Chapter 9, Problem 15P

The Action Toy Company has decided to manufacture a new train set the production of which is broken into six steps. The demand for the train is 4,800 units per 40-hour workweek:

a) Draw a precedence diagram of this operation.

b) Given the demand, what is the cycle time for this operation?

c) What is the theoretical minimum number of workstations?

d) Assign tasks to workstations.

e) How much total idle time a present each cycle?

f) What is the efficiency of the assembly line with five stations? With six stations?

Summary Introduction

To draw: The precedence diagram.

Answer to Problem 15P

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	20	-
B	30	A
C	15	A
D	15	A
E	10	B, C
F	30	D, E
Total	120

• Weekly demand is 4,800 units / 40 hours workweek.

Precedence diagram:

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 15P

The  cycle time is 30 seconds / unit.

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	20	-
B	30	A
C	15	A
D	15	A
E	10	B, C
F	30	D, E
Total	120

• Weekly demand is 4,800 units / 40 hours workweek.

Formula to calculate cycle time:

$\text{Cycle time}=\text{Output / day}\times \text{60 minutes / hour}\times \text{60 seconds / minutes}$

Calculation of cycle time:

$\begin{array}{c}\text{Cycle time}=\frac{40}{4,800}\times \text{60}\times \text{60}\\ \text{=}\frac{240}{8}\\ =30\text{seconds / unit}\end{array}$

The  cycle time is 30 seconds / unit.

Summary Introduction

To determine: The theoretical minimum number of workstations.

Answer to Problem 15P

The theoretical minimum number of workstations is 4 workstations.

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	20	-
B	30	A
C	15	A
D	15	A
E	10	B, C
F	30	D, E
Total	120

• Weekly demand is 4,800 units / 40 hours workweek.
• Average daily demand is 50 chairs.

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:

$\begin{array}{c}\text{Workstations}=\frac{\text{120}}{\text{30}}\\ =4\text{ workstations}\end{array}$

The theoretical minimum number of workstations is 4 workstations.

Summary Introduction

To assign: The different tasks to different workstations.

Explanation of Solution

Assignment of different tasks to different workstations:

Workstation	Elligible tasks	Selected tasks	Task time (seconds)	Available cycle time (seconds)	Remarks
1				30
	A	A	20	10	Task A is the only elligible ask
				10 (Idle Time)	No other elligible task is available
2				30
	B, C, D	B	30	0	Task B has the highest task time
3				30
	C, D	C	15	15	Task C is assigned
	D	D	15	0	Task D is assigned
4				30
	E	E	10	20	Task E is the only elligible task available
				20 (Idle time)	The available cycle time is less than the task time
5	F	F	30	0	Task F is assigned

Workstation	Task assigned	Idle time
1	A	10
2	B	0
3	C, D	0
4	E	20
5	F	0
Total		30

Summary Introduction

To determine: The idle time per cycle.

Answer to Problem 15P

The  idle time is 30 seconds / cycle.

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	20	-
B	30	A
C	15	A
D	15	A
E	10	B, C
F	30	D, E
Total	120

• Weekly demand is 4,800 units / 40 hours workweek.
• Average daily demand is 50 chairs.

Calculation of idle time per cycle:

$\begin{array}{c}\text{Idle time}=10+20\\ =30\text{seconds / cycle}\end{array}$

The  idle time is 30 seconds / cycle.

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 15P

The efficiency with five and six workstations is 80% and 66.6% respectively.

Explanation of Solution

Given information:

Task	Time (seconds)	Immediate predecessors
A	20	-
B	30	A
C	15	A
D	15	A
E	10	B, C
F	30	D, E
Total	120

• Weekly demand is 4,800 units / 40 hours workweek.
• Average daily demand is 50 chairs.

Formula to calculate efficiency:

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

Calculation of efficiency for five workstations:

$\begin{array}{c}\text{Efficiency}=\frac{120}{5\times 30}\times 100\\ =\frac{12,000}{150}\times 100\\ =80\%\end{array}$

Calculation of efficiency for six workstations:

$\begin{array}{c}\text{Efficiency}=\frac{120}{6\times 30}\times 100\\ =\frac{12,000}{180}\times 100\\ =66.6\%\end{array}$

The efficiency with five and six workstations is 80% and 66.6% respectively.