In: Operations Management

Project management

Expediting a Project

Task |
Predecessor |
Normal Time Weeks |
Normal Cost |
Crash Time |
Crash Cost |

A |
- |
4 |
$2000 |
4 |
- |

B |
A |
4 |
$1500 |
2 |
4500 |

C |
A |
6 |
5000 |
4 |
8000 |

D |
B |
2 |
1000 |
2 |
- |

E |
B |
6 |
8000 |
3 |
10000 |

F |
C |
10 |
10000 |
7 |
14000 |

G |
D |
7 |
3500 |
4 |
5000 |

H |
E |
4 |
2500 |
2 |
5000 |

I |
G,H |
3 |
2000 |
2 |
3500 |

J |
I,F |
3 |
3000 |
1 |
4500 |

Consider the project shown above.

a)Draw the network diagram and find the critical path, time and cost for an all-normal level of project activity.

b)Calculate the crash cost-per-week assuming that all activities may be partially crashed.

c)Which tasks should be crashed to do the project in 21 weeks? What is the project cost?

d)Calculate the shortest delivery time for the project. What is the cost?

(i)

Critical path is ABEHIJ with duration 24 weeks.

cost for nromal time =38500

(ii)

Activity | slope | Max crash |

A | None | 0 |

B | 1500 | 2 |

C | 1500 | 2 |

D | None | 0 |

E | 666.66 | 3 |

F | 1333.33 | 3 |

G | 500 | 3 |

H | 1250 | 2 |

I | 1500 | 1 |

J | 750 | 2 |

crashing schedule

(i) E is the cheapest activity which can be crashed for a week at 666 per week. Duration is 23 and cost is 38500+666 =39166

Now ABDGIJ, ABEHIJ and ACFJ are critical paths.

(ii) J can be crashed for 2 weeks at a total cost of 1500. Duration is now 21 weeks and cost is 40666

The cost for crashing the project to 21 days is 2166. Total cost is 40666.

(iii) G, E and F can be crashed at a total cost of 2500. Duration is 20

Total cost is 43166

(iv) G, E and F can be again crashed at a total cost of 2500. Duration is 19

Total cost is 45666

(v) B and f can be crashed for 1 day each at a total cost of 2833, Duration is 18

Total cost is 48000

(vi) B and C can be crashed for 1 day at a cost of 3000. Duration is 17

Total cost is 51000.

(vii) C and I can be crashed at a total cost of 3000. Duration is 16

Cost is 54000.

No more crashing is possible.

Activity
Normal
Time
(days)
Normal Cost ($)
Crash
Time
(days)
Crash Cost ($)
Immediate
Predecessor(s)
A
6
1,000
5
1,200
—
B
4
800
2
2,000
—
C
3
600
2
900
A, B
D
2
1,500
1
2,000
B
E
6
900
4
1,200
C, D
F
2
1,300
1
1,400
E
G
4
900
4
900
E
H
4
500
2
900
G
The Advanced Tech Company has a project to design an integrated
information database for a...

Activity
Optimistic Time Estimate
(weeks)
Most Likely Time Estimates (weeks)
Pessimistic Time Estimates (weeks)
Immediate Predecessor(s)
A
3
6
9
none
B
3
5
7
A
C
4
7
12
A
D
4
8
10
B
E
5
10
16
C
F
3
4
5
D, E
G
3
6
8
D, E
H
5
6
10
F
I
5
8
11
G
J
3
3
3
H, I
A.)Using the information given, construct a network diagram
using AON notation....

1) Consider the network corresponding to the following
information.
Activity
Immediate
Predecessor(s)
Time
(Weeks)
A
---
3
B
---
4
C
A
6
D
B
9
E
B
6
F
C, D
6
G
D, E
8
H
G, F
9
Draw the network corresponding to the above
information.
Using a table format, identify the critical
path.
What is the project completion time?

Consider the project with the listed activities. Normal
durations and costs, as well as crash durations and costs are
listed for each activity. Precedence relationships are implicitly
given by the activity names (e.g., activity (1,2) is represented as
an arc from node 1 to node 2).
Crash
Crash
Normal
Normal
Activity
Time
Cost
Time
Cost
(1,
2)
5
$41,000
8
$29,000
(1,
3)
2
$18,000
3
$10,000
(2,
4)
10
$50,000
12
$46,000
(2,
5)
4
$26,000
6 ...

The Time Numbers represent weeks
a. Find the mean time for completion of the
project
b. Find the probability that the project will be
completed two weeks earlier than the mean
time.
Preceding
Optimistic
Most Likely
Pessimistic
Activity
Activity
Time
Time
Time
A. Write Book
10
13
17
B. Design Book Cover
A
1
1
1
C. Edit Manuscript
A
3
6
9
D. Check Editing
C
2
3
6
E. Accept Design
B
1
1
1
F. Copy Edit...

The time required to complete a project is normally distributed
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finished by the due date in the contract. If a construction company
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by the due date, what due date (project week #) should be
negotiated?

The mean time required to complete a certain type of
construction project is 52 weeks with a standard deviation of 3
weeks. Answer questions 4–7 using the preceding information and
modeling this situation as a normal distribution.
4. What is the probability of the completing the project in no
more than 52 weeks? a) 0.25 b) 0.50 c) 0.75 d) 0.05
5. What is the probability of the completing the project in more
than 55 weeks? a) 0.1587 b) 0.5091...

The mean time required to complete a certain type of
construction project is 52 weeks with a standard deviation of 3
weeks. Answer questions 4–7 using the preceding information and
modeling this situation as a normal distribution.
What is the probability of the completing the project in no
more than 52 weeks?
0.25
0.50
0.75
0.05
What is the probability of the completing the project in more
than 55 weeks?
0.1587
0.5091
0.7511
0.0546
What is the probability of completing...

A project has the following activities, precedence
relationships, and time estimates in weeks:
Activity
Immediate Predecessor
Activities
Optimistic
Time (to)
Most Likely Time (tm)
Pessimistic
Time (tp)
A
—
15
20
25
B
—
8
10
12
C
A
25
30
40
D
B
15
15
15
E
B
22
25
27
F
E
15
20
22
G
D
20
20
22
a. Compute the expected time and variance for
each activity.
b. Determine the critical path and the expected...

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Respond to the following prompts:
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