, the
Qopt value is not feasible.
Interval from 4000 & more, the
Qopt value is not feasible.
Next, determine if the computed Qopt values are feasible or not.
Price-Break Example Solution (Part 3)
Since the feasible solution occurred in the first price-break,
it means that all the other true Qopt values occur at the
beginnings of each price-break interval. Why?
0 1826 2500 4000 Order Quantity
Total
annual
costs So the candidates
for the price-breaks
are 1826, 2500,
and 4000 units.
Because the total annual cost function is a
“u” shaped function.
Annual Usage of Items by Dollar Value
Item
Annual Usage in
Units Unit Cost Dollar Usage
Percentage of
Total Dollar
Usage
1 5,000 1.50$ 7,500$ 2.9%
2 1,500 8.00 12,000 4.7%
3 10,000 10.50 105,000 41.2%
4 6,000 2.00 12,000 4.7%
5 7,500 0.50 3,750 1.5%
6 6,000 13.60 81,600 32.0%
7 5,000 0.75 3,750 1.5%
8 4,500 1.25 5,625 2.2%
9 7,000 2.50 17,500 6.9%
10 3,000 2.00 6,000 2.4%
Total 254,725$ 100.0%
ABC Chart
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
3 6 9 2 4 1 10 8 5 7
Item No.
Pe
rce
nt
Usa
ge
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
Cu
mu
lati
ve
% U
sag
e
Percentage of Total Dollar Usage Cumulative Percentage
A B C
Dependent Demand-
Inventory
Attribute MRP Order Point
Demand Dependent Independent
Order philosophy Requirements Replenishment
Forecast Based on master schedule Based on past demand
Control concept Control all items ABC
Objectives Meet manufacturing needs Meet customer needs
Lot sizing Discrete EOQ
Demand pattern Lumpy but predictable Random
Types of inventory Work in process and raw
materials
Finished goods and spare
parts
Attribute MRP Order Point
Demand Dependent Independent
Order philosophy Requirements Replenishment
Forecast Based on master schedule Based on past demand
Control concept Control all items ABC
Objectives Meet manufacturing needs Meet customer needs
Lot sizing Discrete EOQ
Demand pattern Lumpy but predictable Random
Types of inventory Work in process and raw
materials
Finished goods and spare
parts
MRP versus Order-Point Systems
3
Material Requirements Planning
How much of an item is needed?
When is an item needed to complete
– a specified number of units...
– in a specified period of time?
Dependent demand drives MRP
4
Introductory
Example - Dependent Demand
B(4)
E(1) D(2)
C(2)
F(2) D(3)
A
Product Structure Tree for Assembly A
Lead Times
A 1 day
B 2 days
C 1 day
D 3 days
E 4 days
F 1 day
Demand
Day 10 50 A
Day 8 20 B (Spares)
Day 6 15 D (Spares)
Create a schedule to satisfy demand.
LT = 1 day
Day: 1 2 3 4 5 6 7 8 9 10
A Required 50
Order Placement 50
5
D a y : 1 2 3 4 5 6 7 8 9 1 0
A R e q u ire d 5 0
O rd e r P la c e m e n t 5 0
B R e q u ire d 2 0 2 0 0
O rd e r P la c e m e n t 2 0 2 0 0
Spares LT = 2
B(4)
E(1) D(2)
C(2)
F(2) D(3)
A
6
Day: 1 2 3 4 5 6 7 8 9 10
A Required 50
LT=1 Order Placement 50
B Required 20 200
LT=2 Order Placement 20 200
C Required 100
LT=1 Order Placement 100
D Required 55 400 300
LT=3 Order Placement 55 400 300
E Required 20 200
LT=4 Order Placement 20 200
F Required 200
LT=1 Order Placement 200
B(4)
E(1) D(2)
C(2)
F(2) D(3)
A
40 + 15 spares
Part D: Day 6
7
9
Time Fences
Frozen
– No schedule changes allowed within this window
Moderately Firm
– Specific changes allowed within product groups
as long as parts are available
Flexible
– Significant variation allowed as long as overall
capacity requirements remain at the same levels
10
Time Fences
8 15 26
Weeks
Frozen Moderately
Firm Flexible
Firm Customer Orders
Forecast and available
capacity
Capacity
Firm orders
from known
customers
Forecasts
of demand
from random
customers
Aggregate
product
plan
Master
production
schedule
(MPS)
Material
planning
(MRP)
Engineering
design
changes
Bill of
material
file
Inventory
transactions
Inventory
record
file
Reports
12
18
Another MRP Example
A(2) B(1)
D(5) C(2)
X
C(3)
Item On-Hand Lead Time (Weeks)
X 50 2
A 75 3
B 25 1
C 10 2
D 20 2
Requirements include 95 units (80 firm orders and 15 forecast) of X in week 10
plus the following spares:
Spares 1 2 3 4 5 6 7 8 9 10
A 12
B 7
C 10
D 15
19
Adding some more terminology
Gross Requirements
On-hand
Net requirements
Planned order receipt
Planned order release
C Gross Requirements 45 36 64
LT=2 On-Hand=10 10
Net Requirements 35 36 64
Planned Order Receipt 35 36 64
Planner Order Release 35 36 64
D Gross Requirements 15 135
LT=2 On-Hand=20 15 5
Net Requirements 130
Planned Order Receipt 130
Planner Order Release 130
A(2) B(1)
D(5) C(2)
X
C(3)
20
Day: 1 2 3 4 5 6 7 8 9 10
X Gross Requirements 95
LT=2 On-Hand=50 50
Net Requirements 45
Planned Order Receipt 45
Planner Order Release 45
A Gross Requirements 90 12
LT=3 On-Hand=75 75
Net Requirements 15 12
Planned Order Receipt 15 12
Planner Order Release 15 12
B Gross Requirements 7 45
LT=1 On-Hand=25 7 18
Net Requirements 27
Planned Order Receipt 27
Planner Order Release 27
C Gross Requirements 45 36 54 10
LT=2 On-Hand=10 10
Net Requirements 35 36 54 10
Planned Order Receipt 35 36 54 10
Planner Order Release 35 36 54 10
D Gross Requirements 15 135
LT=2 On-Hand=20 15 5
Net Requirements 130
Planned Order Receipt 130
Planner Order Release 130
21
23
Manufacturing Resource Planning (MRP II)
Goal: Plan and monitor all resources of a
manufacturing firm (closed loop):
– manufacturing
– marketing
– finance
– engineering
Simulate the manufacturing system
Next : Supply Chain Management