Chapter 14, Problem 32P

Using the data for the coffee table in Problem 14.31, build a labor schedule when the labor standard for each top is 2 labor-hours; each leg including brass cap installation requires, $\frac{1}{4}$hour, as does each pair of braces. Base assembly requires 1 labor-hour, and final assembly requires 2 labor-hours. What is the total number of labor-hours required each day, and how many employees are needed each day at 8 hours per day?

Summary Introduction

To determine: The number of labor hours and employees needed each day.

Explanation of Solution

Given information:

• Table requires 1 top, 4 legs, 1/8 gallon of strain, 1/16 gallon of blue, 2 short braces, 2 long braces, and brass cap on the bottom of each leg.
• 100 gallons of glue as inventory.
• All items except brass caps, stain and glue are planned on a Lot for lot basis.
• Caps are purchased in 1000’s, stain and glue by gallon.
• Lead time = 1 (for each item).
• 640 coffee tables needed on day 5 and 6.
• 128 coffee tables needed on days 7 and 8.
• Labor standard for each top is 2 labor hours.
• Each leg with brass cap installation and each pair of braces need ¼ hour.
• Base assembly needs 1 labor hour.
• Final assembly of table requires 2 labor hours.
• Number of hours per day is 8.

Product structure:

Net requirements plan:

Table:

	Period (Day)
Table	1	2	3	4	5	6	7	8
Gross requirements					640	640	128	128
Scheduled receipt
On hand (0)					0	0	0	0
Net requirement					640	640	128	128
Planned order receipt					640	640	128	128
Planned order release				640	640	128	128

Day 5:

The gross requirement is 640 (1 assembly) of Coffee table derived from the given information. The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 640 (1 assembly) of Coffee table derived from the given information. The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 5 which will be the planned order receipt in day 6.

Day 7:

The gross requirement is 128 (1 assembly) of Coffee table derived from the given information. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 6 which will be the planned order receipt in day 7.

Day 8:

The gross requirement is 128 (1 assembly) of Coffee table derived from the given information. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 7 which will be the planned order receipt in day 8.

Top:

	Period (Day)
Top	1	2	3	4	5	6	7	8
Gross requirements				640	640	128	128
Scheduled receipt
On hand (0)				0	0	0	0
Net requirement				640	640	128	128
Planned order receipt				640	640	128	128
Planned order release			640	640	128	128

Day 4:

The gross requirement is 640 (1 assembly) of Top derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 640 (1 assembly) of Top derived from the planned order release of Table.  The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 128 (1 assembly) of Top derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 5 which will be the planned order receipt in day 6.

Day 7:

The gross requirement is 128 (1 assembly) of Top derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 6 which will be the planned order receipt in day 7.

Stain:

	Period (Day)
Stain	1	2	3	4	5	6	7	8
Gross requirements				80	80	16	16
Scheduled receipt
On hand (0)				0	0	0	0
Net requirement				80	80	16	16
Planned order receipt				80	80	16	16
Planned order release			80	80	16	16

Day 4:

The gross requirement is 80 (1 assembly) of Stain derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 80. The lead time is 1 week. The planned order release will be 80 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 80 (1 assembly) of Stain derived from the planned order release of Table.  The On hand is 0. Therefore, the net requirement is 80. The lead time is 1 week. The planned order release will be 80 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 16 (1 assembly) of Stain derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 16. The lead time is 1 week. The planned order release will be 16 in day 5 which will be the planned order receipt in day 6.

Day 7:

The gross requirement is 16 (1 assembly) of Stain derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 16. The lead time is 1 week. The planned order release will be 16 in day 6 which will be the planned order receipt in day 7.

Glue:

	Period (Day)
Glue	1	2	3	4	5	6	7	8
Gross requirements				40	40	8	8
Scheduled receipt
On hand (100)				100	60	20	12	4
Net requirement				0	0	0	0
Planned order receipt
Planned order release

Day 4:

The gross requirement is 40 (1 assembly) of Glue derived from the planned order release of Table. The On hand is 100. Therefore, the net requirement is 0. Therefore there will be no planned order release. The excess inventory 60 will be available at week 5.

Day 5:

The gross requirement is 40 (1 assembly) of Glue derived from the planned order release of Table. The On hand is 60. Therefore, the net requirement is 0. Therefore there will be no planned order release. The excess inventory 20 will be available at week 6.

Day 6:

The gross requirement is 8 (1 assembly) of Glue derived from the planned order release of Table. The On hand is 20. Therefore, the net requirement is 0. Therefore there will be no planned order release. The excess inventory 12 will be available at week 7.

Day 7:

The gross requirement is 8 (1 assembly) of Glue derived from the planned order release of Table. The On hand is 12. Therefore, the net requirement is 0. Therefore there will be no planned order release. The excess inventory 8 will be available at week 8.

