Operations Management
2nd Edition
ISBN: 9781260484687
Author: CACHON, Gerard
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 19, Problem 4PA
Summary Introduction
To determine: The critical path.
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Coleman Rich Control Devices, Inc., produces custom-built relay devices for auto makers. The most recent project undertaken by Rich requires 14 different activities. Rich's managers would like to
determine the total project completion time (in days) and those activities that lie along the critical path. The appropriate data are shown in the following table:
Activity
A
B
с
D
E
F
G
a) The expected completion time of the project =
a
4
1
6
5
1
2
1
Time (days)
m
6
2
6
8
9
3
7
b
7
3
6
11
18
6
8
Immediate
Predecessor(s)
A
A
B, C
D
D
Activity a
H
4
I
1
J
2
K
8
2
1
6
M
N
days (round your response to two decimal places).
Time (days)
=
m
4
6
5
9
4
2
8
b
6
8
7
11
6
3
10
Immediate
Predecessor(s)
E, F
G, H
K
L, M
The activities that represent the project's critical path are
b) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 53 days or less =
decimal places).
c) Using the standard normal table, the…
In the project considered below, activity crashing can take place over a wide
range of reduction times. The cost per day of reduction is given:
Activity
Immediate
Normal Time
Cost/day
Lower Time
Predecessor
(days)
Limit
A
None
3
450
1
B
None
4
300
2
A
3
200
D
E
100
E
A,B
500
1
F
C.D
4
600
3
For example, activity C can be crashed from its normal time of 3 days down to as
little as 1 day or anywhere in between; the cost per day to crash C is 200.
a) Draw a network diagram for this project. What is the critical path? How long
will the project take, if no crashing takes place?
b) Determine the least cost way to crash activities in order to complete the
project in 11 days; in 10 days; in 9 days; in 8 days.
c) Suppose the due date for the project is 5 days and a penalty of $500 a day is
assessed for each day late. What is the optimal number of days to crash the
project? Why?
Coleman Rich Control Devices, Inc., produces custom-built relay devices for auto makers. The most recent project undertaken by Rich requires 14 different activities. Rich's managers would like to determine the total project completion time (in days) and those activities that lie along the critical path. The appropriate data are shown in the following table:
Time (days)
Immediate
Time (days)
Immediate
Activity
a
m
b
Predecessor(s)
Activity
a
m
b
Predecessor(s)
A
4
7
8
—
H
3
3
6
E, F
B
1
2
3
—
I
3
7
9
G, H
C
7
7
7
A
J
2
6
9
I
D
6
9
13
A
K
8
9…
Chapter 19 Solutions
Operations Management
Ch. 19 - A project has four activities that take 4, 3, 6,...Ch. 19 - Consider the simple dependency matrix shown in...Ch. 19 - Consider a project with two activities that are...Ch. 19 - Prob. 4CQCh. 19 - Prob. 5CQCh. 19 - Prob. 6CQCh. 19 - Prob. 7CQCh. 19 - Prob. 8CQCh. 19 - Prob. 9CQCh. 19 - Prob. 10CQ
Ch. 19 - Consider two projects that have the same...Ch. 19 - Prob. 12CQCh. 19 - Prob. 13CQCh. 19 - Prob. 14CQCh. 19 - The key objectives of a project are given by a....Ch. 19 - Which of the following descriptions best captures...Ch. 19 - Prob. 1PACh. 19 - Prob. 2PACh. 19 - Prob. 3PACh. 19 - Prob. 4PACh. 19 - A project activity has an earliest completion time...Ch. 19 - What is the definition of the latest completion...Ch. 19 - Which of the following statements is correct with...Ch. 19 - A project consists of three tasks: A, B, and C....Ch. 19 - Prob. 9PACh. 19 - Prob. 10PACh. 19 - You manage a project with 10 activities....Ch. 19 - Which of the following activities is not part of...Ch. 19 - You have been asked by the CEO of your company to...Ch. 19 - BUILDING A HOUSE IN THREE HOURS Habitat for...Ch. 19 - BUILDING A HOUSE IN THREE HOURS Habitat for...
