Anderson
Sweeney
Williams
QUANTITATIVE
METHODS FOR
BUSINESS 8e
Slides Prepared by JOHN LOUCKS
© 2001 South-Western College Publishing/Thomson Learning
Slide 1
Chapter 14
Inventory Management: Dependent-Demand
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Objectives of MRP
Inputs to MRP
Gross and Net Requirements
Lot Sizing and Safety Stock
MRP and a Time-phased Production Schedule
Implementing an MRP System
Just-in-Time
Slide 2
Material Requirements Planning
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Material requirements planning (MRP) is used to
control a manufacturing inventory system.
The major function of an MRP system is to translate
the demand for finished goods into detailed
inventory requirements for all their components.
MRP serves as part of a data processing system
whose function is to monitor and control the status of
production and perform inventory control.
One goal of MRP is to minimize the investment in
manufacturing inventories.
Another goal is to ensure all new materials, parts and
subassemblies are available when needed, thus
preventing production delays from occurring.
Slide 3
MRP Inputs
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One input to an MRP system is the master
production schedule (MPS) which summarizes
requirements and deadlines for finished goods over
the planning horizon.
Another input is the bill of materials (BOM) which is
a structured parts list detailing the sequencing of the
assembly of the product.
A third input is an MRP inventory record for each
raw material, part or subassembly showing
everything affecting the inventory level over the
planning horizon.
Slide 4
Bill of Materials
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One graphical representation of a bill of materials is
known as a product structure tree.
In this representation, the finished product (end
item) is shown at the top of the hierarchy (level 0).
At the level below this (level 1) are the subassemblies
or parts making up the finished product.
In the next level (level 2) are the subassemblies or
parts making up the subassemblies of level 1.
The parts or subassemblies shown at each level of the
hierarchy are said to be the parent of the parts or
subassemblies directly below them in the hierarchy.
Each item in the bill of materials, except for the end
product, has a parent.
Slide 5
Inventory Record
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Information contained in the inventory record can be
classified as either inventory transaction information
or planning information.
Inventory transaction information includes events
such as the receipt of goods from a supplier, the
disbursement of items from inventory to satisfy
production, the occurrence of scrap, etc.
Planning information includes lead time, safety
stock, lot sizing method, etc.
Slide 6
MRP Calculations
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In manufacturing there is often a dependent demand
between different components. In this case, (Net
Component Requirements) = (Gross Component
Requirements) - (Number of Components in
Inventory).
The process of generating net requirements for
components from the master production schedule for
an end item is called a BOM explosion.
The gross component requirement is the quantity of
the component necessary to support production at
the next higher level of assembly.
Slide 7
MRP Calculations
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The net requirements calculation enables one to
determine the required additions to inventory.
An order placed during a previous planning period but
scheduled to arrive during the current planning period
is called a scheduled receipt.
An order placed during the current planning period is
referred to as a planned order release.
An order’s arrival is known as a planned order receipt.
Items are normally assumed to arrive at the beginning
of a time period.
Both net and gross requirements are assumed to refer to
requirements at the beginning of a time period.
Slide 8
Lot Sizing
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Two often used methods for determining the amount
of inventory to order during the planning period are
the fixed-order-size and the lot-for-lot rules.
The fixed order size rule is appropriate for purchased
components when such a lot size is necessary to take
advantage of quantity discounts, when an economic
order quantity (EOQ) rule is being used, or when
batches must be of a certain size due to equipment
capacities.
The lot for lot rule has the lot size equal to the net
requirement for the period in which the lot will
become available. In this case, the planned order
receipts are identical to the net requirements for a
time period.
Slide 9
Safety Stock
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Safety stock can be used to buffer the production
system against uncertainty.
This includes uncertainty about gross requirements,
lead times, defective parts, pilferage, etc.
Safety stock is indicated in the MRP planning
worksheet as a projected balance in each time bucket.
In calculating net requirements, it should be included
in the total for the gross requirements.
Slide 10
Time Phasing
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MRP determines the date the net requirements are
needed by a procedure called time phasing.
In time phasing, a production plan for components is
developed by working backwards from the desired
completion date of the finished product through the
various manufacturing stages.
Time phasing is used to determine the appropriate
planning horizon for each subassembly or parent
corresponding to the planning horizon for the end
product.
An MRP worksheet can then be prepared for the part or
subassembly over this planning horizon.
Slide 11
MRP Record Updating
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Two approaches used to update MRP records are the
regeneration approach and the net change approach.
In the regeneration approach, the records for all items
are updated periodically.
In the net change approach, the MRP system
recalculates net requirements whenever changes make
it necessary; however, only the records affected by the
new or revised information are updated.
Slide 12
Example: Columbia Mopeds
Columbia Mopeds is a manufacturer of off-road
mopeds. The following product structure tree
represents the bill of materials for its dual carburetor
model 621 moped.
MOPED
ENGINE
ASSEMBLY
MOTOR
GAS
TANK
CARBURETOR
(2)
WHEEL
ASSEMBLY
(2)
HUB
ASSEMBLY
FRAME
TIRE
Slide 13
Example: Columbia Mopeds

