Chapter 9, Problem 20P

a)

Summary Introduction

To draw: The precedence diagram.

Answer to Problem 20P

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	3	-
B	6	-
C	7	A
D	5	A, B
E	2	B
F	4	C
G	5	F
H	7	D, E
I	1	H
J	6	E
K	4	G, I, J
Total	50

• Number of hours / day is 24
• Output is 96 instruments / day.

Precedence diagram:

b)

Summary Introduction

To determine: The cycle time.

Introduction:

Cycle time:

Cycle time is the total time taken to complete an unit of work from the beginning of the process to the end of the process.

Answer to Problem 20P

The  cycle time is 15 minutes / unit.

Explanation of Solution

Formula to calculate cycle time:

$\text{Cycle time}=\frac{\text{Number of hours per day}}{\text{Daily production}}\times \text{ Number of minutes / hour}$

Calculation of cycle time:

$\begin{array}{c}\text{Cycle time}=\frac{\text{24}}{\text{96}}\times \text{60}\\ \text{=}\frac{1,440}{96}\\ =15\text{ minutes / unit}\end{array}$

The  cycle time is 15 minutes / unit.

c)

Summary Introduction

To determine: The production rate.

Answer to Problem 20P

The  production rate is 144 units / day.

Explanation of Solution

Given information:

Cycle time = 10 minutes

Formula to calculate production rate:

$\text{Cycle time}=\frac{\text{Number of hours per day}}{\text{Cycle time}}\times \text{ Number of minutes / hour}$

Calculation of cycle time:

$\begin{array}{c}\text{Cycle time}=\frac{\text{24}}{\text{10}}\times \text{60}\\ \text{=}\frac{1,440}{10}\\ =144\text{ units / day}\end{array}$

The  production rate is 144 units / day.

d)

Summary Introduction

To determine: The theoretical minimum number of workstations.

Answer to Problem 20P

The theoretical minimum number of workstations is 5 workstations.

Explanation of Solution

Given information:

Cycle time = 10 minutes

Formula to calculate theoretical minimum number of workstations:

$\text{Workstations}=\frac{\text{Total task time}}{\text{Cycle time}}$

Calculation of theoretical minimum number of workstations:

$\begin{array}{c}\text{Workstations}=\frac{\text{50}}{\text{10}}\\ =5\text{ workstations}\end{array}$

The theoretical minimum number of workstations is 5 workstations.

e)

Summary Introduction

To determine: The efficiency.

Introduction:

Efficiency:

Efficiency is the measure of  what is actually produced as opposed to what can be theoretically produced with the same amount of resources.

Answer to Problem 20P

The efficiency is 83.3%.

Explanation of Solution

Given information:

Cycle time = 10 minutes

Number of workstations = 6

Formula to calculate efficiency:

$\text{Efficiency}=\frac{\text{Total task time}}{\text{Number of workstations}\times \text{Cycle time}}\times 100$

Calculation of efficiency:

$\begin{array}{c}\text{Efficiency}=\frac{50}{6\times 10}\times 100\\ =\frac{500}{60}\\ =83.3\%\end{array}$

The efficiency is 83.3%.

f)

Summary Introduction

To determine: The total idle time per cycle.

Answer to Problem 20P

The  idle time is 10 minutes / cycle.

Explanation of Solution

Given information:

Number of workstations = 6

Cycle time = 10

Calculation of total idle time per cycle:

$\begin{array}{c}\text{Total idle time}=\text{(Number of workstations}\times \text{Cycle time)}-\text{Total task time}\\ =\left(6\times 10\right)-50\\ =60-50\\ =10\text{ minutes / cycle}\end{array}$

The  total idle time is 10 minutes / cycle.

g)

Summary Introduction

To assign: The different tasks to different workstations and identify the efficiency.

Explanation of Solution

Assignment of different tasks to different workstations:

Workstation	Elligible tasks	Selected tasks	Task time (minutes)	Available cycle time (minutes)
1				10
	A, B	A	3	7
	B	B	6	1
				1 (Idle time)
2				10
	C, D, E	C	7	3
				3 (Idle time)
3				10
	D, E, F	D	5	5
	E, F	E	2	3
				3 (Idle time)
4				10
	F, G, H, I	F	4	6
	G, H, I	G	5	1
				1 (Idle time)
5				10
	J, H, I, K	H	7	3
	H, I, K	I	1	2
				2 (Idle time)
6				10
	K, J	J	6	4
	K	K	4	0

Workstation	Task assigned	Idle time
1	A, B	1
2	C, D	3
3	D, E	3
4	F, G	1
5	H, I	2
6	J, K	0
Total		10

Efficiency:

Formula to calculate efficiency:

$\text{Efficiency}=\frac{\text{Total task time}}{\text{Number of workstations}\times \text{Cycle time}}\times 100$

Calculation of efficiency:

$\begin{array}{c}\text{Efficiency}=\frac{50}{6\times 10}\times 100\\ =\frac{500}{60}\\ =83.3\%\end{array}$

The efficiency is 83.3%.