Base assembly:

	Period (Day)
Base	1	2	3	4	5	6	7	8
Gross requirements				640	640	128	128
Scheduled receipt
On hand (0)				0	0	0	0
Net requirement				640	640	128	128
Planned order receipt				640	640	128	128
Planned order release			640	640	128	128

Day 4:

The gross requirement is 640 (1 assembly) of base assembly derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 640 (1 assembly) of base assembly derived from the planned order release of Table.  The On hand is 0. Therefore, the net requirement is 640. The lead time is 1 week. The planned order release will be 640 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 128 (1 assembly) of base assembly derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 5 which will be the planned order receipt in day 6.

Day 7:

The gross requirement is 128 (1 assembly) of base assembly derived from the planned order release of Table. The On hand is 0. Therefore, the net requirement is 128. The lead time is 1 week. The planned order release will be 128 in day 6 which will be the planned order receipt in day 7.

Short brace:

	Period (Day)
Short Brace	1	2	3	4	5	6	7	8
Gross requirements			1,280	1,280	256	256
Scheduled receipt
On hand (0)			0	0	0	0
Net requirement			1,280	1,280	256	256
Planned order receipt			1,280	1,280	256	256
Planned order release		1,280	1,280	256	256

Day 3:

The gross requirement is 1,280 (2 assembly) of short brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 1,280. The lead time is 1 week. The planned order release will be 1,280 in day 2 which will be the planned order receipt in day 3.

Day 4:

The gross requirement is 1,280 (2 assembly) of short brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 1,280. The lead time is 1 week. The planned order release will be 1,280 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 256 (2 assembly) of short brace derived from the planned order release of base assembly.  The On hand is 0. Therefore, the net requirement is 256. The lead time is 1 week. The planned order release will be 256 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 256 (2 assembly) of short brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 256. The lead time is 1 week. The planned order release will be 256 in day 5 which will be the planned order receipt in day 6.

Long brace:

	Period (Day)
Long Brace	1	2	3	4	5	6	7	8
Gross requirements			1,280	1,280	256	256
Scheduled receipt
On hand (0)			0	0	0	0
Net requirement			1,280	1,280	256	256
Planned order receipt			1,280	1,280	256	256
Planned order release		1,280	1,280	256	256

Day 3:

The gross requirement is 1,280 (2 assembly) of long brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 1,280. The lead time is 1 week. The planned order release will be 1,280 in day 2 which will be the planned order receipt in day 3.

Day 4:

The gross requirement is 1,280 (2 assembly) of long brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 1,280. The lead time is 1 week. The planned order release will be 1,280 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 256 (2 assembly) of long brace derived from the planned order release of base assembly.  The On hand is 0. Therefore, the net requirement is 256. The lead time is 1 week. The planned order release will be 256 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 256 (2 assembly) of long brace derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 256. The lead time is 1 week. The planned order release will be 256 in day 5 which will be the planned order receipt in day 6.

Leg:

	Period (Day)
Leg	1	2	3	4	5	6	7	8
Gross requirements			2,560	2,560	512	512
Scheduled receipt
On hand (0)
Net requirement			2,560	2,560	512	512
Planned order receipt			2,560	2,560	512	512
Planned order release		2,560	2,560	512	512

Day 3:

The gross requirement is 2,560 (4 assembly) of leg derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 2,560. The lead time is 1 week. The planned order release will be 2,560 in day 2 which will be the planned order receipt in day 3.

Day 4:

The gross requirement is 2,560 (4 assembly) of leg derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 2,560. The lead time is 1 week. The planned order release will be 2,560 in day 3 which will be the planned order receipt in day 4.

Day 5:

The gross requirement is 512 (4 assembly) of leg derived from the planned order release of base assembly.  The On hand is 0. Therefore, the net requirement is 512. The lead time is 1 week. The planned order release will be 512 in day 4 which will be the planned order receipt in day 5.

Day 6:

The gross requirement is 512 (4 assembly) of leg derived from the planned order release of base assembly. The On hand is 0. Therefore, the net requirement is 256. The lead time is 1 week. The planned order release will be 512 in day 5 which will be the planned order receipt in day 6.

Brass caps:

	Period (Day)
Brass caps	1	2	3	4	5	6	7	8
Gross requirements		2,560	2,560	512	512
Scheduled receipt
On hand (0)		0	440	880	368	856	856	856
Net requirement		2,560	2,120	0	144
Planned order receipt		3,000	3,000		1,000
Planned order release	3,000	3,000		1,000

Day 2:

The gross requirement is 2,560 (1 assembly) of brass caps derived from the planned order release of legs. The On hand is 0. Therefore, the net requirement is 2,560. The lead time is 1 week. The planned order release will be 3,000 (1 Lot = 1,000) in day 1 which will be the planned order receipt in day 2. The excess inventory of 440 is available at day 3.

Day 3:

The gross requirement is 2,560 (1 assembly) of brass caps derived from the planned order release of legs. The On hand is 440. Therefore, the net requirement is 2,120. The lead time is 1 week. The planned order release will be 3,000 (1 Lot = 1,000) in day 2 which will be the planned order receipt in day 3. The excess inventory of 880 is available at day 4.

Day 4:

The gross requirement is 512 (1 assembly) of brass caps derived from the planned order release of legs. The On hand is 880. Therefore, the net requirement is 0. Therefore, there will be no planned release. The excess inventory of 368 is available at day 5.