Component Lead Times
Component
Engine Assembly
Motor
Carburetor
Gas Tank
Wheel Assembly
Tire
Hub Assembly
Frame
Lead Time (Weeks)
1
1
2
2
1
3
1
3
Slide 14
Example: Columbia Mopeds
The company is currently planning production for
weeks 10 through 16. Based on existing orders and
demand forecasts, the master production schedule is as
follows:
WEEK
10
11
12
13
14
15
16
PROD. QTY.
1000
0
1300
800
0
1400
900
a) Determine how many units of each component will be
needed to support the production of 1000 mopeds in
week 10.
b) Determine the planned order release date for each
component to support the production of 1000 mopeds
in week 10.
Slide 15
Example: Columbia Mopeds

To find the gross requirements of each component to
support the production of 1000 mopeds in week 10:
• Each moped requires one engine assembly, one gas
tank, two wheel assemblies and one frame. Thus,
1000 engine assemblies, 1000 gas tanks, 2000 ( = 2 x
1000) wheel assemblies, and 1000 frames will be
needed to support production.
• Each engine assembly requires one motor and two
carburetors. Hence the 1000 engine assemblies
require 1000 motors and 2000 carburetors.
• Since each wheel assembly requires one tire and one
hub assembly, 2000 tires and 2000 hub assemblies
will be required to produce 2000 wheel assemblies.
Slide 16
Example: Columbia Mopeds

Gross Requirements
Item
Units
Moped
1000
Engine Assembly
1000
Motor
Carburetor
Gas Tank
1000
Wheel Assembly
2000
Tire
Hub Assembly
Frame
1000
1000
2000
2000
2000
Slide 17
Example: Columbia Mopeds

To determine the planned order release date for each of
the components required to support the production of
1000 mopeds in week 10:
• Note that each of the four level 1 components
(engine assembly, gas tank, wheel assembly, and
frame) must be available in week 10.
• Given that the lead time for the engine assembly is
one week, its planned order release date should be
week 9 (= 10 -1).
• Similarly, as the lead time for gas tanks is two
weeks, its planned release date should be week 8 (=
10- 2). Following the same reasoning, the planned
order release date for the wheel assembly should be
week 9 (= 10 - 1) and for the frame, week 7 (= 10 - 3).
Slide 18
Example: Columbia Mopeds
• Considering the level 2 components, observe that in
order to have engine assemblies ready for assembly
in week 9 (their planned release date), the motor and
carburetor must be available by week 9. Given that
the motors have a one-week lead time, this means
they should have a planned release date of week 8 (=
9 -1). Similarly, the planned release date for the
carburetors should be week 7 (= 9 - 2).
• Repeating this process for the level 2 components of
the wheel assemblies, the planned release date for
the tires should be week 6 (= 9 - 3), and the planned
release date for the hubs should be week 8 (= 9 - 1).
Slide 19
Example: Columbia Mopeds

