17) Using Table 7.6, suppose activity D can be shortened from four days to one day. Assume all other
activity times remain the same. How much shorter will the total project earliest completion time become?
A) zero days
B) one day
C) two days
D) three days
18) Using Table 7.6, suppose activity I is delayed, taking eight days to complete instead of two days.
Assume all other activity times remain the same. How much longer will the total project earliest
completion time become?
A) zero days
B) one or two days
C) three or four days
D) five or six days
19) Using Table 7.6, what is the latest start time for activity A?
A) day 0
B) day 1
C) day 2
D) day 3 or later
Figure to accompany Table 7.7
Table 7.7
ACTIVITY
NORMAL
TIME
CRASH
TIME
NORMAL
COST ($000s)
CRASH
COST
($000s)
AVAILABLE
WEEKS OF
CRASHING
CRASHING COST
/ WEEK
A
4
2
8
14
B
3
2
9
11
C
4
4
10
10
D
5
3
10
15
E
4
1
11
14
F
1
1
6
6
20) What is the critical path for the project shown in the above network and Table 7.7, using the normal times?
A) A-B-D-F
B) A-C-D-F
C) A-C-E-F
D) A-B-C-D-E-F
21) Determine the information missing from Table 7.7; then answer the following questions. How many
week(s) of crashing are available for activity D in Table 2.9?
A) 0
B) 1
C) 2
D) 6
22) How many week(s) of crashing are available for activity B in Table 7.7?
A) 0
B) 1
C) 2
D) 3
23) How many weeks of crashing are available for activity C in Table 7.7?
A) 0
B) 1
C) 2
D) 6
24) What is the crashing cost per week for activity A in Table 7.7?
A) $2,000
B) $3,000
C) $4,000
D) This activity cannot be crashed.
25) What is the crashing cost per week for activity E in Table 7.7?
A) $1,000
B) $2,000
C) $3,000
D) This activity cannot be crashed.
26) What is the crashing cost per week for activity F in Table 7.7?
A) $2,000
B) $3,000
C) $4,000
D) This activity cannot be crashed.
27) If a decision is made to crash activity D in Table 7.7 by one week, what is the cost for this one week of
crashing?
A) $3,000
B) $2,000
C) $2,500
D) This activity cannot be crashed.
28) Which activity should be crashed first for the project shown in Table 7.7?
A) A
B) B
C) C
D) D
Table 7.8
Activity
Predecessor
Normal
Time
(days)
Crashing
Time (days)
Crashing
Cost/day
A
—
5
1
$200
B
—
7
1
$500
C
—
5
1
$200
D
A
10
2
$300
E
B
6
1
$400
F
A, C
7
2
$650
G
B
4
1
$500
H
E, D, G
6
1
$350
29) Using Table 7.8, what is the critical path for this project using the normal times?
A) A–D–H
B) C–F
C) B–E–H
D) B–G–H
30) Using Table 7.8, what is the minimum completion time for this project after crashing?
A) 23 days
B) 21 days
C) 19 days
D) 17 days
31) Using Table 7.8, what is the minimum crashing cost to finish this project in 18 days?
A) $3,450
B) $850
C) $1,150
D) $1,500
32) Using Table 7.8, what is the activity with the greatest amount of slack?
A) A
B) B
C) C
D) D
33) Using Table 7.8, what is the latest start time for activity E?
A) day 7
B) day 8
C) day 9
D) day 10
34) Using Table 7.8, what is the earliest possible completion time for activity E after crashing?
A) day 11
B) day 13
C) day 15
D) day 17
Table 7.9
35) Using Table 7.9, what is the earliest completion time of this project if normal times are used for all
activities?
A) fewer than 13 weeks
B) 13 weeks
C) 14 weeks
D) more than 14 weeks
36) Using Table 7.9, what is the minimum time schedule for this project?
A) fewer than 8 weeks
B) 8 weeks
C) 9 weeks
D) more than 9 weeks
37) Using Table 7.9, if the project completion time has to be reduced by one week, which of the following
activities should be crashed to minimize the extra cost of earlier completion?
A) Activity B
B) Activity E
C) Activity H
D) Activity J
38) Using Table 7.9, what is the difference, in dollars, between the minimum-time schedule and the
schedule created by crashing all activities to their limits? Assume that there are no indirect or penalty
costs.
A) less than or equal to $1,000
B) greater than $1,000 but less than or equal to $2,000
C) greater than $2,000 but less than or equal to $3,000
D) greater than $3,000
39) Using Table 7.9, if the project’s normal earliest completion time is to be reduced by two weeks, what is
the minimum additional cost that will be incurred in achieving this two-week reduction?
A) less than or equal to $1,000
B) greater than $1,000 but less than or equal to $1,500
C) greater than $1,500 but less than or equal to $2,000
D) greater than $2,000
40) A project is currently scheduled to be finished on its normal earliest completion date. The project
manager has the opportunity to earn a bonus if the project can be completed three weeks ahead of
schedule. The increase in project direct costs related to crashing activities would be $40,000. Also, project
indirect costs are $15,000 per week. What is the smallest bonus that the project manager should accept if
he or she wants to avoid increasing overall project costs?
A) less than or equal to $5,000
B) greater than $5,000 but less than or equal to $10,000
C) greater than $10,000 but less than or equal to $15,000
D) greater than $15,000
41) You are given the following information about activity A:
Normal time
= 9 weeks
Crash time
= 7 weeks
Normal cost
= $20,000
Crash cost
= $30,000
What will it cost to complete activity A in 8 weeks?
