4.1 Dr. Honghui Deng Associate Professor MIS Department UNLV MIS 746 IS Project Management

4.2 Today Course schedule and datesCourse schedule and dates Questions from PERT lecture 1Questions from PERT lecture 1 In class exercise for PERT lecture 1In class exercise for PERT lecture 1 Review some of your ‘exam’ questionsReview some of your ‘exam’ questions Activity time exampleActivity time example Lecture 2 on PERTLecture 2 on PERT Exercise 2 on PERTExercise 2 on PERT Project team and topicProject team and topic

4.3 Review of PERT/CPM Video 5 PERT/CPM

4.4 Let’s try this exercise before Lecture 2 - Calculate: ES,EF,LS,LF, Slacks, and CP B2B2 A2A2 C1C1 D3D3 E5E5 F1F1 G2G2 H1H1 I2I2

4.5 Solution: ES,EF,LS,LF, Slacks, and CP B[0,2] 2[0,2] A[0,2] 2[1,3] C[2,3] 1[2,3] D[3,6] 3[3,6] E[6,11] 5[6,11] F[11,12] 1[11,12] G[12,14] 2[12,14] H[0,1] 1[13,14] I[14,16] 2[14,16] CP: B,C,D,E,F,G, and I

4.6 PERT - Estimating activity time Consider following questionConsider following question –What is the average waiting time in line at the registrar’s office? How would you go about calculating an average score?How would you go about calculating an average score?

4.7 PERT - Estimating activity time Consider following questionConsider following question –How long does it take to test codes for an accounts receivable program? How would you get an average score? Different from previous question?How would you get an average score? Different from previous question?

4.8 PERT - Estimating activity time Consider following questionConsider following question –How long does it take to get sufficient responses to a RFP? How would you estimate that?How would you estimate that?

4.9 PERT - Estimating activity time Calculating the duration of the entire project and the scheduling of the specific activities depends on how we calculate time for each activity.Calculating the duration of the entire project and the scheduling of the specific activities depends on how we calculate time for each activity. Obtaining estimates for projects that are repeat or projects that we have experience with is relatively easy. Estimating activity time for new and unique projects is significantly more difficult.Obtaining estimates for projects that are repeat or projects that we have experience with is relatively easy. Estimating activity time for new and unique projects is significantly more difficult. To factor uncertainly into the network analysis, often three estimates are used: Optimistic time (a), most probable time (m), and pessimistic time (b).To factor uncertainly into the network analysis, often three estimates are used: Optimistic time (a), most probable time (m), and pessimistic time (b).

4.10 Estimating uncertain activity time The three estimates (a, m, b) enable the systems analyst to develop the most likely activity time that ranges from the best possible (optimistic) time to the worst possible (pessimistic) time.The three estimates (a, m, b) enable the systems analyst to develop the most likely activity time that ranges from the best possible (optimistic) time to the worst possible (pessimistic) time. The expected time (t) can be calculated using the following formula:The expected time (t) can be calculated using the following formula: t = (a+4m+b)/6 To measure the dispersion or variation in the activity time values, the common statistical measure of the variance can be used:To measure the dispersion or variation in the activity time values, the common statistical measure of the variance can be used:  2 = [(b-a)/6] 2 (This formula assumes that a standard deviation is approximately 1/6 of the difference between the extreme values of the distribution: (b-a)/6. The variance is simply the square of the standard deviation).

4.11 Example of estimating activity time Consider the optimistic, most probable, and pessimistic time estimates for a project that involves the following activities: ActivityOptimisticMost probablePessimistic (a) (m) (b) (a) (m) (b) A4512 B C23 4 D3411 E23 4 F G H I J12 3

4.12 Estimating time for activity A Using the expected time (t) formula t = (a + 4m + b)/6 we have an estimated average or expected completion time of t A = [4 + 4(5) + 12]/6 = 36/6 = 6 weeks and using the variance formula  2 = [(b - a)/6] 2 we can determine the measure of uncertainty or the variance for activity A:  2 A = [(12 - 4)/6] 2 = (8/6) 2 = 1.78

4.13 Estimating time for all activities ActivityExpected timeVariance (in weeks) (in weeks) A [ 4 + 4(5) + 12]/6 6 [(12 - 4)/6] B C [2 + 4(3) + 4]/6 3 [(4 - 2)/6] D51.78 E F20.03 G30.25 H [ (3.5) + 7.5]/6 4 [(7.5 – 2.5)/6] I20.03 J20.11 Total 32 Once expected activity times are calculated, we can proceed with the critical path calculations to determine the expected project completion time and a detailed activity schedule.

