Question 6.P.1: The tasks shown in the following precedence diagram are to b......
The tasks shown in the following precedence diagram are to be assigned to workstations with the intent of minimizing idle time. Management has designed an output rate of 275 units per day. Assume 440 minutes are available per day.
a. Determine the appropriate cycle time.
b. What is the minimum number of stations possible?
c. Assign tasks using the “positional weight” rule: Assign tasks with highest following times (including a task’s own time) first. Break ties using greatest number of following tasks.
d. Compute efficiency.
a. \mathrm{Cycle~time}\;=\;{\frac{\mathrm{Operating~time}}{\mathrm{Desired~output}}}\;=\;{\frac{440~\mathrm{minutes~per~day}}{275\ \mathrm{units~per~day}}}\;=\;1.6\ \mathrm{minutes~per~unit}
b. N\;=\;{\frac{\Sigma t}{\mathrm{Cycle~time}}}\;=\;{\frac{4.2}{1.6\;\mathrm{minutes}}}\;=\;2.625\;{\mathrm{(round~to~3)}}
c. Add positional weights (task time plus the sum of all following times) to the diagram. Start at the right end and work backward(Figure 1):
The resulting assignments are shown below(Figure 2).
d. \mathrm{Efficiency}\,=\,100\%-\,\mathrm{Percent~idle~time}\,=\,100\%-\,\frac{0.6~\mathrm{min.}}{3\times1.6~\mathrm{min}.}100=87.5\%.
| Station | Time Remaining^{*} |
Eligible | Will Fit | Assign Task/Time |
Station Idle Time |
| 1 | 1.6 | a, b | a, b | b/0.6 | |
| 1.0 | a, d | a | a/0.3 | ||
| 0.7 | c, d | c | c/0.4 | ||
| 0.3 | e, d | e | e/0.2 | ||
| 0.1 | g, d | g | g/0.1 | ||
| 0 | — | — | — | 0 | |
| 2 | 1.6 | d | d | d/1.2 | |
| 0.4 | f | none | none | 0.4 | |
| 3 | 1.6 | f | f | f/0.6 | |
| 1.0 | h | h | h/0.5 | ||
| 0.5 | i | i | i/0.3 | ||
| 0.2 | — | — | — | \underline{0.2} | |
| 0.6 |
*The initial time for each station is the cycle time computed in part a.
