Discuss the below problem:
Q: Twelve tasks, with times and precedence requirements as shown in the following table, are to be assigned to workstations that have a fixed machine cycle time of 1.5 minutes. Two heuristic rules will be tried: (1) greatest positional weight, and (2) greatest number of following tasks.
In each case, the tiebreaker will be shortest task time.
| Task |
Length
(minutes) |
Immediate
Predecessor |
| a |
0.1 |
- |
| b |
0.2 |
a |
| c |
0.9 |
b |
| d |
0.6 |
c |
| e |
0.1 |
- |
| 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 |
a. Assign tasks to stations under each of the two rules.
(1) greatest positional weight (shortest task time as tiebreaker)
(2) greatest number of following tasks (shortest task time as tiebreaker)
b. Compute the percentage of idle time for each rule.