A) LF − EF. B) EF − LF. C) EF − LS. D) LF − ES. A) LF − EF. B) EF − LF. C) EF − LS. D) LF − ES.

Exam 13: Project Scheduling

A project consists of five activities.Naturally the paint mixing precedes the painting activities.Also,both ceiling painting and floor sanding must be done prior to floor buffing. Activity Optimistic Time (hr) Most Probable Time (hr) Pessimistic Time (hr) Floor sanding 3 4 5 Floor buffing 1 2 3 Paint mixing 0.5 1 1.5 Wall painting 1 2 9 Ceiling painting 1 5.5 7 a.Construct the PERT/CPM network for this problem. b.What is the expected completion time of this project? c.What is the probability that the project can be completed within 9 hr.?

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Question 1

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a.

b. 8 hrs.
c. $.8264$

Given the following network with activities and times estimated in days, $Given the following network with activities and times estimated in days, \begin{array} { c c c c } \text { Activity } & \text { Optimistic } & \begin{array} { c } \text { Most } \\ \text { Probable } \end{array} & \text { Pessimistic } \\ \hline \text { A } & 2 & 5 & 6 \\ \text { B } & 1 & 3 & 7 \\ \text { C } & 6 & 7 & 10 \\ \text { D } & 5 & 12 & 14 \\ \text { E } & 3 & 4 & 5 \\ \text { F } & 8 & 9 & 12 \\ \text { G } & 4 & 6 & 8 \\ \text { H } & 3 & 6 & 8 \\ \text { I } & 5 & 7 & 12 \\ \text { J } & 12 & 13 & 14 \\ \text { K } & 1 & 3 & 4 \end{array} a.What are the critical path activities? b.What is the expected time to complete the project? c.What is the probability the project will take more than 28 days to complete?$ Activity Optimistic Most Probable Pessimistic A 2 5 6 B 1 3 7 C 6 7 10 D 5 12 14 E 3 4 5 F 8 9 12 G 4 6 8 H 3 6 8 I 5 7 12 J 12 13 14 K 1 3 4 a.What are the critical path activities? b.What is the expected time to complete the project? c.What is the probability the project will take more than 28 days to complete?

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$\begin{array}{l}\text { a. and } b \text {. }\\\begin{array} { l c l } \text { Activity } & \text { Expected Time } & \text { Variance } \\\hline \text { A } & 4.67 & 0.44 \\\text { B } & 3.33 & 1.00 \\\text { C } & 7.33 & 0.44 \\\text { D } & 11.17 & 2.25 \\\text { E } & 4.00 & 0.11 \\\text { F } & 9.33 & 0.44 \\\text { G } & 6.00 & 0.44 \\\text { H } & 5.83 & 0.69 \\\text { I } & 7.50 & 1.36 \\\text { J } & 13.00 & 0.11 \\\text { K } & 2.83 & 0.25\end{array}\end{array}$ $\begin{array}{l} \text { a. and } b \text {. }\\ \begin{array} { l c l } \text { Activity } & \text { Expected Time } & \text { Variance } \\ \hline \text { A } & 4.67 & 0.44 \\ \text { B } & 3.33 & 1.00 \\ \text { C } & 7.33 & 0.44 \\ \text { D } & 11.17 & 2.25 \\ \text { E } & 4.00 & 0.11 \\ \text { F } & 9.33 & 0.44 \\ \text { G } & 6.00 & 0.44 \\ \text { H } & 5.83 & 0.69 \\ \text { I } & 7.50 & 1.36 \\ \text { J } & 13.00 & 0.11 \\ \text { K } & 2.83 & 0.25 \end{array} \end{array} CRITICAL PATH: C-H-J-K EXPECTED PROJECT COM PLETION TIME = 29 VARIANCE OF PROJECT COMPLETION TIME = 1.5 The probability that the project will take more than 28 days is P ( z > ( 28 - 29 ) / 1.22 ) = P ( z > - .82 ) = .7939$
CRITICAL PATH: C-H-J-K
EXPECTED PROJECT COM PLETION TIME $= 29$
VARIANCE OF PROJECT COMPLETION TIME $= 1.5$
The probability that the project will take more than 28 days is $P ( z > ( 28 - 29 ) / 1.22 ) = P ( z > - .82 ) = .7939$

Which is not a significant challenge of project scheduling?

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Question 3

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A critical activity can be part of a noncritical path.

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Question 4

The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.

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Question 5

Consider the following PERT/CPM network with estimated times in weeks.The project is scheduled to begin on May 1. The three-time estimate approach was used to calculate the expected times and the following table gives the variance for each activity: $Consider the following PERT/CPM network with estimated times in weeks.The project is scheduled to begin on May 1. The three-time estimate approach was used to calculate the expected times and the following table gives the variance for each activity: \begin{array} { c c | c c } \text { Activity } & \text { Variance } & \text { Activity } & \text { Variance } \\ \hline \text { A } & 1.1 & \mathrm { E } & 0.3 \\ \text { B } & 0.5 & \mathrm {~F} & 0.6 \\ \text { C } & 1.2 & \mathrm { G } & 0.6 \\ \text { D } & 0.8 & \mathrm { H } & 1.0 \end{array} a.Give the expected project completion date and the critical path. b.By what date are you 99% sure the project will be completed?$ Activity Variance Activity Variance A 1.1 0.3 B 0.5 0.6 C 1.2 0.6 D 0.8 1.0 a.Give the expected project completion date and the critical path. b.By what date are you 99% sure the project will be completed?

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Question 6

The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.

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Question 7

Activities require time to complete while events do not.

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Question 8

Joseph King has ambitions to be mayor of Williston,North Dakota.Joe has determined the breakdown of the steps to the nomination and has estimated normal and crash costs and times for the campaign as follows (times are in weeks). Joe King is not a wealthy man and would like to organize a 16-week campaign at minimum cost.Write and solve a linear program to accomplish this task.

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Which is not a significant challenge of project scheduling?

A critical activity can be part of a noncritical path.

The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.

The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.

Activities require time to complete while events do not.

The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.

A path through a project network must reach every node.

Activities following a node

For an activity with more than one immediate successor activity,its latest-finish time is equal to the

Activities with zero slack

Arcs in a project network indicate

Which of the following is always true about a critical activity?

Slack equals

Crashing refers to an unanticipated delay in a critical path activity that causes the total time to exceed its limit.

The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity.

The difference between an activity's earliest finish time and latest finish time equals the difference between its earliest start time and latest start time.

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