4.14 Network with expected activity times A 6 B 2 E3E3 C3C3 G3G3 H4H4 J2J2 I2I2 F2F2 D5D5

4.15 Network with ES & EF A [0,6] 6 B [0,2] 2 E [6,9] 3 C [6,9] 3 G [11,14] 3 H [9,13] 4 J [15,17] 2 I [13,15] 2 F [9,11] 2 D [6,11] 5

4.16 Network with ES, EF, LS & LF A [0,6] 6 [0,6] B [0,2] 2 [7,9] E [6,9] 3 [6,9] C [6,9] 3 [10,13] G [11,14] 3 [12,15] H [9,13] 4 [9,13] J [15,17] 2 [15,17] I [13,15] 2 [13,15] F [9,11] 2 [13,15] D [6,11] 5 [7,12] Latest Finish Time Latest Start Time Earliest Start Time Earliest Finish Time

4.17 Activity schedule (in weeks) Earliest Latest Earliest Latest Earliest Latest Earliest Latest Start StartFinish Finish SlackCritical Start StartFinish Finish SlackCritical Activity (ES) (LS) (EF) (LF) (LS - ES) Path? A Yes B C D E Yes F G H Yes I Yes J Yes Critical path - A, E, H, I, and JProject duration - 17 weeks

4.18 Variance in critical path activities Variation in critical path activities can cause variation in the project completion date.Variation in critical path activities can cause variation in the project completion date. If a non-critical activity is delayed beyond its slack time, then that activity would become part of the new critical path, and further delays would affect the project completion date.If a non-critical activity is delayed beyond its slack time, then that activity would become part of the new critical path, and further delays would affect the project completion date. Variation in critical path activities resulting in shorter critical path will result in an earlier than expected completion date.Variation in critical path activities resulting in shorter critical path will result in an earlier than expected completion date. The variance in the project duration is the same as the sum of the variance of the critical path activities.The variance in the project duration is the same as the sum of the variance of the critical path activities.

4.19 Probability of meeting deadline The expected (E) project time (T) for the previous example isThe expected (E) project time (T) for the previous example is E(T) = t A + t E + t H + t I + t J = = 17 weeks = = 17 weeks The variance (  2 ) for that example isThe variance (  2 ) for that example is Var (T) =  2 =  2 A +  2 E +  2 H +  2 I +  2 J Since standard deviation is the square root of the variance, thenSince standard deviation is the square root of the variance, then  =   2 =  2.72 = 1.65  =   2 =  2.72 = 1.65

4.20 Estimating time for all activities ActivityExpected timeVarianceVariance (in weeks)  2 (for critical path) (in weeks)  2 (for critical path) A(CP) B C30.11 D51.78 E(CP) F20.03 G30.25 H(CP) I(CP) J (CP) Total Var (T) Standard deviation for critical path activities: Standard deviation for critical path activities:  =   2 =  2.72 = 1.65

4.21 Probability of meeting deadline Assuming a normal (bell-shaped) distribution of the project completion time allows us to compute the probability of meeting a specified project completion date.Assuming a normal (bell-shaped) distribution of the project completion time allows us to compute the probability of meeting a specified project completion date. Suppose the management has allowed 20 weeks for the previous project. What is the probability that we will meet the 20-week deadline?Suppose the management has allowed 20 weeks for the previous project. What is the probability that we will meet the 20-week deadline? We are looking for the probability of T <=20.We are looking for the probability of T <=20. The z value for the normal distribution of T = 20 isThe z value for the normal distribution of T = 20 is z = ( )/1.65 = 1.82 We need to use the normal distribution table.We need to use the normal distribution table.

