Strategic Project Management1SPM Basic PERT/CPM (Part 2) The Concept of Float zActivities that are not on the critical path contain positive slack or float. ycritical path activities have zero slack or float zSlack or float represents the amount by which an activity can be delayed without impacting the completion date of the project. ythe terms float and slack are interchangeable

Strategic Project Management2SPM Basic PERT/CPM (Part 2) The Concept of Float (continued) zThere are two types of float. yTotal Float is the amount by which an activity can be delayed without delaying the completion of the project. yAn activity with initial node i and terminal node j xTF(i,j) = LC(j) - ES(i) - D(i,j) TF is total float LC is latest completion ES is earliest start D is duration

Strategic Project Management3SPM Basic PERT/CPM (Part 2) The Concept of Float (continued) yFree Float is the amount by which an activity can be delayed without delaying the start of at least one other activity in the network. yFor an activity with initial node i and terminal node j xFF(i,j) = ES(j) - ES(i) - D(i,j) FF is free float ES is earliest start D is duration

Strategic Project Management4SPM Basic PERT/CPM (Part 2) The Concept of Float (continued) zLet’s re-examine our prior example and calculate the total and free float. zExample to be shown in class yUse the Excel calculation template provided in ADM_Float_Calcs.xls

Strategic Project Management5SPM Basic PERT/CPM (Part 2) Float Calculations Excel Template

Strategic Project Management6SPM Basic PERT/CPM (Part 2) The Concept of Float (continued) zThe following general observations can be made regarding float calculations: yFree Float will always be less than or equal to Total Float. yFree Float may be zero when Total Float is non-zero. yTotal Float for critical path activities will always be zero xFree Float will also be zero

Strategic Project Management7SPM Basic PERT/CPM (Part 2) Why is Float Important ? zFloat is flexibility (i.e., wiggle room). zFloat tells us that we don’t need to worry about some activities if they fall behind. zFloat helps us separate the “trivial many” from the “vital few”.

Strategic Project Management8SPM Basic PERT/CPM (Part 2) Probability Considerations zGenerally time estimates for activity durations are not deterministic. zA common approach to incorporate non- deterministic durations is to develop three time estimates for each activity yOptimistic time yPessimistic time yMost Likely time

Strategic Project Management9SPM Basic PERT/CPM (Part 2) Time Estimates zOptimistic xtime which will be required if execution goes extremely well zPessimistic xtime which will be required if execution goes very badly zMost Likely xtime which will be required if execution is normal

Strategic Project Management10SPM Basic PERT/CPM (Part 2) Time Estimates (continued) zIt is important to note that the most likely estimate does not have be the midpoint between the optimistic and pessimistic. zAt this point in the methodology it is common to assume that the activity times follow a Beta distribution. yThis is largely based on empirical evidence. yExamples to be shown in class.

Strategic Project Management11SPM Basic PERT/CPM (Part 2) Time Estimates (continued) zNext we calculate the mean and variance of each activity time under the Beta assumption. yMean = (opt + 4*ml + pess) / 6 yVariance = ((pess - opt) / 6)^2

Strategic Project Management12SPM Basic PERT/CPM (Part 2) Mean and Variance of an Activity Duration zLet’s work an example. zAssume that in our previous network example, Activity (0,1) had the following estimates yopt = 1; ml = 2; pess = 3 zThe resulting mean and variance are: ymean = (1 + 4*2 + 3) / 6 = 12/6 = 2.0 yvar = ((3 - 1) / 6)^2 = 0.33^2 = 0.11 xLet's review the results in ADM_Mean_Variance.xls

Strategic Project Management13SPM Basic PERT/CPM (Part 2) Results of Duration Mean and Variance Calculations

Strategic Project Management14SPM Basic PERT/CPM (Part 2) Probabilistic Completion Times zWe can now determine the critical path based on the mean activity times. zWe can also make probability statements about the project completion time. zThe expected time to completion of the critical path is the sum of the mean activity times for the activities on the critical path.

Strategic Project Management15SPM Basic PERT/CPM (Part 2) Expected Duration of the Critical Path zThe Critical Path is y(0,2) with mean duration of 3.0 y(2,3) with mean duration of 3.0 y(3,4) with mean duration of 0.0 (dummy) y(4,5) with mean duration of 7.0 y(5,6) with mean duration of 6.0 zThe mean time to completion is 19.0

Strategic Project Management16SPM Basic PERT/CPM (Part 2) Probabilistic Completion Times (continued) zThe variance of the expected time to completion of the critical path is the sum of the variances of the activity times for the activities on the critical path. yAs we move forward, BE CAREFUL to differentiate between the VARIANCE and the STANDARD DEVIATION. yWe will be using both and it is important that you are using the correct one in each case.

Strategic Project Management17SPM Basic PERT/CPM (Part 2) Critical Path Variance of Expected Duration zThe Critical Path is y(0,2) with variance of 1.00 y(2,3) with variance of 2.78 y(3,4) with variance of 0.00 (dummy) y(4,5) with variance of 0.11 y(5,6) with variance of 0.44 zThe variance of time to completion is 4.33

Strategic Project Management18SPM Basic PERT/CPM (Part 2) What Now? zWe now have the mean and variance of the time to complete the critical path. yMean time to completion= 19.0 yVariance of time to completion = 4.33 zBut what do we do now? zWe can now make probability statements about project completion.

Strategic Project Management19SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zFirst, we invoke the Central Limit Theorem y We will assume that the distribution of completion time is approximately Normal. yThis is actually not a very risky assumption since the sum of random variables quickly approaches Normality. zWe can now estimate the probability of completing by specified times.

Strategic Project Management20SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zIn our example, ymean = 19.0, variance = 4.33 ywe will need the standard deviation (rather than variance) of expected time to completion ystd dev = SQRT(variance) = 4.33^0.5 = 2.08 zWe will also need “Standard Normal Tables” found in most Statistics books yor in file: ADM_Standard_Normal_Table.xls

Strategic Project Management21SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zWhat is the probability of completing by time 20.0? yStep 1: Convert to Standard Normal (also known as a “z statistic”) xz = (point of interest - mean) / (std. dev.) xz = ( ) / 2.08 = 0.48

Strategic Project Management22SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zWhat is the probability of completing by time 20? yStep 2: Look up the probability for the z value in a standard Normal table xz = 0.48 xPr(z<0.48) = yProbability of completing the project in 20.0 time units or less is

Strategic Project Management23SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zWhat is the probability of completing by time 19.0? yz = ( ) / 2.08 = 0.0 yPr(z<0) = yProbability of completing in 19 or less is 0.50 yConclusion: traditional critical path calculations are optimistic! They actually give us the 50/50 probability point.

Strategic Project Management24SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zBy what time are we 90% sure we will be complete? yPr(z<?) = 0.9 ysearch the standard Normal table y? = 1.28 y(time-19)/2.08 = 1.28 ytime = 21.7

Strategic Project Management25SPM Basic PERT/CPM (Part 2) Probability Statements about Project Completion zBy what time are we 99% sure we will be complete? yPr(z<?) = 0.99 ysearch the standard Normal table y? = 2.33 y(time-19)/2.08 = 2.33 ytime = 23.8