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- Consider a project that has been modeled as in the table below. Part a) Draw the PERT/CPM network for this project and determine the project’s expected completion time μP and its critical path. Part b) Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP . Part c) Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)? *Please answer a-c and type your work and answers or write them neatly please* Thank youarrow_forwardConsider a project that has been modeled as in the table below. Part a) Draw the PERT/CPM network for this project and determine the project’s expected completion time μP and its critical path. Part b) Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP . Part c) Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)? *Please answer a-c and either type your work and answers or write them neatly showing each step, please* NO EXCEL Thank you!arrow_forwardThe activity times are 3, 4, 2, 5, 7, 2, 2, and 3 days for activities A1 through A8,respectively. What is the critical path?a. A1, A2, A3, A4, A8b. A1, A2, A3, A6, A7, A8c. A1, A2, A5, A7, A8d. None of these options is the critical path.arrow_forward
- You are in charge of a project at the local community center. The center needs to remodel one of the rooms in time for the start of a new program. Delays in the project mean that the center must rent other space at a nearby church at additional cost. Time and cost data for your project are contained in 7.10. Your interest is in minimizing the cost of theproject to the community center.a. Using the normal times for each activity, what is the earliest date you can complete the project?b. Suppose the variable overhead costs are $50 per day for your project. Also, suppose that the center must pay $40 per day for a temporary room on day 15 or beyond. Find the minimum-cost project schedule.arrow_forwardA project consist of 5 activities A,B,C,D,E with ES, EF, LS and LF of A (0, 6, 9, 15); B (0, 7, 0, 7); C (6, 13, 15, 22); D (7, 13, 7, 13); E (13, 22, 13, 22). Normal Time (in month), Crash time (in month), Normal cost (in million Rp), Crash cost (in million Rp) from each activity are A (6, 4, 20, 24); B (7, 5, 30, 35); C (7, 6, 10, 13); D (6, 4, 20, 26); E (9, 8, 88, 90) a. What activities are in the critical path? How long is the project duration? b. If we want to crash the project for 2 months, what activities need to be crashed? How much additional cost required?arrow_forwardThe client of a project has requested the project team to crash 8 hours of time. The table below provides the necessary information about the possible project crashing. (a) What is the crash cost for 8 hours of time-savings? (b) Assume the team calls the client and asks for a project extension, reducing the amount of time they need to crash. The project team has a $20 crash budget. Is the budget sufficient to crash 4 hours of time? Activity Normal Duration (hours) Normal Cost ($) Crash Duration (hours) Crash Cost (S) Immediate Predecessors A 2 10 2 0 None B 3 15 2 23 A C 5 25 4 30 B D 3 20 1 24 C E 6 30 4 45 C F 1 5 1 0 E G 7 35 6 50 F H 10 50 7 80 D, Garrow_forward
- Development of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table: Activity Normal Time (weeks) Crash Time (weeks) Normal Cost Total Cost with Crashing Immediate Predecessor(s) A 4 3 $2,100 $2,750 — B 2 1 $2,300 $3,100 — C 3 3 $600 $600 — D 8 4 $2,400 $2,720 A E 6 3 $1,000 $1,450 B F 3 2 $3,000 $4,400 C G 4 2 $1,500 $2,000 D, E a) Based on the given information regarding the activities for the project, the project length = enter your response here weeks. b) The total cost required for completing this project on normal time = $enter your response here. c) For…arrow_forwardDevelopment of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table: Activity Normal Time (weeks) Crash Time (weeks) Normal Cost Total Cost with Crashing Immediate Predecessor(s) A 4 3 $2,100 $2,800 — B 2 1 $2,300 $3,100 — C 3 3 $600 $600 — D 8 4 $2,400 $2,680 A E 6 3 $1,000 $1,450 B F 3 2 $3,200 $4,600 C G 4 2 $1,400 $2,000 D, E Part 2 a) Based on the given information regarding the activities for the project, the project length = enter your response here weeks.arrow_forwardDevelopment of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table: Activity Normal Time(weeks) Crash Time(weeks) Normal Cost Total Cost with Crashing Immediate Predecessor(s) A 4 3 $2,000 $2,650 — B 2 1 $2,100 $2,900 — C 3 3 $750 $750 — D 8 4 $2,300 $2,620 A E 6 3 $900 $1,275 B F 3 2 $3,200 $4,700 C G 4 2 $1,400 $1,900 D, E I have answers for the frist part of the question: a) Based on the given information regarding the activities for the project, the project length = 16 weeks. b) The total cost required for completing this project on normal time = $12,650. c) For reducing the duration of the project by one week, the activity that should be crashed first is activity…arrow_forward
- Development of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table: Activity Normal Time(weeks) Crash Time(weeks) Normal Cost Total Cost with Crashing Immediate Predecessor(s) A 4 3 $2,000 $2,650 — B 2 1 $2,100 $2,900 — C 3 3 $750 $750 — D 8 4 $2,300 $2,620 A E 6 3 $900 $1,275 B F 3 2 $3,200 $4,700 C G 4 2 $1,400 $1,900 D, E a) Based on the given information regarding the activities for the project, the project length = 16 weeks. b) The total cost required for completing this project on normal time = $12,650. c) For reducing the duration of the project by one…arrow_forwardThe information in the table below is available for a large fund-raising project. Activity Activity Times (days) Activity Cost ($) Immediate Predecessor A 3 100 None B 4 150 None C 2 125 A D 5 175 B E 2 150 B F 4 200 C, D G 6 75 C H 2 50 C, D, E I 1 100 E J 4 75 D, E K 5 350 F, G L 3 150 G, H, I M 4 400 I, J N 4 175 K, M O 1 200 H, M P 5 150 N, L, O Draw the precedence network diagram. Perform the CPM (Critical Path Method) and give the complete activity schedule table, the project completion time, and the critical path. Plot on the same graph the total project costs per day, starting from day one to the completion date, assuming the earliest start times and then assuming the latest start times. What implications does the time differential have for cash flows and project scheduling? Show step by step solutionarrow_forwardA project consists of seven activities, lettered A through F below. For each activity, the estimated normal time in number of weeks, crash time, normal cost, crash cost, and its preceding activity are given. Normal Time Crash Time Normal Cost Crash Cost Immediate Activity (weeks) (weeks) (Peso) (Peso) Predecessor(s) A 4 3 2,000 2,600 2 1 2,200 2,800 3 500 500 D 8. 4 2,300 2,600 A E 6 3 900 1,200 F 3 2 3,000 4,200 G 4 2 1,400 2,000 D, E What is the maximum time that can be crashed? O Not in the choices Seven weeks Five weeks O Four weeks O Six weeksarrow_forward
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