Concept explainers
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.
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)
To draw: The precedence diagram.
Answer to Problem 6P
Precedence diagram:
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:
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)
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)
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)
To determine: The percentage of idle time.
Answer to Problem 6P
Explanation of Solution
Formula to calculate percentage of idle time:
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.
The percentage of idle time is 11.11%.
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Chapter 6 Solutions
OPERATIONS MANAGEMENT (LL) >CUSTOM<
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