Planned Order Release Dates
Item
Planned Order Release Date (Week)
Moped
10
Engine Assembly
9
Motor
8
Carburetor
7
Gas Tank
8
Wheel Assembly
9
Tire
6
Hub Assembly
8
Frame
7
Slide 20
Example: Columbia Mopeds

MRP Worksheet for Gas Tanks for Weeks 10 - 16,
assuming:
• There is a projected balance of 400 gas tanks at the
beginning of week 10.
• There is a scheduled receipt of 900 tanks in week 10.
• Columbia Mopeds uses a lot-for-lot rule for ordering
gas tanks.
• A safety stock of 200 gas tanks is desired.
• Lead time for gas tanks is two weeks.
• The following gross requirements, by week:
WEEK
10
11
12
13
14
15
16
GR. REQ.
1000
0
1300
800
0
1400
900
Slide 21
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Initially
ITEM:: GAS TANK
LEAD TIME: 2
LOT SIZE: L-F-L SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
12
13
14
1300 800
0
15
16
1400 900
400
NET REQUIREMENTS
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 22
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 10
To complete the worksheet, begin at week 10. Since
there is a projected balance of 400 gas tanks at the
beginning of week 10 and scheduled receipts of 900 gas
tanks in week 10 (assumed to arrive at the beginning of
the week), a total of 1300 (= 400 + 900) gas tanks are
available at the beginning of week 10.
As the gross requirements in week 10 are for 1000
gas tanks, this leaves a projected balance of 300 (= 400 +
900 - 1000) at the end of week 10 (i.e. at the beginning of
week 11). Since 300 gas tanks is greater than the
desired safety stock of 200 gas tanks, there are no net
requirements in week 10 and therefore no planned
order receipts.
Slide 23
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 10
The worksheet now looks as follows:
ITEM:: GAS TANK
LEAD TIME: 2
LOT SIZE: L-F-L SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
12
13
14
1300 800
0
15
16
1400 900
300
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 24
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 11
There are no gross requirements for week 11. Thus,
the projected balance at the end of week 11 (the
beginning of week 12) remains at 300 and there are no
net requirements for week 11.
ITEM: GAS TANK
LOT SIZE: L-F-L
LEAD TIME: 2
SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
300
300
0
0
12
13
14
1300 800
0
15
16
1400 900
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 25
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 12
In week 12 there are gross requirements for 1300
gas tanks. In addition, 200 gas tanks must remain in
inventory as safety stock. Hence, the total requirement
for week 12 is 1500 (= 1300 + 200) gas tanks. Since there
is a projected balance of 300 at the beginning of week
12, the net requirement for week 12 is 1200 (= 1300 +
200 - 300) gas tanks.
As a lot-for-lot rule is being used, this means that
there should be a planned order receipt of 1200 gas
tanks in week 12 (at the beginning of the week). Since
the lead time for gas tanks is two weeks, this means that
there should be a planned order release for the 1200 gas
tanks in week 10 (= 12 - 2).
Slide 26
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 12
The MRP worksheet would now look as follows:
ITEM: GAS TANK
LOT SIZE: L-F-L
LEAD TIME: 2
SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
13
14
1300 800
0
300
300
200
0
0
1200
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
15
16
1400 900
1200
1200
Slide 27
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 13
The same approach is used to calculate the net
requirements for week 13. The formula for determining
the net requirements using the lot-for-lot rule is:
(Net Requirements) = (Gross Requirements) +
(Projected Balance) - (Desired Safety Stock)
The projected balance at the end of the week will
equal the desired safety stock. Hence net requirements
for week 13 will be 800 (= 800 + 200 - 200), and the
projected balance at the end of the week will be 200.
Because a lot for lot rule is being used, this implies
there should be a planned order receipt of 800 gas tanks
in week 13. Given the two week lead time, the planned
order release of these 800 gas tanks would be week 11.
Slide 28
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 13
Now the MRP worksheet would be:
ITEM: GAS TANK
LEAD TIME: 2
LOT SIZE: L-F-L SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
300
300
0
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
13
14
1300 800
0
200
15
16
1400 900
200
1200 800
1200 800
1200 800
Slide 29
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Weeks 14 & 15
In week 14, since the gross requirements are 0, the
net requirements will also be 0 and there will be no
planned order receipt. The projected balance at the end
of week 14 will remain at the safety stock level of 200
units.
For week 15, 1400 gas tanks are required. Hence,
the net requirements for this week will be 1400 (= 1400
+200 - 200). Thus, there should be a planned order
receipt of 1400 units in week 15. These should have a
planned order release date of week 13 (= 15 - 2). The
projected balance at the end of week 15 will be 200
units.
Slide 30
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Weeks 14 & 15
Now, the MRP worksheet is:
ITEM: GAS TANK
LEAD TIME: 2
LOT SIZE: L-F-L SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
300
300
0
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
13
14
1300 800
0
200
200
1200 800
1200 800
1200 800
15
16
1400 900
200
200
0
1400
1400
1400
Slide 31
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 16
For week 16, the gross requirements of 900
translates into net requirements of 900 (= 900 + 200 200), and a planned order receipt of 900. The planned
order release date for this order will be week 14 (= 16 2). The projected balance at the end of week 16 will
then be equal to the desired safety stock of 200 units.
Slide 32
Example: Columbia Mopeds

