Exam 13: Project Scheduling

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All activities on a critical path have zero slack time.

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When activity times are uncertain,total project time is normally distributed with mean equal to the sum of the means of all of the critical activities.

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From this schedule of activities,draw the PERT/CPM network. Activity Immediate Predecessor A \@cdots B A C B D B E A F C, D G E, F

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In CPM,for activities with more than one immediate predecessor activity,which of the following is used to compute its earliest finish (EF)time​

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​Precedence relationships among activities is critical in CPM analysis but not in PERT.

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The variance in the project completion time is the sum of the variances of all activities in the project.

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The critical path for this network is A - E - F and the project completion time is 22 weeks.  The critical path for this network is A - E - F and the project completion time is 22 weeks.    ​   \begin{array} { c c c r r }  \text { Activity } & \begin{array} { c }  \text { Normal } \\ \text { Time } \end{array} & \begin{array} { c }  \text { Crash } \\ \text { Time } \end{array} & \begin{array} { c }  \text { Normal } \\ \text { Cost } \end{array} & \multicolumn{1}{c} { \begin{array} { c }  \text { Crash } \\ \text { Cost } \end{array} } \\ \hline \text { A } & 12 & 8 & 8,000 & 12,000 \\ \text { B } & 14 & 10 & 5,000 & 7,500 \\ \text { C } & 8 & 8 & 10,000 & 10,000 \\ \text { D } & 5 & 3 & 6,000 & 8,000 \\ \text { E } & 4 & 3 & 5,000 & 7,000 \\ \text { F } & 6 & 5 & 9,000 & 12,000 \\ \text { G } & 10 & 8 & 5,000 & 8,000 \end{array}  If a deadline of 17 weeks is imposed,give the linear programming model for the crashing decision. ​ Activity Normal Time Crash Time Normal Cost \multicolumn 1 c Crash Cost A 12 8 8,000 12,000 B 14 10 5,000 7,500 C 8 8 10,000 10,000 D 5 3 6,000 8,000 E 4 3 5,000 7,000 F 6 5 9,000 12,000 G 10 8 5,000 8,000 If a deadline of 17 weeks is imposed,give the linear programming model for the crashing decision.

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A critical activity is one that​

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A project network is shown below.Use a forward and a backward pass to determine the critical path,and then fill out the table below.Activity times are in weeks. A project network is shown below.Use a forward and a backward pass to determine the critical path,and then fill out the table below.Activity times are in weeks.    Now assume that the times listed are only the expected times instead of being fixed times.Is the probability of being finished in fewer than 25 weeks more or less than 50%?   Now assume that the times listed are only the expected times instead of being fixed times.Is the probability of being finished in fewer than 25 weeks more or less than 50%? A project network is shown below.Use a forward and a backward pass to determine the critical path,and then fill out the table below.Activity times are in weeks.    Now assume that the times listed are only the expected times instead of being fixed times.Is the probability of being finished in fewer than 25 weeks more or less than 50%?

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The earliest start time rule

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​A critical activity is

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PERT and CPM are applicable only when there is no dependence among activities.

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The length of time an activity can be delayed without affecting the project completion time is the slack.

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From this PERT/CPM network,determine the list of activities and their predecessors. ​ From this PERT/CPM network,determine the list of activities and their predecessors. ​

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Consider a project that has been modeled as follows: ​ Activity Immediate Predecessors Duration (hr) A \@cdots 7 B \@cdots 10 C A 4 D A 30 E A 7 F B,C 12 G B,C 15 H E,F 11 I E,F 25 J E,F 6 K D, H 21 L G,J 25 a.Draw the PERT/CPM network for this project and determine project's expected completion time and its critical path. b.Can activities E and G be performed simultaneously without delaying the minimum project completion time? c.Can one person perform A,G,and I without delaying the project? d.By how much can activities G and L be delayed without delaying the entire project? e.How much would the project be delayed if activity G was delayed by 7 hours and activity L was delayed by 4 hours? Explain.

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Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.

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​The main difference between CPM and PERT is

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The earliest finish time for the final activity is the project duration.

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