A) less than or equal to $24,000
B) greater than $24,000 but less than or equal to $27,000
C) greater than $27,000 but less than or equal to $30,000
D) greater than $30,000
42) You are given the following information about activity B:
Normal time
= 9 weeks
Crash time
= 5 weeks
Cost to crash per week
= $2,000
Crash cost
= $41,000
What will it cost to complete activity B in 6 weeks?
A) less than or equal to $34,000
B) greater than $34,000 but less than or equal to $36,000
C) greater than $36,000 but less than or equal to $38,000
D) greater than $38,000
43) You are given the following information about activity F:
Normal time
= 16 weeks
Crash time
= 10 weeks
Crash cost
= $45,000
Cost to crash per week
= $2,000
What is the normal cost for activity F?
A) greater than or equal to $55,000
B) less than $55,000 but greater than or equal to $47,000
C) less than $47,000 but greater than or equal to $40,000
D) less than $40,000
44) A company could add $10,000 per week in revenues if the project depicted in Table 7.10 could be
shortened.
Table 7.10
Activity
Immediate
Predecessor(s)
Time
(weeks)
A
—
7
B
—
9
C
A
8
D
A, B
8
E
B
9
F
C
10
G
D, E
5
H
E
10
I
F, G
5
Four possible options exist to crash activities: crash A by one week at a cost of $6,000; crash C by two
weeks at a cost of $15,000; crash E by one week at a cost of $2,000; and crash I one week at a cost of $7,000.
What is the maximum amount of additional profit that can be made by crashing an option (or options)?
A) less than or equal to $4,000
B) greater than $4,000 but less than or equal to $8,000
C) greater than $8,000 but less than or equal to $12,000
D) greater than $12,000
45) If a project has exactly one critical path, which of the following statements is true?
A) Crashing an activity on the critical path will always result in an increase in total project profits.
B) Activities on the critical path cannot be crashed.
C) Crashing an activity on the critical path will always result in a reduced total project completion time.
D) The best schedule is one in which all activities are crashed as much as possible.
32
46) The ________ is the shortest possible time to complete the activity.
47) The ________ is determined by starting with the normal time schedule and crashing activities along
the critical path in such a way that the costs of crashing do not exceed the savings in indirect and penalty
costs.
48) Describe how time–cost tradeoffs for project activities should be identified and analyzed.
Answer: There are always time–cost tradeoffs in project management situations. Overall project length is
driven by the length of the critical path, so if it is necessary to finish the project more quickly, the
33
49) The following table contains a list of activities, with early- and late-start and finish times and crash
costs for the network shown in the figure. All start and finish times and crash costs are on a per-week
basis. Each activity can be reduced by one week at the most.
a. Determine the uncrashed activity lengths for activities A though K.
b. Determine the minimum completion cost for this project if each week carries a fixed cost of $1,000.
Activity
ES
EF
LS
LF
Crash
Cost/week
A
0
5
0
5
$1,100
B
5
9
13
17
$250
C
5
11
5
11
$1,200
D
0
6
1
7
$350
E
6
10
7
11
$900
F
9
14
17
22
$875
G
11
17
16
22
$1,500
H
11
18
11
18
$500
I
18
26
18
26
$300
J
17
21
22
26
$625
K
26
34
26
34
$750
34
Answer: Activity lengths for A–K can be found by subtracting the early start of each activity from the
late start of each activity.
The activity lengths appear in this table:
a.
Activity
Length
LS
LF
Crash
Cost/week
A
5
0
5
$1,100
B
4
13
17
$250
C
6
5
11
$1,200
D
6
1
7
$350
E
4
7
11
$900
F
5
17
22
$875
G
6
16
22
$1,500
H
7
11
18
$500
I
8
18
26
$300
J
4
22
26
$625
K
8
26
34
$750
b.
The critical path is ACHIK = 34 weeks. Other paths are DEHIK = 33; ACGJK = 29; DEGJK = 28; and ABFJK
= 26. With a fixed cost of $1,000/week, the initial cost is 34 weeks @ $1,000 = $34,000.
The cheapest critical-path activity is I @ $300, so reducing I from 8 weeks to 7 weeks costs $300 but saves
$1,000, resulting in a net savings of $700.
35
50) The following table contains a list of activities, with precedence requirements and crash costs. All start
and finish times and crash costs are on a per-week basis.
a. Determine the project cost and duration without crashing.
b. Determine the least expensive project cost if the duration is to be 10% shorter than normal project
duration.
c. Determine the least expensive project cost if the duration is to be 20% shorter than normal project
duration.
d. Create a graph that shows project expediting cost plotted as a function of the reduction in project
duration.
Activity
Normal
Time
Crash Time
Normal
Cost
Crash Cost
Predecessor
A
10
7
2,000
2,600
B
12
8
1,500
2,000
A
C
16
12
2,200
3,000
A
D
8
7
2,500
3,000
B
E
13
10
1,950
2,275
C
F
9
8
800
1,000
D
G
24
29
3,650
4,000
E, F
H
17
14
1,200
1,800
G
Answer:
a. Crash costs per week are shown in the table. The uncrashed project duration is 80 weeks at a cost of
$15,800.
Activity
Normal
Time
Crash Time
Normal
Cost
Crash Cost
Crash
cost/week
A
10
7
2,000
2,600
$ 200
B
12
8
1,500
2,000
125
C
16
12
2,200
3,000
200
D
8
7
2,500
3,000
500
E
13
10
1,950
2,275
108.33
F
9
8
800
1,000
200
G
20
15
3,650
4,000
70
H
17
14
1,200
1,800
200
b. The least expensive way to reduce the project duration by 10% (eight weeks) is by crashing activity G
c. Reducing the project by 20% from normal duration requires the actions indicated in part b, plus these