MRP Worksheet for Gas Tank . . . Week 16
Thus the completed MRP worksheet for weeks 10
through 16 is:
ITEM: GAS TANK
LOT SIZE: L-F-L
LEAD TIME: 2
SAFETY STK: 200
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
900
PROJECTED BALANCE
NET REQUIREMENTS
400
300
300
0
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
13
14
1300 800
0
200
200
1200 800
200
0
1200 800
1200 800
15
16
1400 900
200
200
1400 900
1400 900
1400 900
Slide 33
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 10
Assume there is a projected balance of 600 frames
at the beginning of week 10 and a scheduled receipt of
2000 frames in week 10. The firm uses a fixed order size
of 2000 frames and desires no safety stock of frames.
Lead time for frames is 3 weeks.
The following chart gives the weekly gross
requirements for frames:
WEEK
10
11
12
13
14
15
16
GR. REQ.
1000
0
1300
800
0
1400
900
Slide 34
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Initially
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
12
13
14
1300 800
0
15
16
1400 900
600
NET REQUIREMENTS
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 35
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 10
Note that there are 2600 frames (the 600 projected
balance plus the 2000 scheduled receipt) available for
week 10, but only 1000 frames are required. Hence the
projected balance at the end of week 10 (the beginning
of week 11) is 1600 (= 600 + 2000 - 1000). Thus, there are
no net requirements and no planned order receipts are
necessary.
Slide 36
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 10
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
12
13
14
1300 800
0
15
16
1400 900
600 1600
NET REQUIREMENTS
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 37
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Weeks 11 & 12
Since the gross requirements in week 11 are 0, the
projected balance at the end of week 11 remains at 1600
units. Hence, there are no net requirements and no
planned order receipts for week 11.
In week 12, the gross requirements of 1300 are less
than the projected balance of 1600 units. Therefore, the
net requirements and the planned order receipts for
week 12 are 0. The projected balance is now 300 (= 1600
- 1300).
Slide 38
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Weeks 11 & 12
The MRP worksheet is now:
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
NET REQUIREMENTS
12
13
14
1300 800
0
15
16
1400 900
600 1600 1600 300
0
0
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
Slide 39
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 13
In week 13, the gross requirements of 800 frames
exceed the projected balance of 300 at the beginning of
the week. The net requirements for week 13 would
then be 500 (= 800 - 300).
Hence there must be a planned order receipt. As
the lot size is 2000, this is the planned order receipt.
Since the lead time is 3 weeks, the planned order release
date for this order must be week 10 (= 13 - 3).
This order will leave a projected balance of 1500 (=
2000 - 500) at the end of week 13.
Slide 40
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 13
Now the MRP worksheet is:
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
NET REQUIREMENTS
13
14
1300 800
0
15
16
1400 900
600 1600 1600 300 1500
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
0
0
500
2000
2000
Slide 41
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Weeks 14 & 15
Since the gross requirements for week 14 are 0,
there are no net requirements and no planned order
receipt and the projected balance at the end of week 14
remains at 1500.
In week 15, the gross requirements of 1400 units is
less than the projected balance of 1500 units at the
beginning of the week. Thus the net requirements and
the planned order receipts are both 0. However, the
projected balance at the end of week 15 is now 100 (=
1500 - 1400).
Slide 42
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Weeks 14 & 15
The MRP worksheet is now:
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
NET REQUIREMENTS
13
14
1300 800
0
15
16
1400 900
600 1600 1600 300 1500 1500 100
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
0
0
500
0
0
2000
2000
Slide 43
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 16
In week 16, the gross requirements of 900 units
exceed that of the projected balance of 100 units. Hence
the net requirements in week 16 are 800 units (= 900 100). Thus, there must be a planned order receipt in
week 16 of the fixed order size of 2000.
Given the 3 week lead time, the planned order
release of these 2000 units must be week 13 (= 16 - 3).
The projected balance at the end of week 16 will be 1200
units (= 2000 - 800).
Slide 44
Example: Columbia Mopeds

