Solutions Chapter14

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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 1 2 3 4 5 6 7 8 9 10 11 12

A Gross requirement 100 50 150

Order release 100 50 150

H Gross requirement 100 50

Order release 100 50

C Gross requirement 100 100 50 50 150

Order release 100 100 50 50 150

(b)

Level: 0 Parent: — Quantity:

Item: A Lead Time: 1 Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 100 50 150

Scheduled receipt

On hand 0 0 0

Net requirement 100 50 150

Planned order receipt 100 50 150

Planned order release 100 50 150


Item: H Lead Time: 1 Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 100 50

Scheduled receipt

On hand 0 0

Net requirement 100 50

Planned order receipt 100 50

Planned order release 100 50

Level: 1 Parent: A, H Quantity: 1X

Item: C Lead Time: 2 Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 100 100 50 50 150

Scheduled receipt

On hand 50 0 0 0 0

Net requirement 50 50 100 50 50 150

Planned order receipt 50 100 50 50 150

Planned order release 50 100 50 50 150

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Question 14.12

(a)

Week

Item 1 2 3 4 5 6 7 8 9 10 11 12

A Gross requirement 100 50 150

On hand: — 0 0 0 0

Net requirement 100 50 150

Order receipt 100 50 150

Order release 100 50 150

H Gross requirement 100 50

On hand: — 0 0 0


Order receipt 100 50


B Gross requirement 100 50 150

On hand: 100 100 0 0




C Gross requirement 100 100 50 50 150

On hand: 50 50 0 0 0 0

Net requirement 50 100 50 50 150

Order receipt 50 100 50 50 150

Order release 50 100 50 50 150

J Gross requirement 100 50

On hand: 100 100 0


Order receipt 0 50

Order release 50

K Gross requirement 100 50

On hand: 100 100 0


Order receipt 0 50

Order release 50

D Gross requirement 50 150

On hand: 50 50 0

Net requirement 150

Order receipt 150

Order release 150

E Gross requirement 50 100 150

On hand: 75 75 25 0




F Gross requirement 50 100 50 100 150

On hand: 75 75 25 0 0 0

Net requirement 75 50 100 150

Order receipt 75 50 100 150

Order release 75 50 100 150

G Gross requirement 50 100 50 100 150

On hand: 75 75 25 0 0 0

Net requirement 75 50 100 150

Order receipt 75 50 100 150

Order release 75 50 100 150

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(b)

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Question 14.13

(a)

(b)

(c)


Item: 20 fan Lead Time: 1 Lot Size:

Week No. 1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 1,000

Scheduled receipt

On hand 100 100

Net requirement 900

Planned order receipt 900

Planned order release 900

Level: 1 Parent: 20 fan Quantity: 1X

Item: housing Lead Time: 1 week Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 900

Scheduled receipt

On hand 100 100

Net requirement 800



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Item: grills Lead Time: 2 weeks Lot Size: 500

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 200 200 400

Net requirement 1,600

Planned order receipt 2,000

Planned order release 2,000


Item: fan assembly Lead Time: 3 weeks Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 150 150

Net requirement 750




Item: electrical unit Lead Time: 1 week Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand

Net requirement 900



Level: 2 Parent: housing Quantity: 1X

Item: frame Lead Time: 2 weeks Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand

Net requirement 800




Item: supports Lead Time: 1 week Lot Size: 100

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 50





Item: handle Lead Time: 1 week Lot Size: 500

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 400 100

Net requirement 400



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Level: 2 Parent: fan assembly Quantity: 1X

Item: hub Lead Time: 1 week Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand

Net requirement 750



Level: 2 Parent: fan assembly Quantity: 5X

Item: blades Lead Time: 2 weeks Lot Size: 100

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 50




Level: 2 Parent: electrical unit Quantity: 1X

Item: motor Lead Time: 1 week Lot Size: L4L

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand

Net requirement 900




Item: switch Lead Time: 1 week Lot Size: 12

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt

On hand 20 20 8

Net requirement 880




Item: knob Lead Time: 1 week Lot Size: 25

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


Scheduled receipt 200

On hand: 20 200 200 200

Net requirement



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Question 14.17 Lot-for-lot (L4L) Ordering Policy

