Material Requirements
Planning
Dr. Everette S. Gardner, Jr.
End item
R
LT
Time
Component
LT
R
Raw material
LT
Time
R
LT
Time
Order point system with dependent demand
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End item
R
Component
Time
Raw material
Time
Time
The MRP approach
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The simultaneous probability
problem
• When components are ordered independently with an order point
system, the probability that all will be in stock at the same time is
much lower than the probabilities for individual components
• Computation:
Let Pn = Prob. that n components are
in stock simultaneously
Si = Prob. of stockout on one
order cycle for component i
Then
Pn = S1 x S2 x S3 … Sn
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The simultaneous probability
problem (cont.)
• Example:
End Item
1
2
3
S1 = .9
S2 = .9
S3 = .9
P3 = .9 x .9 x .9 = .729
= Prob. that all 3 components will be available at any given time to
build the end item
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Probabilities of simultaneous
availability of components
Number of
component items
1
2
3
4
5
6
7
8
9
10
15
20
25
Service level
90%
95%
.900
.950
.810
.902
.729
.857
.656
.814
.590
.774
.531
.735
.478
.698
.430
.663
.387
.630
.348
.599
.206
.463
.121
.358
.071
.277
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Demand
forecasts and
customer orders
Aggregate
planning/
master
scheduling
Product
design
changes
Bill
of
materials
MRP
system
Mfg. orders
Inventory
records
Capacity report
Purchase
orders
Detailed
scheduling
system
Inventory
transactions
Performance/
exceptions
Purchasing
dept.
MRP inputs and outputs
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Product tree vs. indented parts list
• Product tree
A
B(2)
D(1)
E(3)
D(2)
Level 0
C(4)
Level 1
F(1) G(3)
Level 2
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Product tree vs. indented parts list
(cont.)
• Indented parts list
● A
● B(2)
● D(1)
● E(3)
● C(4)
● D(2)
● F(1)
● G(3)
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Week
1
2
3
4
5
6
7
8
9
Lead
time
A
Gross Rqmts.
Planned order rls.
1
B
Gross Rqmts.
Planned order rls.
2
C
Gross Rqmts.
Planned order rls.
3
D
Gross Rqmts.
Planned order rls.
3
E
Gross Rqmts.
Planned order rls.
2
F
Gross Rqmts.
Planned order rls.
3
G
Gross Rqmts.
Planned order rls.
4
Quiz: MRP plan to produce 10 units
of A — due in week 9
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Problems in requirements
computations
• Product structure
• Recurring requirements within the planning
horizon
• Multilevel items
• Rescheduling open orders
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Product structure
• Bills of material are hierarchical with distinct levels
• To compute requirements, always proceed down bill of
materials, processing all requirements at one level before
starting another
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Product structure (cont.)
• Example:
Truck
Level
0
Inventory O.H.
0
A. Transmission (1)
1
2
B. Gearbox (1)
2
15
C. Gear (1)
3
7
D. Forging Blank (1)
4
46
Suppose we are to produce 100 trucks. What are the net
requirements for each component?
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Recurrence of requirements within
the planning horizon
• The same item may be required for several different lots within
the planning horizon – always process one lot entirely, level by
level, before starting the next.
• Example: One lot of 12 trucks, followed by 2nd lot of 100
Lot 1
Lot 2
Level 1: Gross requirements
12
100
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Multilevel items
The same item may appear at different levels on one or more BOMs –
result is multiple retrievals of same record to update system.
Examples:
1
2
3
X
Z
Y
A
A
A
4
A
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Multilevel items (cont.)
Solution: Low-level coding. Lowest level an item appears is coded
on inv. record. Processing delayed until that level reached.
1
X
Z
Y
2
3
4
A
A
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A
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Rescheduling open orders
• Tests for open order misalignment:
1. Are open orders scheduled for periods following the period in
which a net requirement appears?
2. Is an open order scheduled for a period in which
gross requirement ≤ inv. O. H. at end of preceding period?
3. Is lead-time sufficient?
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Rescheduling open orders (cont.)
• Example:
1
Gross requirements
30
Scheduled receipts
On hand
●
27
-3
Week
3
4
5
6
5
10
10
10
20
20
12
2
2
12
12
22
Most MRP systems make such schedule changes automatically.
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Tactical questions in MRP
• Regeneration vs. net change
• Lot sizing
• Safety stocks
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Regeneration vs. net change
• Regeneration
• Complete replanning of requirements and update of inventory
status for all items
• High data processing efficiency
• Usually initiated by weekly update of master schedule
• Net change
• Daily update based on inventory transactions
• More responsive to changing conditions
• Requires more discipline in file maintenance
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Lot sizing implications in MRP
• The load profiles at work centers in the system depend on the lot
sizing rules used
• Load profiles determine:
undertime / overtime
leadtimes
• Example:
Lot size
Lot size
Pd.
Demand
Rule 1
Rule 2
1
5
5
20
2
15
15
0
3
15
15
20
4
5
5
0
(Assume 1 unit requires 1 machine hour.)
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Machine hrs.
Lot sizing implications in MRP (cont.)
20
20
15
15
10
10
5
5
0
1
2
3
0
4
Load profile –
Rule 1
1
2
3
4
Load profile –
Rule 2
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Lot sizing techniques used in MRP
systems
• Lot-for-lot (L4L) – most used
• Economic order quantity (EOQ)
• Period order quantity (POQ)
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Lot-for-lot (L4L) example
Period
1
2
Net rqmts.
35
10
Planned order
35
10
3
4
5
6
7
8
9
Total
40
20
5
10 30
150
40
20
5
10 30
150
(Assume Ø LT)
The L4L technique:
Minimizes carrying costs
Is certainly the best method for
- highly discontinuous demand
- expensive purchased items
MRP
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EOQ example
Setup cost, S = $100
Unit price, C = $50
Holding costs, HR = .24 per annum
HP = .02 per period
Annual demand, D = 200
Q = (2DS / CHR)1/2 = 58
Period
1
2
Net rqmts.
35
10
Planned orders
58
Remnants
23
3
4
5
40
6
7
8
9
20
5
10
30
58
13
13
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10
58
31
11
6
54
24
24
25
Period order quantity example
Technique:
1. Compute EOQ to determine number of orders per year
2. Divide number of periods in one year by number of orders to get
ordering interval
EOQ = 58
Number of periods in one year = 12
D = 200
200 / 58 = 3.4 (orders per year)
12 / 3.4 = 3.5 (ordering interval)
Period
1
2
Net rqmts.
35
10
Planned orders
85
3
4
40
5
6
7
8
9
Total
20
5
10 30
150
35
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Safety stocks in MRP systems
• Need for safety stocks:
• Variations in demand due to end-item forecast errors and
inventory errors
• Variations in supply – both lead-times and quantities
• Since demand is not random, traditional statistical
techniques do not apply.
• Options to provide safety factors:
• Fixed quantity buffer stocks
• Safety lead-time
• Increase gross requirements
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Safety stocks in MRP systems (cont.)
• Fixed quantity buffer stocks
• Good rule of thumb: Set buffer = max. demand likely in a single
period
• Never generate order solely to replenish buffer stocks
• Safety time method
•
•
•
•
Simply order early
Distorts LTs and priorities
Better than buffer stocks for items with infrequent demand
Also better for purchases outside company
• Increase in gross requirements
• Should be done at end item level only so that
» Components available in matched sets
» Safety stocks are not duplicated at different levels
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