ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ ﻭﺍﻟﺪﺭﺍﺳﺎﺕ ﺍﻻﻧﺴﺎﻧﻴﺔ ﺑﺎﻟﻐﺎﻁ Chapter 2: Project Management (PERT/CPM) ﻣﺤﻤــﺪ ﺍﻟــﺤﺪﺍﺩ mhaddad@mu. edu. sa http: //tel. archives-ouvertes. fr/tel 00411282/fr/ 1
Project Planning n Given: q Statement of work n n q n written description of goals work & time frame of project Work Breakdown Structure Be able to: develop precedence relationship diagram which shows sequential relationship of project activities 2
Project n “A project is a series of activities directed to accomplishment of a desired objective. ” Plan your work first…. . then work your plan
Network analysis Introduction Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects.
History n n n Developed in 1950’s CPM by Du. Pont for chemical plants PERT by U. S. Navy for Polaris missile CPM was developed by Du Pont and the emphasis was on the trade-off between the cost of the project and its overall completion time (e. g. for certain activities it may be possible to decrease their completion times by spending more money how does this affect the overall completion time of the project? ) PERT was developed by the US Navy for the planning and control of the Polaris missile program and the emphasis was on completing the program in the shortest possible time. In addition PERT had the ability to cope with uncertain activity completion times (e. g. for a particular activity the most likely completion time is 4 weeks but it could be anywhere between 3 weeks and 8 weeks).
CPM - Critical Path Method n Definition: In CPM activities are shown as a network of precedence relationships using activity-on-node network construction q Single estimate of activity time q Deterministic activity times USED IN : Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existence of past experience.
PERT Project Evaluation & Review Techniques n Definition: In PERT activities are shown as a network of precedence relationships using activity-on-arrow network construction q Multiple time estimates q Probabilistic activity times USED IN : Project management - for non-repetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates.
The Network construction n Use of nodes and arrows Arrows q An arrow leads from tail to head directionally Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work. Nodes - - A node is represented by a circle Indicate EVENT, a point in time where one or more activities start and/or finish. A dummy shows precedence for two activities with same start & end nodes
Activity on Node & Activity on Arrow Activity on Node Activity on Arrow
Gantt Chart n n A Gantt chart is a type of bar chart, that illustrates a project schedule. Gantt charts illustrate the start and finish dates of a project. Gantt charts can be used to show current schedule status using percent-complete shadings and a vertical "TODAY" line as shown here.
Gantt Chart n n Popular tool for project scheduling Graph with bar representing time for each task Provides visual display of project schedule Also shows slack for activities q (amount of time activity can be delayed without delaying project) 11
Gantt Chart (continued)
Gantt chart Originated by H. L. Gantt in 1918 Advantages Limitations - Gantt charts are quite commonly used. - Do not clearly indicate details regarding the progress of activities - They provide an easy graphical representation of when activities (might) take place. - easy to maintain and read. - Do not give a clear indication of interrelation ship between the separate activities
The Project Network consists of branches & nodes Node 1 2 3 Branch 14
Concurrent Activities Lay foundation 2 3 Order material Incorrect precedence relationship 3 Lay foundation Dummy 2 4 Order material Correct precedence relationship 15
