CHAPTER 14: MATERIALS REQUIREMENT PLANNING (MRP) – Suggested Solutions to Selected Questions
Summer II, 2009
Question 14.1 An exploded bill yields the following: Item J: 200 units Item K: 200
1 = 200 units
Item L: 200
4 = 800 units
Item M: 200
2 = 400 units.
Question 14.2 The time-phased assembly plan for the gift bags is:
Production of item M should be started by noon. Question 14.3 (a) Product structure:
(b)
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Question 14.11 (a) Week Item
A H C
1
2
3
4
5
6
Gross requirement Order release
7
8
9
100 100
Gross requirement Order release
10
50 50
100
100
100 50
100 50
12
150 150
100 100
Gross requirement Order release
11
50 50
50 150
50
150
Quantity: Lot Size: L4L 7 8 9
10
11
100
50
150
0 100 100
0 50 50
0 150 150
(b) Level: 0 Item: A Week No.
1
Parent: — Lead Time: 1 2 3
4
5
6
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release Level: 0 Item: H Week No.
100
1
Parent: — Lead Time: 1 2 3
4
5
6
Quantity: Lot Size: L4L 7 8 9
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release Level: 1 Item: C Week No.
Gross requirement Scheduled receipt On hand Net requirement 50 Planned order receipt Planned order release
2
1
Parent: A, H Lead Time: 2 2 3
4
5
50
6
100
50
12
150
10
11
100
50
0 100 100
0 50 50
100
50
Quantity: 1X Lot Size: L4L 7 8 9
10
11
100
100
50
50
150
50 50 50 50
0 100 100 50
0 50 50 150
0 50 50
0 150 150
12
12
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Question 14.12 (a) Week Item
A
H
B
C
J
K
D
E
F
G
3
1
Gross requirement On hand: — Net requirement Order receipt Order release Gross requirement On hand: — Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release Gross requirement On hand: Net requirement Order receipt Order release
2
3
4
5
6
7
8
9
100 0 100 100
0
100 0
100 100
50
50
100
100 50 50 50 50
100
100
100 0 100 100 50
150
100 0 100 100
50 0 50 50
50
50
50 0 50 50 150
150 0 150 150 50 0 50 50
100 100 0 0 50
50 0 50 50
100 100 0 0 50
50 0 50 50
50 50
12
150 0 150 150
50
50 0 50 50 150
50
11
50 0 50 50
100 100
10
150 0 150 150
150 0 150 150 150
50 75
75
50 75
75
75 75
50 50 75
75
100 25 75 75
150 0 150 150
75
150
100 25 75 75 100
50 0 50 50 150
100 0 100 100
150 0 150 150
100 25 75 75 50
50 0 50 50 100
100 0 100 100 150
150 0 150 150
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(b)
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Question 14.13 (a)
(b)
(c) Level: 0 Item: 20 fan Week No.
1
Parent: — Lead Time: 1 2 3
4
5
Gross requirement Scheduled receipt On hand 100 Net requirement Planned order receipt Planned order release Level: 1 Item: housing Week No.
Gross requirement Scheduled receipt On hand 100 Net requirement Planned order receipt Planned order release
5
6
Quantity: Lot Size: 7 8
9
10
11
12
9
10
11
12
1,000 100 900 900 900
1
Parent: 20 fan Lead Time: 1 week 2 3 4
5
6
Quantity: 1X Lot Size: L4L 7 8
900 100 800 800 800
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Level: 1 Item: grills Week No.
1
Parent: 20 fan Lead Time: 2 weeks 2 3 4
Gross requirement Scheduled receipt On hand 200 Net requirement Planned order receipt Planned order release
Level: 1 Item: fan assembly Week No.
Parent: 20 fan Lead Time: 3 weeks 1 2 3 4
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
6
11
12
Quantity: 1X Lot Size: L4L 7 8
9
10
11
12
Quantity: 1X Lot Size: L4L 7 8
9
10
11
12
6
Quantity: 1X Lot Size: L4L 7 8
9
10
11
12
6
Quantity: 2X Lot Size: 100 7 8
9
10
11
12
6
Quantity: 1X Lot Size: 500 7 8
9
10
11
12
400
5
6
900 150 750 750 750
Parent: 20 fan Lead Time: 1 week 1 2 3 4
5
6
900
900 900 900
1
Parent: housing Lead Time: 2 weeks 2 3 4
5
800
800 800 800
1
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: handle Week No.
10
2,000
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: supports Week No.
9
200 1,600 2,000
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: frame Week No.
6
1,800
Gross requirement Scheduled receipt On hand 150 Net requirement Planned order receipt Planned order release
Level: 1 Item: electrical unit Week No.
5
Quantity: 2X Lot Size: 500 7 8
Parent: housing Lead Time: 1 week 2 3 4
5
1,600 50 1,550 1,600 1,600
1
Parent: housing Lead Time: 1 week 2 3 4
5
800 400 400 500
100
500
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Level: 2 Item: hub Week No.
1
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: blades Week No.
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: motor Week No.
Parent: fan assembly Lead Time: 1 week 2 3 4 5
Gross requirement Scheduled receipt On hand: 20 Net requirement Planned order receipt Planned order release
7
10
11
12
6
Quantity: 5X Lot Size: 100 7 8
9
10
11
12
6
Quantity: 1X Lot Size: L4L 7 8
9
10
11
12
6
Quantity: 1X Lot Size: 12 7 8
9
10
11
12
Quantity: 1X Lot Size: 25 7 8
9
10
11
12
750 750 750
1
Parent: fan assembly Lead Time: 2 weeks 2 3 4
5
3,750 50 3,750 3,800 3,800
1
Parent: electrical unit Lead Time: 1 week 2 3 4 5
900
900 900 900
1
Parent: electrical unit Lead Time: 1 week 2 3 4 5
Gross requirement Scheduled receipt On hand 20 Net requirement Planned order receipt Planned order release
Level: 2 Item: knob Week No.