MRP Worksheet for Frames . . . Week 16
The complete MRP worksheet is:
ITEM: FRAME
LOT SIZE: 2000
LEAD TIME: 3
SAFETY STK: 0
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
NET REQUIREMENTS
13
14
1300 800
0
15
16
1400 900
600 1600 1600 300 1500 1500 100 1200
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
12
0
0
500
2000
2000
0
0
800
2000
2000
Slide 45
Example: Columbia Mopeds

MRP Worksheet for Frames . . . With Safety Stock
Now consider a desired safety stock of 300 for
frames. Note in the completed worksheet for frames
that the projected balance exceeds the desired safety
stock level of 300 in weeks 10 through 14. In week 13,
however, the true net requirements are 800 (= gross
requirements (800) + safety stock (300) - projected
balance at the end of week 12 (300)).
In week 15, the completed worksheet shows a
projected balance of only 100. This is less than the
desired safety stock of 300. Hence the new net
requirements for week 15 is 200 units (= gross
requirements (1400) + safety stock (300) - projected
balance at the end of week 14 (1500)).
Slide 46
Example: Columbia Mopeds

MRP Worksheet for Frames . . . With Safety Stock
There should be a planned order receipt of the
fixed size of 2000 in week 15. Since there is a 3 week
lead time, this means a planned order release date of
week 12 (= 15 - 3).
In week 16, the gross requirements of 500 plus the
desired safety stock of 300 does not exceed the
projected balance of 2100 at the beginning of week 16
(end of week 15). Hence, the net requirements are 0
and there is no planned order receipt.
Then the projected balance at the end of week 16
will be 1200 units (= 2100 - 900).
Slide 47
Example: Columbia Mopeds

MRP Worksheet for Frames . . . With Safety Stock
Thus the completed MRP worksheet when a safety
stock of 300 is desired is as follows:
ITEM: FRAME
LEAD TIME: 3
LOT SIZE: 2000 SAFETY STOCK: 300
WEEK
10
11
GROSS REQUIREMENTS
1000
0
SCHEDULED RECEIPTS
2000
PROJECTED BALANCE
NET REQUIREMENTS
12
13
14
1300 800
0
16
1400 900
600 1600 1600 300 1500 1500 2100 1200
0
0
0
PLANNED ORDER RECEIPTS
PLANNED ORDER RELEASES
15
800
2000
2000
0
200
0
2000
2000
Slide 48
The End of Chapter 14
Slide 49