Chapter 9, Problem 23P

a)

Summary Introduction

To determine: The theoretical minimum number of workstations.

Answer to Problem 23P

The theoretical minimum number of workstations is 5 workstations.

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	40	-
B	30	A
C	50	A
D	40	B
E	6	B
F	25	C
G	15	C
H	20	D, E
I	18	F, G
J	30	H, I
Total	274

• Output is 60 iStars / hour

Calculation of cycle time:

The requirement is to produce 60 iStars / hour. Hence, the cycle time for one iStar will be:

$\begin{array}{c}\text{Cycle time}=\frac{60\text{ iStars / hour}}{60\text{minutes / hour}}\times 60\text{ seconds}\\ =1\times 60\text{ seconds}\\ =60\text{ seconds / iStar}\end{array}$

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:

$\begin{array}{c}\text{Workstations}=\frac{\text{274}}{\text{60}}\\ =4.57\\ =5\text{ workstations}\end{array}$

The theoretical minimum number of workstations is 5 workstations.

b)

Summary Introduction

To balance: The assembly line.

Explanation of Solution

Precedence diagram:

List of most following tasks:

Tasks	Following tasks
A	9
B	4
C	4
D	2
E	2
F	2
G	2
H	1
I	1
J	0

Assignment of different tasks to different workstations:

Workstation	Elligible tasks	Selected tasks	Task time (seconds)	Available cycle time (seconds)	Remarks
1				60
	A	A	40	20
	B,C			20 (Idle time)	Cycle time is less than task time
2				60
	B, C	C	7	50	Tie broken randomnly
	B, F, G			10 (Idle time)	Cycle time is less than task time
3				60
	B, F, G	B	30	30	Task B has most following tasks.
	D, E, F, G	F	25	24	Tie broken randomnly
	D, E, G			1 (Idle time)	Cycle time is less than task time
4				60
	D, E, G	D	40	20	Tie broken randomnly
	E, G	G	15	5	Tie broken randomnly
	E,I			5 (Idle time)	Cycle time is less than task time
5				60
	E, I	E	6	54	Task E has most following tasks.
	I, H	H	20	34	Tie broken randomnly
	I	I	18	2	Task I is only elligible task
				2 (Idle time)
6				60
	J	J	30	30	Task J is the remaining task
				30 (Idle time)

Workstation	Task assigned	Idle time
1	A	20
2	C	10
3	B, F	1
4	D, G	5
5	E, H, I	2
6	J	30
Total		68

c)

Summary Introduction

To determine: The actual number of workstations.

Answer to Problem 23P

The actual number of workstations is 6.

Explanation of Solution

Workstation	Task assigned	Idle time
1	A	20
2	C	10
3	B, F	1
4	D, G	5
5	E, H, I	2
6	J	30
Total		68

The actual number of workstations is 6.

d)

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 23P

The efficiency is 76.11%.

Explanation of Solution

Formula to calculate efficiency:

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

Calculation of efficiency:

$\begin{array}{c}\text{Efficiency}=\frac{274}{6\times 60}\times 100\\ =\frac{274,00}{360}\\ =76.11\%\end{array}$

The efficiency is 76.11%.