9
750
Gross requirement Scheduled receipt On hand Net requirement Planned order receipt Planned order release
Level: 2 Item: switch Week No.
6
Quantity: 1X Lot Size: L4L 7 8
900 20 880 888
8
888
1
Parent: electrical unit Lead Time: 1 week 2 3 4 5
6
900 200 200
200
200 700
700
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Question 14.17
Lot-for-lot (L4L) Ordering Policy
Gross requirements Beginning inventory Ending inventory Order receipts Order releases
C T T =
40
Week 5
1
2
3
4
30 40 10
10 10
40 10 0 30
0 0
30
30 0 0 30 70
30
Order cost + holding cost = 7 orders
Question 14.18
6
7
8
70 0 0 70 20
20 0 0 20
0 0 10
$150/order + 20 units
9
10
11
12
10 0 0 10 80
80 0 0 80
0 0
50 0 0 50
50
$2.50/unit/period = $1,100
Economic Order Quantity (EOQ)
Q
2 DS
2
330 2.50
H
150 12
57.4, or 57 units
where D = period demand, S = setup or order cost, H = holding cost.
Reorder point
330
Demand during lead time
12
unit s week
1 week
27.5, 27.5, or 28 units
Gross requirement Beginning inventory Ending inventory 40 Order receipts Order release
1
2
3
4
5
6
30 40 10
0 10
40 67 27 57
27 27
30 84 54 57
70 54 – 16* 16*
57
57
57
Week 7
20 – 16 16 21 57
8
9
10
11
21 21
10 78 68 57
80 68 – 12* 12*
– 12 12 – 12 12
57
57
12
50 – 12 12 – 5* 5* 57 57
* Stockouts = 16 + 12 + 5 = 33
Total inventory = 10 + 10 + 27 + 27 + 54 + 21 + 21 + 68 = 238 Actual total cost: CT
= Order cost + Holding cost + Stockout cost = 6 orders x $150/order + 238 units x $2.50 + 33 units x $10/unit stockout = 900.00 + 595.00 + 330.00 = $1,825.00
Theoretical
C T
total cost:
Order co cost
Holding co cost =
330
57
150
57 868.42
855.00
(12
DS
QH
Q
2
2.50)
2 $1, 72 723.42
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.
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Note: The actual cost of using the EOQ policy under this case of varying demand is more than the theoretical cost. In addition, we were forced to use back orders when stockouts occurred. The poor performance with respect to stockout is due to the fact that ―average necessar y reorder point. demand during lead time‖ is not a very good measure of the necessary You may wish to double the size of the fourth order in order to get: Level: Item: Week No.
1
Gross requirements On hand 40 Net requirement Planned order receipt Planned order release
30 40 0
Parent: Lead Time: 1 2 3
10
40 10 30 57
57
4
27
57
5
6
30 27 3 57 57
70 54 16 57
Quantity: Lot Size: EOQ 7 8 9
20 41
21
10 21
114
10
80 11 69 114
11
45
12
50 45 5 57
52
57
Total cost with this approach: Setups: 5
150 = $750
Holding: 2.50
364 = $910
Setup + holding = total cost = $1,660.00
Question 14.19
Part-Period Balancing (PPB)
First, calculate the EPP:
EPP
Setup cost
150
Holding co cost
2.50
60
Next, determine the cumulative part periods that are a re closest to your computed EPP: Periods Combined
1 1, 2 1, 2, 3 1, 2, 3, 4 1, 2, 3, 4, 5* 1, 2, 3, 4, 5, 6
Cumulative Net Req.
0 0 30 30 60 130
Part Periods
30 30
0 + 30 0 + 30
2 = 60 2 + 70
3 = 270
Costs Order Hold
0 0 150 150 150 150
+ + + + + +
25 50 50 50 200 725
* The part periods for an order encompassing periods 1, 2, 3, 4, and 5 most nearly approximates the EPP of 60.
Note: (1) We have assumed that: (a) a product ordered during a calendar week is available at the beginning of the following week; (b) shipments during a week take place at the beginning of the week. (2) DS and POM for Windows will produce the same result.
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Periods Combined 6 6, 7 6, 7, 8 6, 7, 8, 9* 6, 7, 8, 9, 10
Cumulative Net Req. 70 90 90 100 180
Part Periods
70 70 70 70 70
0=0 0 + 20 0 + 20 0 + 20 0 + 20
1 = 20 1 = 20 1 + 10 1 + 10
3 = 50 3 + 80
4 = 370
Costs Order Hold 150 + 0 150 + 50 150 + 50 150 + 125 150 + 925
* The part periods for an order encompassing periods 6, 7, 8, and 9 most nearly approximates the EPP of 60.
Periods Combined 10 10, 11 10, 11, 12*
Cumulative Net Req. 80 80 80 80 130 80
Costs Order Hold 150 + 0 150 0 + 150 + 250
Part Periods
0=0 0=0 0 + 50
2 = 100
* The part periods for an order encompassing periods 6, 7, 8, and 9 most nearly approximates the EPP of 60.
Finally, complete the materials requirement schedule with order receipts in weeks 3, 6 and 10:
Gross requirements Beginning inventory Ending inventory Order receipts Order releases
1 30 40 10
2
10 10
3 40 10 30 60
4
30 30
60
Week 5 6 7 30 70 20 30 0 30 0 30 10 100 100
8
10 10
9 10 10 0
10 11 12 80 50 0 50 50 50 50 0 130
130
Calculate total cost: C T T
10
= Order cost + holding cost = 3 orders $150/order + 230 units = $1,025.00
$2.50/unit/period
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