Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
12th Edition
ISBN: 9781259580093
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 6, Problem 6P

Twelve tasks, with times and precedence requirements as shown in the following table, are 10 be assigned to workstations using a cycle time of 1.5 minutes. Two heuristic rules will be tried: (1) greatest positional weight, and (2) most following tasks. In each case, the tiebreaker will be shortest processing time.

Chapter 6, Problem 6P, Twelve tasks, with times and precedence requirements as shown in the following table, are 10 be

a. Draw the precedence diagram for this line.

b. Assign tasks to stations under each of the two rules.

c. Compute the percentage of idle tune fox each rule.

a)

Expert Solution
Check Mark
Summary Introduction

To draw: The precedence diagram.

Answer to Problem 6P

Precedence diagram:

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences), Chapter 6, Problem 6P , additional homework tip  1

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 = 1.5 minutes

Precedence diagram:

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences), Chapter 6, Problem 6P , 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)

1)

Expert Solution
Check Mark
Summary Introduction

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

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 = 1.5 minutes

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

Task Following tasks Number of following tasks Calculation of positional weight Positional weight Processing time
a b, c, d, f, g, h, i, j, k, l 10 0.1 + 0.2 + 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.9 0.1
b c, d, f, g, h, i, j, k, l 9 0.2 + 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.8 0.2
c d, f, g, h, i, j, k, l 8 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.6 0.9
d f, g, h, i, j, k, l 7 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.7 0.6
e f, g, h, i, j, k, l 7 0.1 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.2 0.1
f g, h, i, j, k, l 6 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.1 0.2
g h, i, j, k, l 5 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 1.9 0.4
h i, j, k, l 4 0.1 + 0.2 + 0.7+ 0.3 + 0.2 1.5 0.1
i j, k, l 3 0.2 + 0.7+ 0.3 + 0.2 1.4 0.2
j k, l 2 0.7+ 0.3 + 0.2 1.2 0.7
k l 1 0.3 + 0.2 0.5 0.3
l Nil 0 0.2 0.2 0.2

Assigning tasks to workstations:

Workstation number Eligible task Assigned task Task time Unassigned cycle time Reason
1.5
1 a, e a 0.1 1.4 Task 'a' has highest positional weight
b, e b 0.2 1.2 Task 'b' has highest positional weight
c, e c 0.9 0.3 Task 'c' has highest positional weight
d, e e 0.1 0.2 Task 'e' is the only eligible task available
d None 0.2 (Idle time) The task time is greater than the unassigned cycle time.
1.5
2 d d 0.6 0.9 Task 'd' is the only eligible task available
f f 0.2 0.7 Task 'f' is the only eligible task available
g g 0.4 0.3 Task 'g' is the only eligible task available
h h 0.1 0.2 Task 'h' is the only eligible task available
i i 0.2 0 Task 'i' is the only eligible task available
1.5
3 j j 0.7 0.8 Task 'j' is the only eligible task available
k k 0.3 0.5 Task 'k' is the only eligible task available
l l 0.2 0.3 Task 'l' is the only eligible task available
0.3 (Idle time) All tasks completed

Overview of tasks assignment:

Workstation Assigned tasks Total cycle time used Idle time
1 a, b, c, e 1.3 0.2
2 d, f, g, h, i 1.5 0
3 j, k, l 1.2 0.3

2)

Expert Solution
Check Mark
Summary Introduction

To assign: Tasks on the basis of most following tasks.

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 = 1.5 minutes

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

Task Following tasks Number of following tasks Calculation of positional weight Positional weight Processing time
a b, c, d, f, g, h, i, j, k, l 10 0.1 + 0.2 + 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.9 0.1
b c, d, f, g, h, i, j, k, l 9 0.2 + 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.8 0.2
c d, f, g, h, i, j, k, l 8 0.9 + 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 3.6 0.9
d f, g, h, i, j, k, l 7 0.6 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.7 0.6
e f, g, h, i, j, k, l 7 0.1 + 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.2 0.1
f g, h, i, j, k, l 6 0.2 + 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 2.1 0.2
g h, i, j, k, l 5 0.4 + 0.1 + 0.2 + 0.7+ 0.3 + 0.2 1.9 0.4
h i, j, k, l 4 0.1 + 0.2 + 0.7+ 0.3 + 0.2 1.5 0.1
i j, k, l 3 0.2 + 0.7+ 0.3 + 0.2 1.4 0.2
j k, l 2 0.7+ 0.3 + 0.2 1.2 0.7
k l 1 0.3 + 0.2 0.5 0.3
l Nil 0 0.2 0.2 0.2

Assigning tasks to workstations:

Workstation number Eligible task Assigned task Task time Unassigned cycle time Reason
1.5
1 a, e a 0.1 1.4 Task 'a' has the most following tasks
b, e b 0.2 1.2 Task 'b' has the most following tasks
c, e c 0.9 0.3 Task 'c' has the most following tasks
d, e e 0.1 0.2 Task 'e' is the only eligible task available
d None 0.2 (Idle time) The task time is greater than the unassigned cycle time.
1.5
2 d d 0.6 0.9 Task 'd' is the only eligible task available
f f 0.2 0.7 Task 'f' is the only eligible task available
g g 0.4 0.3 Task 'g' is the only eligible task available
h h 0.1 0.2 Task 'h' is the only eligible task available
i i 0.2 0 Task 'i' is the only eligible task available
1.5
3 j j 0.7 0.8 Task 'j' is the only eligible task available
k k 0.3 0.5 Task 'k' is the only eligible task available
l l 0.2 0.3 Task 'l' is the only eligible task available
0.3 (Idle time) All tasks completed

Overview of tasks assignment:

Workstation Assigned tasks Total cycle time used Idle time
1 a, b, c, e 1.3 0.2
2 d, f, g, h, i 1.5 0
3 j, k, l 1.2 0.3

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The percentage of idle time.

Answer to Problem 6P

The percentage of idle time is 11.11%.

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:

The solutions for most following tasks rule and highest positional weight is same. Hence, the percentage of idle time will also be the same.

Idle time=0.2+0.0+0.33×1.5×100=0.54.5×100=0.1111×100=11.11%

The percentage of idle time is 11.11%.

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Chapter 6 Solutions

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)

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