Week

1 2 3 4 5 6 7 8 9 10 11 12

Gross requirements 30 40 30 70 20 10 80 50

Beginning inventory 40 10 10 0 0 0 0 0 0 0 0 0

Ending inventory 40 10 10 0 0 0 0 0 0 0 0 0 0

Order receipts 30 30 70 20 10 80 50

Order releases 30 30 70 20 10 80 50

CT = Order cost + holding cost = 7 orders $150/order + 20 units $2.50/unit/period = $1,100

Question 14.18 Economic Order Quantity (EOQ)

2 2 330 15057.4, or 57 units

2.50 12

DSQ

H

where D = period demand, S = setup or order cost, H = holding cost.

Week

1 2 3 4 5 6 7 8 9 10 11 12

Gross requirement 30 40 30 70 20 10 80 50

Beginning inventory 40 0 67 27 84 54 –16 21 78 68 –12 –12

Ending inventory 40 10 10 27 27 54 –16* 21 21 68 –12* –12 –5*

Order receipts 57 57 57 57 57

Order release 57 57 57 57 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 total cost:

Order cost Holding cost =2

330 150 57 (12 2.50)

57 2

868.42 855.00 $1,723.42

T

DS QHC

Q

Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.

330Reorder point Demand during lead time units week 1 week

12

27.5, or 28 units

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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

demand during lead time‖ is not a very good measure of the necessary reorder point.

You may wish to double the size of the fourth order in order to get:

Level: Parent: Quantity:

Item: Lead Time: 1 Lot Size: EOQ

Week No. 1 2 3 4 5 6 7 8 9 10 11 12


On hand 40 40 10 10 27 27 54 41 21 21 11 45 45 52

Net requirement 0 30 3 16 69 5

Planned order receipt 57 57 57 114 57

Planned order release 57 57 57 114 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:

Setup cost 150EPP 60

Holding cost 2.50

Next, determine the cumulative part periods that are closest to your computed EPP: Periods Cumulative Costs

Combined Net Req. Part Periods Order Hold

1 0 0 + 25

1, 2 0 0 + 50

1, 2, 3 30 150 + 50

1, 2, 3, 4 30 150 + 50

1, 2, 3, 4, 5* 60 30 0 + 30 2 = 60 150 + 200

1, 2, 3, 4, 5, 6 130 30 0 + 30 2 + 70 3 = 270 150 + 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 Cumulative Costs Combined Net Req. Part Periods Order Hold

6 70 70 0 = 0 150 + 0 6, 7 90 70 0 + 20 1 = 20 150 + 50 6, 7, 8 90 70 0 + 20 1 = 20 150 + 50 6, 7, 8, 9* 100 70 0 + 20 1 + 10 3 = 50 150 + 125 6, 7, 8, 9, 10 180 70 0 + 20 1 + 10 3 + 80 4 = 370 150 + 925

* The part periods for an order encompassing periods 6, 7, 8, and 9 most nearly approximates the EPP of 60.

Periods Cumulative Costs Combined Net Req. Part Periods Order Hold

10 80 80 0 = 0 150 + 0 10, 11 80 80 0 = 0 150 + 0 10, 11, 12* 130 80 0 + 50 2 = 100 150 + 250

* 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:

Week

1 2 3 4 5 6 7 8 9 10 11 12


Beginning inventory 40 10 10 30 30 0 30 10 10 0 50 50

Ending inventory 10 10 30 30 0 30 10 10 0 50 50 0

Order receipts 60 100 130

Order releases 60 100 130

Calculate total cost: CT = Order cost + holding cost

= 3 orders $150/order + 230 units $2.50/unit/period = $1,025.00

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Solutions Chapter14