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REVIEW QUESTIONS AND EXERCISES 9.1 (a) Using PERT, calculate expected project duration and determine the critical path in the network defined by the data below. (b) What is the probability of completing this project in 32 weeks or less? Duration (Weeks) Successor Activity Description Prefab Wall Forms Туре 40 Constant 2 10 50, 60, 70 Excavate Cols and Walls Constant 3 20 в0, 70 Im to 3,4, 8 Let Elec and Mech Subcontract 30 80, 90, 100 Constant 4 40 Deliver Wall Forms Im to 6,7, 8 m to 5,7, 10 В0,90, 100 Forms, Pour & Cure Wall & Col Fig 50 110 60 Rough-in Plumbing fm o 9,11, 15 110 Install Conduit 70 Constant 9 110 Erect Wall Forms & Steel 80 Fabricate & Set Interior Column Forms Constant 6 120 00 tm to 12, 16, 18 140 100 Erect Temporary Roof Pour, Cure & Strip Walls Constant 10 130 110 120 Pour, Cure & Strip Int. Wals Constant 6 140 140 Backfil for Slab on Grade Constant 1 130 Constant 5 Grade & Pour Floor Slab END 140 92/e) Couen the date helow for e mall nineline nrniect hased on a PERT analvsis what is the expected proiect duration?.(b) What is the probability a otina this

Answer 1

Step 1: For each activity, find the expected time Tx = (a + 4m + b)/6, and Variance oʻ = [(b-a)/6]" Step 2: Find the Earliest start and finish and Latest start and finish times and Slack for each activity. Earliest Start is calculated by forward path method as latest of the predecessors Earliest Finish. Latest Start is calculated using reverse path method as earliest of the successors Latest Start. Earliest Finish = Earliest Start + Activity Duration Latest Start=Latest Finish - Activity Duration Slack = Latest Finish - Earliest Finish, or Latest Start - Earliest Start Activity Activity Predecesso Critical ES LS EF LF Slack Successor Activity 3.00 E,F,G Critical 5.G Α HIJ HIJ B 0.11 Critical lol Expected variance (Ts) (6) 2.00 0.00 0.00 4.50 0.69 4.00 0.00 7.00 7.17 0.69 11.33 1.00 9.00 0.00 6.00 0.00 15.67 1.00 10.00 0.00 6.00 0.00 1.00 0.00 5.00 0.00 B,C B,C DE DE DE F,G,H 120 130 MI 140 N J,L, ML 0.00 0.00 0.00 2.00 3.00 4.50 4.50 10.00 10.00 10.00 19.00 16.00 29.00 30.00 4.00 0.00 3.17 6.00 3.00 11.83 7.67 10.00 18.00 14.33 19.00 24.00 29.00 30.00 2.00 3.00 4.50 6.00 10.00 11.67 15.83 19.00 16.00 25.67 29.00 22.00 30.00 35.00 6.00 3.00 7.67 10.00 10.00 19.00 19.00 19.00 24.00 30.00 29.00 30.00 30.00 35.00 4.00 0.00 3.17 4.00 0.00 7.33 3.17 0.00 8.00 4.33 0.00 8.00 0.00 0.00 Critical 100 M Critical N Critical 1 5 5 5 1 Critical Step 3: Find the critical path. Critical path is that path in the network diagram, which has maximum length (duration) as per expected time (u) The expected duration of critical path is the sum of expected duration of each activity on critical path. Similarly, variance of critical path is the sum of individual variance of each activity on critical path. Project paths B-E-H-K-M-N Length Variance 35.00 0.11 S.D. 0.33 Critical path Critical path Expected duration, variance and standard deviation of Critical path Expected Completion Time (Tx) = 35.00 weeks Expected variance (v) = 0.11 weeks Standard Deviation = vv = 0.33 weeks Step 4: Probability that the project will be completed in specified time 32.00 weeks Target Time (Ts) = Calculate z score as below z score = Ts - Tx = = -9.000 (32-35) 0.333 See the probablity from the standard normal table corresponding to z score (or using excel formula NORMSDIST) Probability that the project will take AT MOST 32 weeks to complete ENORMSDIST(-9.0001) 0.0000