Operations Management
Operations Management
13th Edition
ISBN: 9781259667473
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 6, Problem 7P

For the given set of tasks, do the following:

a. Develop the precedence diagram

b. Determine the minimum cycle time and then calculate the cycle time for a desired output of 500 units in a seven-hour day. Why might a manager use a cycle tune of 50 seconds?

c. Determine the minimum number of workstations for output of 500 units per day

d. Balance the line using the greatest positional weight heuristic. Break ties with the most following tasks heuristic. Use a cycle tune of 50 seconds.

e. Calculate the percentage idle time for the line.

Chapter 6, Problem 7P, For the given set of tasks, do the following: a. Develop the precedence diagram b. Determine the

a)

Expert Solution
Check Mark
Summary Introduction

To draw: The precedence diagram.

Introduction:

Process selection:

It is the tactical choices made by a firm in picking the kind of production procedure to be followed in the process of production. The process is selected after reviewing many numbers of criteria and constraints.

Answer to Problem 7P

Precedence diagram:

Operations Management, Chapter 6, Problem 7P , additional homework tip  1

Explanation of Solution

Given information:

Task Task time (seconds) Immediate predecessor
A 45 Nil
B 11 A
C 9 B
D 50 Nil
E 26 D
F 11 E
G 12 C
H 10 C
I 9 F, G , H
J 10 I
Total 193

Precedence diagram:

Operations Management, Chapter 6, Problem 7P , additional homework tip  2

The precedence diagram is drawn circles and arrows. The tasks are represented in circles and weights for each task are represented outside the circle. The arrows are represented to show which task is preceding the other task and so on.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The minimum cycle time and the cycle time for the desired output.

Introduction:

Process selection:

It is the tactical choices made by a firm in picking the kind of production procedure to be followed in the process of production. The process is selected after reviewing many numbers of criteria and constraints.

Answer to Problem 7P

The minimum cycle time is 50 seconds / unit. The cycle time for the desired output is 50.4 seconds / unit.

Explanation of Solution

Given information:

Task Task time (seconds) Immediate predecessor
A 45 Nil
B 11 A
C 9 B
D 50 Nil
E 26 D
F 11 E
G 12 C
H 10 C
I 9 F, G , H
J 10 I
Total 193

Operating hours per day = 7

Sum of all task times = 193 seconds

Desired output per day = 500

Calculation of minimum cycle time:

The minimum cycle time is equal to the time of the longest task.

Minimum cycle time=Longest task time=50 seconds / unit

The minimum cycle time is 50 seconds / unit.

Calculation of cycle time for the desired output:

The cycle time is calculated by dividing the operating time per day in seconds by the desired output per day.

Cycle time=7×60minutes×60 seconds500=25,200500=50.4 minutes / unit

The cycle time for the desired output is 50.4 seconds / unit.

The manager might use a cycle time of 50 seconds because it is closer to the calculated time. Also the task times are integers giving it a good chance to balance the line effectively.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The minimum number of workstations for the desired output.

Introduction:

Process selection:

It is the tactical choices made by a firm in picking the kind of production procedure to be followed in the process of production. The process is selected after reviewing many numbers of criteria and constraints.

Answer to Problem 7P

The minimum number of workstations for the desired output is 4 workstations.

Explanation of Solution

Given information:

Task Task time (seconds) Immediate predecessor
A 45 Nil
B 11 A
C 9 B
D 50 Nil
E 26 D
F 11 E
G 12 C
H 10 C
I 9 F, G , H
J 10 I
Total 193

Operating hours per day = 7

Sum of all task times = 193 seconds

Desired output per day = 500

Calculation of minimum number of workstations:

The minimum number of workstations is calculated by dividing the sum of all task times with the calculated cycle time.

Minimum number of workstations=19350.4=3.83=4 workstations

The minimum number of workstations for the desired output is 4 workstations.

d)

Expert Solution
Check Mark
Summary Introduction

To assign: Tasks on the basis of greatest positional weight.

Introduction:

Process selection:

It is the tactical choices made by a firm in picking the kind of production procedure to be followed in the process of production. The process is selected after reviewing many numbers of criteria and constraints.

Explanation of Solution

Given information:

Task Duration (minutes) Immediate (Predecessor)
a 0.1 Nil
b 0.2 a
c 0.9 b
d 0.6 c
e 0.1 Nil
f 0.2 d, e
g 0.4 f
h 0.1 g
i 0.2 h
j 0.7 i
k 0.3 j
l 0.2 k

Cycle time = 50 seconds

The number of following tasks, calculation of positional weight for each task is shown below.

Task Following tasks Number of following tasks Calculation of positional weight Positional weight
A B, C, G, H, I, J 6 45 + 11 + 9 + 12 + 10 + 9 + 10 106
B C, G, H, I, J 5 11 + 9 + 12 + 10 + 9 + 10 61
C G, H, I, J 4 9 + 12 + 10 + 9 + 10 50
D E, F, I, J 4 50 + 26 + 11 + 9 + 10 106
E F, I, J 3 26 + 11 + 9 + 10 56
F I, J 2 11 + 9 + 10 30
G I, J 2 12 + 9 + 10 31
H I, J 2 10 + 9 + 10 29
I J 1 9 + 10 19
J Nil 0 10 10

Assigning tasks to workstations:

Workstation number Eligible task Assigned task Task time Unassigned cycle time Reason
50
1 A, D A 45 5 Task 'A' has more following tasks
B, D None 5 (Idle time) The task time is greater than the unassigned cycle time.
50
2 B, D D 50 0 Task 'D' has the highest positional weight
50
3 B, E B 11 39 Task 'B' has the highest positional weight
C, E E 26 13 Task 'E' has the highest positional weight
C, F C 9 4 Task 'C' has the highest positional weight
F, G, H None 4 (Idle time) The task time is greater than the unassigned cycle time.
50
4 F, G, H G 12 38 Task 'G' has the highest positional weight
F, H F 11 27 Task 'F' has the highest positional weight
H H 10 17 Task 'H' is the only eligible task available
I I 9 8 Task 'I' is the only eligible task available
J None 8 (Idle time) The task time is greater than the unassigned cycle time.
50
5 J J 10 40 Task 'J' is the only task remaining
40 (Idle time) All tasks completed

Overview of tasks assignment:

Workstation Assigned tasks Total cycle time used Idle time
1 A 45 5
2 D 50 0
3 B, E, C 46 4
4 G, F, H, I 42 8
5 J 10 40

e)

Expert Solution
Check Mark
Summary Introduction

To determine: The percentage of idle time.

Introduction:

Process selection:

It is the tactical choices made by a firm in picking the kind of production procedure to be followed in the process of production. The process is selected after reviewing many numbers of criteria and constraints.

Answer to Problem 7P

The percentage of idle time is 22.80%.

Explanation of Solution

Formula to calculate percentage of idle time:

Idle time=Total idle timeNumber of workstations×Cycle time×100

Calculation of percentage of idle time:

Idle time=5+0+4+8+405×50×100=57250×100=0.228×100=22.80%

The percentage of idle time is 22.80%.

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Students have asked these similar questions
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Chapter 6 Solutions

Operations Management

Ch. 6.5 - Prob. 1.1RQCh. 6.5 - Prob. 1.2RQCh. 6 - Explain the importance of process selection in...Ch. 6 - Briefly describe the five process types, and...Ch. 6 - Prob. 3DRQCh. 6 - Briefly describe computer-assisted approaches to...Ch. 6 - What is a flexible manufacturing system, and under...Ch. 6 - Prob. 6DRQCh. 6 - Why might the choice of equipment that provides...Ch. 6 - Prob. 8DRQCh. 6 - Prob. 9DRQCh. 6 - Briefly describe the two main layout types.Ch. 6 - Prob. 11DRQCh. 6 - Prob. 12DRQCh. 6 - What is the goal of Line balancing? What happens...Ch. 6 - Why are routing and scheduling continual problems...Ch. 6 - Prob. 15DRQCh. 6 - Prob. 16DRQCh. 6 - The City Transportation Planning Committee must...Ch. 6 - Identify the fixed-path and variable-path...Ch. 6 - Prob. 19DRQCh. 6 - Prob. 20DRQCh. 6 - Prob. 21DRQCh. 6 - Prob. 22DRQCh. 6 - What is cellular manufacturing? What are its main...Ch. 6 - Prob. 24DRQCh. 6 - Prob. 25DRQCh. 6 - Prob. 1TSCh. 6 - What trade-offs are involved when deciding how...Ch. 6 - Who needs to be involved in process selection?Ch. 6 - Prob. 4TSCh. 6 - Prob. 5TSCh. 6 - Prob. 1CTECh. 6 - Prob. 2CTECh. 6 - What are the risks of automating a production...Ch. 6 - Consider an assembly line such as the burrito...Ch. 6 - Prob. 1PCh. 6 - A manager wants to assign tasks to workstations as...Ch. 6 - A manager wants to assign tasks to workstations as...Ch. 6 - A producer of inkjet printer is planning to add a...Ch. 6 - As part of a major plant renovation project, the...Ch. 6 - Twelve tasks, with times and precedence...Ch. 6 - For the given set of tasks, do the following: a....Ch. 6 - A shop works a 400-minute day. The manager of the...Ch. 6 - Arrange six departments into a 2 3 grid so that...Ch. 6 - Using the information given in the preceding...Ch. 6 - Using the information in the following grid,...Ch. 6 - Arrange the eight departments shown in the...Ch. 6 - Arrange the departments so they satisfy the...Ch. 6 - a. Determine the placement of departments fix a...Ch. 6 - Prob. 15PCh. 6 - Develop a process layout that will minimize the...Ch. 6 - Prob. 17PCh. 6 - Rebalance the assembly line in Problem 7. This...
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