Project Planning. