Chapter 9, Problem 13P

Illinois Furniture, Inc., produces all types of office furniture. The “Executive Secretary” is a chair that has been designed using ergonomics to provide comfort during long work hours. The chair sells for $130. There are 480 minutes available during the day, and the average daily demand has been 50 chairs. There are eight tasks:

a) Draw a precedence diagram of this operation.

b) What is the cycle time for this operation?

c) What is the theoretical minimum number of workstations?

d) Assign tasks to workstations.

e) What is the idle time per cycle?

f) How much total idle time is present in an 8-hour shift?

g) What is the efficiency of the assembly line, given your answer in (d)?

Summary Introduction

To draw: The precedence diagram.

Answer to Problem 13P

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• Average daily demand is 50 chairs.

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 13P

The  cycle time is 9.6 minutes / unit.

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• Average daily demand is 50 chairs.

Formula to calculate cycle time:

$\text{Cycle time}=\frac{\text{Number of minutes available per day}}{\text{Average daily demand}}$

Calculation of cycle time:

$\begin{array}{c}\text{Cycle time}=\frac{480}{\text{50}}\\ =9.6\text{ minutes}\end{array}$

The  cycle time is 9.6 minutes / unit.

Summary Introduction

To determine: The theoretical minimum number of workstations.

Answer to Problem 13P

The theoretical minimum number of workstations is 6 workstations.

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• 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:

$\begin{array}{c}\text{Workstations}=\frac{\text{49}}{\text{9}\text{.6}}\\ =5.1\\ =6\text{ workstations}\end{array}$

The theoretical minimum number of workstations is 6 workstations.

Summary Introduction

To assign: The different tasks to different workstations.

Explanation of Solution

Assignment of different tasks to different workstations:

Task A is assigned to station 1. Task B is assigned to station 2. Task C is assigned to station 3. Task D is assigned to station 4. Task E is assigned to station 5. Task G is assigned to station 6. Task F is assigned to station 7. Task H is assigned to station 8.

Summary Introduction

To determine: The idle time per cycle.

Answer to Problem 13P

The  idle time is 15 minutes / cycle.

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• Average daily demand is 50 chairs.

Calculation of idle time per cycle:

$\begin{array}{c}\text{Idle time}=4+1+2+3+2+1+2\\ =15\text{ minutes / cycle}\end{array}$

The  idle time is 15 minutes / cycle.

Summary Introduction

To determine: The total idle time present in an 8 hour shift.

Answer to Problem 13P

The  total idle time present in an 8 hour shift is 15 hours.

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• Average daily demand is 50 chairs.

Calculation of total idle time present in an 8 hour shift:

There are 480 minutes available in a day. The longest operation time is 8 minutes. Therefore the number of cycles in a day is given by:

$\begin{array}{c}\text{Cycles}=\frac{\text{Number of minutes / day}}{\text{Longest operation time}}\\ =\frac{480}{8}\\ =60\text{ cycles}\end{array}$

The total idle time is calculated by multiplying the number of cycles with the total idle time per cycle.

$\begin{array}{c}\text{Total idle time}=15\text{ minutes}\times 60\text{ cycles}\\ =900\text{ minutes}\\ \text{=15 hours}\end{array}$

The total idle time present in an 8 hour shift is 15 hours.

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 13P

The efficiency is 76.6%.

Explanation of Solution

Given information:

Task	Time (minutes)	Immediate predecessors
A	4	-
B	7	-
C	6	A, B
D	5	C
E	6	D
F	7	E
G	8	E
H	6	F, G
Total	49

• The chair is sold for $130.
• Number of minutes available = 480 / day.
• Average daily demand is 50 chairs.

Formula to calculate efficiency:

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

Calculation of efficiency:

$\begin{array}{c}\text{Efficiency}=\frac{49}{8\times 8}\times 100\\ =\frac{49}{64}\times 100\\ =76.6\%\end{array}$

The efficiency is 76.6%