MCS 115 Problem Set 3
-
Chapter 7 problems: 2, 4, 10, 12, 14
-
The following problems are modified versions of problems in chapter 2
of For All Practical Purposes 5/e by COMAP, Freeman, 2000.
Write Ti --> Tj if task Ti must be
completed before task Tj is started.
-
(1)
Assume that seven tasks take the following times (in hours)
| Task
| T1
| T2
| T3
| T4
| T5
| T6
| T7
|
| Time
| 18
| 12
| 13
| 18
| 11
| 17
| 7
|
and that the following order precedences must be observed:
| T1 --> T4
|
| T2 --> T5
|
| T3 --> T6
|
| T4 --> T7
|
| T5 --> T7
|
| T6 --> T7
|
- (a) Construct an order-requirement digraph model for this
situation, writing the task times in circles representing the vertices.
- (b) Find the earliest completion time and critical path.
-
(2)
Assume that nine tasks take the following times (in hours)
| Task
| T1
| T2
| T3
| T4
| T5
| T6
| T7
| T8
| T9
|
| Time
| 8
| 11
| 12
| 7
| 10
| 14
| 14
| 9
| 8
|
and that the following order precedences must be observed:
| T1 --> T4
|
| T2 --> T5
|
| T3 --> T5
|
| T3 --> T6
|
| T4 --> T7
|
| T4 --> T8
|
| T5 --> T7
|
| T6 --> T8
|
| T6 --> T9
|
- (a) Construct an order-requirement digraph model for this
situation, writing the task times in circles representing the vertices.
- (b) Find the earliest completion time and critical path.
-
(3)
Assume that seven tasks take the following times (in hours)
| Task
| T1
| T2
| T3
| T4
| T5
| T6
| T7
|
| Time
| 12
| 9
| 11
| 10
| 12
| 10
| 12
|
and that the following order precedences must be observed:
| T1 --> T4
|
| T1 --> T5
|
| T2 --> T5
|
| T3 --> T6
|
| T4 --> T7
|
| T5 --> T7
|
| T6 --> T7
|
- (a) Construct an order-requirement digraph model for this
situation, writing the task times in circles representing the vertices.
- (b) Find the earliest completion time and critical path.
- (c) Which tasks, if done more quickly, would reduce the earliest
completion time?
- (d) Which tasks would not?
- (e) Find the earliest completion time and critical path if
the time it takes to do task T5 is shortened to 9 hours.