Consider the following table which describes the activities to be done to build a house and its sequence Activity predecessors Duration A Design house and obtain financing 3 B Lay foundation A 2 C Order and receive materials A 1 D Build house B, C 3 E Select paint B, C 1 F Select carpet E 1 G Finish work D, F 1 16
Project Network For A House 3 Lay foundation 1 3 Design house and obtain financing 2 2 0 1 Order and receive materials Dummy 4 Select paint Build house 1 3 5 6 Finish work 1 7 1 Select carpet 17
Critical Path n A path is a sequence of connected activities running from the start to the end node in a network n The critical path is the path with the longest duration in the network n A project cannot be completed in less than the time of the critical path (under normal circumstances) 18
All Possible Paths path 1: 1 -2 -3 -4 -6 -7 3 + 2 + 0 + 3 + 1 = 9 months; the critical path 2: 1 -2 -3 -4 -5 -6 -7 3 + 2 + 0 + 1 + 1 = 8 months path 3: 1 -2 -4 -6 -7 3 + 1 + 3 + 1 = 8 months path 4: 1 -2 -4 -5 -6 -7 3 + 1 + 1 = 7 months 19
Forward and Backward Pass n n n Forward pass is a technique to move forward through a diagram to calculate activity duration. Backward pass is its opposite. Early Start (ES) and Early Finish (EF) use the forward pass technique. Late Start (LS) and Late Finish(LF) use the backward pass technique. 20
Early Times (House building example) n n n ES - earliest time activity can start Forward pass starts at beginning of network to determine ES times EF = ES + activity time q q ESij = maximum (EFi) EFij = ESij + tij ES 12 = 0 EF 12 = ES 12 + t 12 = 0 + 3 = 3 months i j 21
Computing Early Times -ES 23 = max (EF 2) = 3 months - ES 46 = max (EF 4) = max (5, 4) = 5 months - EF 46 = ES 46 + t 46 = 5 + 3 = 8 months - EF 67 =9 months, the project duration 22
Late Times n n n LS - latest time activity can be started without delaying the project Backward pass starts at end of network to determine LS times LF - latest time activity can be completed without delaying the project q q LSij = LFij - tij LFij = minimum (LSj) 23
Computing Late Times q q q q If a deadline is not given take LF of the project to be EF of the last activity LF 67 = 9 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LF 56 = minimum (LS 6) = 8 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LF 24 = minimum (LS 4) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months 24
Project cost analysis: ES=5, EF=5 ES=3, EF=5 LS=3, LF=5 1 3 ES=0, EF=3 LS=0, LF=3 2 LS=5, LF=5 ES=5, EF=8 0 1 ES=3, EF=4 4 ES=8, EF=9 LS=5, LF=8 LS=8, LF=9 LS=4, LF=5 1 ES=5, EF=6 LS=6, LF=7 3 1 5 6 1 7 ES=6, EF=7 LS=7, LF=8 25
Activity Slack n Slack is defined as the LS-ES or LF-EF Activities on critical path have ES = LS & EF = LF (slack is 0) n Activities not on critical path have slack n q q q Sij = LSij - ESij = LFij - EFij S 24 = LS 24 - ES 24 = 4 - 3 = 1 month 26
Total slack/float or Slack of an activity n n n Total slack/ float means the amount of time that an activity can be delayed without affecting the entire project completion time. The activity on a given path share the maximum possible slack of the activity along that path according to its share. Sum of the possible slacks of the activities can not exceed the maximum slack along that path. 27
Free slack of an activity This is the maximum possible delay of an activity which does not affect its immediate successors. n This is evaluated as n FSij = ESj – EFij n 28
Activity Slack Data Activity ES 1 -2* 0 2 -3 3 2 -4 3 3 -4* 5 4 -5 5 4 -6* 5 5 -6 6 6 -7* 8 LS 0 3 4 5 6 5 7 8 EF 3 5 4 5 6 8 7 9 LF 3 5 5 5 7 8 8 9 Slack (S) Free slack 0 0 1 1 0 0 * Critical path 29
Probability of completing the project within given time: 0 n 2 4 6 8 10 Activity n Design house and obtain financing n Lay foundation n n Order and receive materials n Build house n Select paint n Select carpet n Finish work n 1 3 5 7 9 30