4.22 Normal distribution of project time Time (weeks) Time (weeks)

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4.24 Normal distribution of project time z = z = = (20 -17)/1.65 = 1.82 p(T<= 20) p(T<= 20) Time (weeks) Time (weeks)

4.25 Summary PERT procedure can be used to schedule projects with uncertain activity times.PERT procedure can be used to schedule projects with uncertain activity times. The three time estimates (optimistic, most likely, pessimistic) help calculate an expected time and variance for each activity.The three time estimates (optimistic, most likely, pessimistic) help calculate an expected time and variance for each activity. The time for critical path activities provides the expected project completion time.The time for critical path activities provides the expected project completion time. The sum of the variances of activities on the critical path provides the variance in the project completion time.The sum of the variances of activities on the critical path provides the variance in the project completion time. Normal probability distribution assumption and procedures are used to compute the probability of the project being completed by a specific time.Normal probability distribution assumption and procedures are used to compute the probability of the project being completed by a specific time.

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4.27 Time-Cost Trade-off: Crashing Video 6 Time Crashing

4.28 Resource Limitations critical path crashing (cost/time tradeoff) other methods

4.29Crashing can shorten project completion time by adding extra resources (costs)can shorten project completion time by adding extra resources (costs) start off with NORMAL TIME CPM schedulestart off with NORMAL TIME CPM schedule get expected duration Tn, cost Cnget expected duration Tn, cost Cn Tn should be longest durationTn should be longest duration Cn should be most expensive in penalties, cheapest in crash costsCn should be most expensive in penalties, cheapest in crash costs

4.30 Time Reduction to reduce activity time, pay for more resourcesto reduce activity time, pay for more resources develop table of activities with times and costsdevelop table of activities with times and costs for each activity, usually assume linear relationship for relationship between cost & timefor each activity, usually assume linear relationship for relationship between cost & time

4.31 Crash Example Activity: programming Tn: 7 weeks Cn: $14,000 (7 weeks, 2 programmers) if you add a third programmer, done in 6 weeks Tc: 6 weeks Cn: $15,000 cost slope = ( )/(6-7)=-$1000/week

4.32 Example Problem activityPred TnCnTcCcslope max A requirements none 3can’t crash B programmingA week C get hardwareA week D train users B,C 3can’t crash Crashing Algorithm: 1 crash only critical activities B only choice 2 crash cheapest currently critical B is cheapest 3 after crashing one time period, recheck critical

4.33 Crash Example Import critical software from Australia: late penalty $500/d > 12 d A get import license5 daysno predecessor B ship7 daysA is predecessor C train users11 daysno predecessor D train on system2 daysB,C predecessors can crashC: $2000/day more than current for up to 3 days B: faster boat6 days$300 more than current bush plane5 days$400 more than current bush plane5 days$400 more than current commercial3 days$500 more than current commercial3 days$500 more than current

4.34 Crash Example Original schedule: 14 days, $1,000 in penalties= $1000 crash B to 6 days:13 days, $500 penalties, $300 cost = $800* crash B to 5 C to 10:12 days, no penalties, $ cost= $2400 to 11 days is worse NOW A SELECTION DECISION risk versus cost

4.35 Crashing Limitations assumes linear relationship between time and costassumes linear relationship between time and cost –not usually true (indirect costs don’t change at same rate as direct costs) requires a lot of extra cost estimationrequires a lot of extra cost estimation time consumingtime consuming ends with tradeoff decisionends with tradeoff decision

4.36 Resource Constraining CPM & PERT both assume unlimited resourcesCPM & PERT both assume unlimited resources NOT TRUE –may have only a finite number of systems analysts, programmers RESOURCE LEVELING - balance the resource loadRESOURCE LEVELING - balance the resource load RESOURCE CONSTRAINING - don’t exceed available resourcesRESOURCE CONSTRAINING - don’t exceed available resources