32CPM

CPM analysis ‡ Draw the CPM network ‡ Analyze the paths through the network ‡ Determine the float for each activity ± Compute the activity¶s float float = ÿS - ES = ÿF - EF ± Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project ‡ Find the critical path is that the sequence of activities and events where there is no ³slack´ i.e.. Zero slack ± ÿongest path through a network ‡ Find the project duration is minimum project completion time

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Critical Path Analysis ‡ A critical path consists that set of dependent tasks (each dependent on the preceding one), which together take the longest time to complete. ‡ One way is to draw critical path tasks with a double line instead of a single line. ‡ The critical path for any given method may shift as the project progresses; this can happen when tasks are completed either behind or ahead of schedule, causing other tasks which may still be on schedule to fall on the new critical path

PEaT ‡ PEaT is based on the assumption that an activity¶s duration follows a probability distribution instead of being a single value ‡ Three time estimates are required to compute the parameters of an activity¶s duration distribution: ± pessimistic time (tp ) - the time the activity would take if things did not go well ± most likely time (tm ) - the consensus best estimate of the activity¶s duration ± optimistic time (to ) - the time the activity would take if things did go well u Y
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PEaT analysis ‡ Draw the network. ‡ Analyze the paths through the network and find the critical path. ‡ The length of the critical path is the mean of the project duration probability distribution which is assumed to be normal ‡ The standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum ‡ Probability computations can now be made using the normal distribution table.

Probability computation Determine probability that project is completed within specified time x-Ë Z= where Ë = tp = project mean time = project standard mean time x = (proposed ) specified time

PEaT Example Immed. Optimistic Most ÿikely Pessimistic Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -4 6 8 | -1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F |,C 3 4 5 G |,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7

PEaT Example PEaT Network

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PEaT Example Activity A | C D E F G H I J K

Expected Time 6 4 3 5 1 4 2 6 5 3 5

Variance 4/ 4/ 0 1/ 1/36 1/ 4/ 1/ 1 1/ 4/

PEaT Example Activity ES A | C D E F G H I J K

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Slack 0 *critical 5 0* 6 0* 7 1 0* 1 0*

PEaT Example Vpath = VA + VC + VF + VI + VK = 4/ + 0 + 1/ + 1 + 4/ = 2 path = 1.414 o = (22 - 23)/
(22-23)/1.414 = -0.71 From the Standard Normal Distribution table: P(z < 0.71) = .5 + .2612 = .7612

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Generate PEaT Chart: Enter Data for Each Task ‡ ‡ ‡ ‡


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Forward Pass: Determine Earliest Start (ES) and Earliest Complete (EC) for each Task ‡  / 
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|ackward Pass: Determine ÿatest Start (ÿS) and ÿatest Complete (ÿC) for each Task ‡   
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Determine Total Float (TF): Allowable delay in start of task which will not delay Project Completion ‡ 
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Determine Free Float (FF): Allowable delay in start of task which will not delay start of any other task. ‡ 
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Determine Critical Path

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