Probabilistic Time Estimates n Reflect uncertainty of activity times n Beta distribution is used in PERT a + 4 m + b Mean (expected time): t = 6 where, Variance: s 2 = ( b - a) 6 2 a = optimistic estimate m = most likely time estimate b = pessimistic time estimate 31
P (time) Example Beta Distributions a b t a t m b P (time) m a m=t b 32
Activity Information Activity 1– 2 A 1– 3 B 1– 4 C 2– 5 D 2 -6 E 3 -5 F 4– 5 G 4– 7 H 5– 8 I 5– 7 J 7– 8 K 6– 9 L 8– 9 M Time estimates (wks) a m b 6 3 1 0 2 2 3 2 0 1 1 8 6 3 0 4 3 4 2 7 4 0 4 10 Mean Time t Variance s 2 10 9 5 0 12 4 5 2 11 6 0 7 13 33
Activity Information Activity 1 – 2 A 1 – 3 B 1 – 4 C 2 – 5 D 2 – 6 E 3 -5 F 4 – 5 G 4 – 7 H 5 – 8 I 5 – 7 J 7 – 8 K 6 – 9 L 8 – 9 M Time estimates (wks) a m b 6 3 1 0 2 2 3 2 0 1 1 8 6 3 0 4 3 4 2 7 4 0 4 10 10 9 5 0 12 4 5 2 11 6 0 7 13 Mean Time t 8 6 3 0 5 3 4 2 7 4 0 4 9 Variance s 2. 44 1. 00. 44. 00 2. 78. 11. 00 1. 78. 44. 00 1. 00 4. 00 34
Network With Times 2 6 E 5 A 8 L 4 D 0 1 3 B 6 5 F 3 G 4 C 3 4 H 2 8 I 7 9 M 9 K 0 J 4 7 35
PERT Example Equipment testing and modification 2 Final debugging Dummy Equipment installation 1 6 System development 3 Manual Testing Job training Position recruiting 4 Orientation 5 System Training 8 System Testing System changeover 9 Dummy 7 36
Early And Late Times Activity t s 2 ES 1 -2 1 -3 1 -4 2 -5 2 -6 3 -5 4 -7 5 -8 5 -7 7 -8 6 -9 8 6 3 0 5 3 4 2 7 4 0 4 9 0. 44 1. 00 0. 44 0. 00 2. 78 0. 11 0. 00 1. 78 0. 44 0. 00 1. 00 4. 00 0 8 8 6 3 3 9 9 13 13 16 EF 8 6 3 8 13 9 7 5 16 13 13 17 25 LS 1 0 2 9 16 6 5 14 9 12 16 21 16 LF 9 6 5 9 21 9 9 16 16 25 25 S 1 0 2 1 8 0 2 11 0 3 3 8 0 37
Network With Times ES=8, EF=13 2 ES=0, EF=8 (LS=1, LF=9 ) ( LS=16 LF=21 ) 6 5 8 0 (LS=0, LF=6 ) 6 (LS=9, LF=9 ) 4 ES=9, EF=16 3 ES=0, EF=3 3 ( LS=21 LF=25 ) ES=8, EF=8 ES=0, EF=6 1 ES=13, EF=17 (LS=2, LF=5 ) 4 3 ( LS=9, LF=16 ) 5 ES=6, EF=9 (LS=6, LF=9 ) 8 7 ES=9, EF=13 4 ES=3, EF=7 (LS=5, LF=9 ) ( LS=12, LF=16) 2 ES=3, EF=5 ( LS=14, LF=16) 0 9 ES=16, EF=25 ( LS=16 LF=25 ) ES=13, EF=13 ( LS=16 LF=16 ) 4 9 7 38
Project Variance Project variance is the sum of the variances along the critical path s 2 = s 2 13 + s 2 35 + s 2 58 + s 2 89 = s 2 B + s 2 F + s 2 I + s 2 M = 1. 00 +0. 11 + 1. 78 + 4. 00 = 6. 89 weeks 39
Probabilistic Network Analysis Determine the probability that a project is completed (project completion time is ) within a specified period of time x-m Z = where s m = tp = project mean time s = project standard deviation x = project time (random variable) Z = number of standard deviations of x from the mean (standardized random variable) 40
Normal Distribution Of Project Time Probability Zs m = tp x Time 41
Standard Normal Distribution Of transformed Project Time Probability Z m =0 z Time 42
Probabilistic Analysis Example What is the probability that the project is completed within 30 weeks? P(X 30) = ? s 2 = 6. 89 weeks s = 6. 89 = 2. 62 weeks Z = x - m =30 - 25 = 1. 91 2. 62 P(Z s 1. 91) = ? 43
Determining Probability From Z Value Z 0. 00 . . 1. 1. . . 0. 3643. 1. 9 0. 4713 0. 01. . 04 . . 0. 3665 0. 3729. +0. 4719 … … 0. 09 0. 4767 P( x < 30 weeks) = 0. 50+ 04719 = 0. 9719 m = 25 x = 30 Time (weeks) 44
What is the probability that the project will be completed within 22 weeks? 22 - 25 = -3 = -1. 14 Z= 2. 62 P(Z< -1. 14) = 0. 1271 x = 22 m = 25 x=28 Time (weeks) P( x< 22 weeks) = 0. 1271 45
Benefits of PERT/CPM n n n Useful at many stages of project management Mathematically simple Uses graphical displays Gives critical path & slack time Provides project documentation Useful in monitoring costs 46
Limitations of PERT/CPM n n n Assumes clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over-emphasis on critical path 47
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