Day 5:

The gross requirement is 512 (1 assembly) of brass caps derived from the planned order release of legs.  The On hand is 368. Therefore, the net requirement is 144. The lead time is 1 week. The planned order release will be 1,000 (1 Lot = 1,000) in day 4 which will be the planned order receipt in day 5. The excess inventory of 856 is available at the next day.

Calculation of labor hours / day:

Master Schedule	Hours Required	Day 1	Day 2	Day 3	Day 4	Day 5	Day 6	Day 7	Day 8
Table assembly	2				1280	1280	256	256
Top preparation	2			1280	1280	256	256
Assemble base	1			640	640	128	128
Long brace (2)	0.25		320	320	64	64
Short brace (2)	0.25		320	320	64	64
Leg (4)	0.25		640	640	128	128
Total Hours		0	1280	3200	3456	1920	640	256
Employees need  @ 8 hours / day		0	160	400	432	240	80	32

The master production schedule is derived from net requirements plan.

Formula to calculate number of hours / each day:

$\text{Number of hours}=\text{Number of hours per assembly}\times \text{Planned order release}$

Formula to calculate the number of employees per 8 hour day:

$\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}$

Day 2:

Calculation of total hours for each day for each component:

Long brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 1,280\\ =320\end{array}$

Short brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 1,280\\ =320\end{array}$

Leg:

$\begin{array}{c}\text{Number of hours}=0.25\times 2,560\\ =640\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\begin{array}{c}\text{Total hours}=320+320+640\\ =1,280\end{array}$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{1,280}{8}\\ =160\text{ employees}\end{array}$

Day 3:

Calculation of total hours for each day for each component:

Top preparation:

$\begin{array}{c}\text{Number of hours}=2\times 640\\ =1,280\end{array}$

Assemble base:

$\begin{array}{c}\text{Number of hours}=1\times 640\\ =640\end{array}$

Long brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 1,280\\ =320\end{array}$

Short brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 1,280\\ =320\end{array}$

Leg:

$\begin{array}{c}\text{Number of hours}=0.25\times 2,560\\ =640\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\begin{array}{c}\text{Total hours}=1,280+640+320+320+640\\ =3,200\end{array}$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{3,200}{8}\\ =400\text{ employees}\end{array}$

Day 4:

Calculation of total hours for each day for each component:

Table assembly:

$\begin{array}{c}\text{Number of hours}=2\times 640\\ =1,280\end{array}$

Top preparation:

$\begin{array}{c}\text{Number of hours}=2\times 640\\ =1,280\end{array}$

Assemble base:

$\begin{array}{c}\text{Number of hours}=1\times 640\\ =640\end{array}$

Long brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 256\\ =64\end{array}$

Short brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 256\\ =64\end{array}$

Leg:

$\begin{array}{c}\text{Number of hours}=0.25\times 512\\ =128\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\begin{array}{c}\text{Total hours}=1,280+1,280+640+64+64+128\\ =3,456\end{array}$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{3,456}{8}\\ =432\text{ employees}\end{array}$

Day 5:

Calculation of total hours for each day for each component:

Table assembly:

$\begin{array}{c}\text{Number of hours}=2\times 640\\ =1,280\end{array}$

Top preparation:

$\begin{array}{c}\text{Number of hours}=2\times 128\\ =256\end{array}$

Assemble base:

$\begin{array}{c}\text{Number of hours}=1\times 128\\ =128\end{array}$

Long brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 256\\ =64\end{array}$

Short brace:

$\begin{array}{c}\text{Number of hours}=0.25\times 256\\ =64\end{array}$

Leg:

$\begin{array}{c}\text{Number of hours}=0.25\times 512\\ =128\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\begin{array}{c}\text{Total hours}=1,280+256+128+64+64+128\\ =1,920\end{array}$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{1,920}{8}\\ =240\text{ employees}\end{array}$

Day 6:

Calculation of total hours for each day for each component:

Table assembly:

$\begin{array}{c}\text{Number of hours}=2\times 128\\ =256\end{array}$

Top preparation:

$\begin{array}{c}\text{Number of hours}=2\times 128\\ =256\end{array}$

Assemble base:

$\begin{array}{c}\text{Number of hours}=1\times 128\\ =128\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\begin{array}{c}\text{Total hours}=256+256+128\\ =640\end{array}$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{640}{8}\\ =80\text{ employees}\end{array}$

Day 7:

Calculation of total hours for each day for each component:

Table assembly:

$\begin{array}{c}\text{Number of hours}=2\times 128\\ =256\end{array}$

Calculation of total hours / day:

The total hours is calculated by summing all the hours needed for each component in a day.

$\text{Total hours}=256$

Calculation of number of employees per 8 hour day:

The number of employees is calculated by dividing the total hours per day with the number of hours per day.

$\begin{array}{c}\text{Number of employees}=\frac{\text{Total hours required per day}}{\text{Number of hours available per day}}\\ =\frac{256}{8}\\ =32\text{ employees}\end{array}$