Chapter 9 Project Management Project Evaluation Review Technique

Chapter 9 Project Management (Project Evaluation & Review Technique – PERT)

Lecture Outline • Probabilistic Activity Times • Project Crashing and Time-Cost Trade-off Copyright 2011 John Wiley & Sons, Inc. 9 -2

Probabilistic Time Estimates • Beta distribution • probability distribution traditionally used in CPM/PERT Mean (expected time): Variance: where a + 4 m + b t= 6 b-a = 6 2 2 a = optimistic estimate m = most likely time estimate b = pessimistic time estimate Copyright 2011 John Wiley & Sons, Inc. 9 -3

P(time) Examples of Beta Distributions a m t b a t Time m b P(time) Time a m=t b Time Copyright 2011 John Wiley & Sons, Inc. 9 -4

Project with Probabilistic Time Estimates Equipment installation Equipment testing and modification 1 4 6, 8, 10 2, 4, 12 System development Start 2 3, 6, 9 Position recruiting 3 Manual testing System training 8 3, 7, 11 5 2, 3, 4 Job Training 6 1, 3, 5 3, 4, 5 Final debugging 10 1, 4, 7 Finish 11 9 2, 4, 6 System testing 1, 10, 13 System changeover Orientation 7 2, 2, 2 Copyright 2011 John Wiley & Sons, Inc. 9 -5

Activity Time Estimates TIME ESTIMATES (WKS) ACTIVITY 1 2 3 4 5 6 7 8 9 10 11 MEAN TIME VARIANCE a m b t б 2 6 3 1 2 2 3 2 1 1 8 6 3 4 2 7 4 4 10 10 9 5 12 4 5 2 11 6 7 13 8 6 3 5 3 4 2 7 4 4 9 0. 44 1. 00 0. 44 2. 78 0. 11 0. 00 1. 78 0. 44 1. 00 4. 00 Copyright 2011 John Wiley & Sons, Inc. 9 -6

Activity Early, Late Times & Slack ACTIVITY 1 2 3 4 5 6 7 8 9 10 11 t б ES EF LS LF S 8 6 3 5 3 4 2 7 4 4 9 0. 44 1. 00 0. 44 2. 78 0. 11 0. 00 1. 78 0. 44 1. 00 4. 00 0 8 6 3 3 9 9 13 16 8 6 3 13 9 7 5 16 13 17 25 1 0 2 16 6 5 14 9 12 21 16 9 6 5 21 9 9 16 16 16 25 25 1 0 2 8 0 2 11 0 3 8 0 Copyright 2011 John Wiley & Sons, Inc. 9 -7

Earliest, Latest, and Slack 1 0 8 1 Start 2 0 6 0 3 2 8 9 3 5 10 13 17 8 9 7 9 6 6 Critical Path 2 -5 -8 -11 4 8 13 5 16 21 5 6 3 6 6 3 4 5 16 7 3 Finish 16 9 9 1 0 9 9 13 4 12 16 11 16 25 9 7 3 5 2 14 16 Copyright 2011 John Wiley & Sons, Inc. 9 -8

Total Project Variance 2 = б 22 + б 52 + б 82 + б 112 = 1. 00 + 0. 11 + 1. 78 + 4. 00 = 6. 89 weeks Copyright 2011 John Wiley & Sons, Inc. 9 -9

Probabilistic Network Analysis Determine probability that project is completed within specified time where = = x= Z= Z= x- tp = project mean time project standard deviation proposed project time number of standard deviations that x is from the mean Copyright 2011 John Wiley & Sons, Inc. 9 -10

Normal Distribution of Project Time Probability Z = tp Copyright 2011 John Wiley & Sons, Inc. x Time 9 -11

Southern Textile What is probability that project is completed within 30 weeks? P(x 30 weeks) = 6. 89 weeks 2 = 6. 89 = 2. 62 weeks = 25 x = 30 Z= x- 30 - 25 = 2. 62 = 1. 91 Time (weeks) From Table A. 1, (appendix A) a Z score of 1. 91 corresponds to a probability of 0. 4719. Thus P(30) = 0. 4719 + 0. 5000 = 0. 9719 Copyright 2011 John Wiley & Sons, Inc. 9 -12

Southern Textile What is probability that project is completed within 22 weeks? P(x 22 weeks) = 0. 1271 0. 3729 = 6. 89 weeks 2 = 6. 89 = 2. 62 weeks x = 22 = 25 Z= x- 22 - 25 = 2. 62 = -1. 14 Time (weeks) From Table A. 1, (appendix A) a Z score of 1. 14 corresponds to a probability of 0. 3729. Thus P(22) = 0. 5000 - 0. 3729 = 0. 1271 Copyright 2011 John Wiley & Sons, Inc. 9 -13

Project Crashing • reducing project time by expending additional resources • Crash time • an amount of time an activity is reduced • Crash cost • cost of reducing activity time • Goal • reduce project duration at minimum cost Copyright 2011 John Wiley & Sons, Inc. 9 -14

Project Network – Building a House 4 2 8 12 7 4 1 12 3 4 Copyright 2011 John Wiley & Sons, Inc. 5 4 6 4 9 -15

Normal Time and Cost vs. Crash Time and Cost $7, 000 – $6, 000 – Crash cost $5, 000 – Crashed activity Slope = crash cost per week $4, 000 – $3, 000 – $2, 000 – Normal activity Normal cost $1, 000 – – 0 Normal time Crash time | 2 Copyright 2011 John Wiley & Sons, Inc. | 4 | 6 | 8 | 10 | 12 | 14 Weeks 9 -16

Project Crashing ACTIVITY 1 2 3 4 5 6 7 NORMAL TIME (WEEKS) CRASH TIME (WEEKS) NORMAL COST 12 8 4 12 4 4 4 7 5 3 9 1 1 3 $3, 000 2, 000 4, 000 500 500 15, 000 $5, 000 3, 500 7, 000 71, 000 1, 100 22, 000 $75, 000 $110, 700 Copyright 2011 John Wiley & Sons, Inc. CRASH COST TOTAL ALLOWABLE CRASH TIME (WEEKS) 5 3 1 3 3 3 1 CRASH COST PER WEEK $400 500 3, 000 7, 000 200 7, 000 9 -17

$500 $7000 4 2 8 FROM … $7000 12 7 4 1 12 $400 3 4 $3000 Project Duration: 36 weeks 6 4 5 4 $200 $7000 $500 TO… Project Duration: 31 weeks Additional Cost: $2000 $7000 12 7 4 1 7 $400 3 4 $3000 Copyright 2011 John Wiley & Sons, Inc. 4 2 8 5 4 6 4 $200 9 -18

Time-Cost Relationship • Crashing costs increase as project duration decreases • Indirect costs increase as project duration increases • Reduce project length as long as crashing costs are less than indirect costs Copyright 2011 John Wiley & Sons, Inc. 9 -19

Time-Cost Tradeoff Minimum cost = optimal project time Total project cost Cost ($) Indirect cost Direct cost Crashing Time Project duration Copyright 2011 John Wiley & Sons, Inc. 9 -20

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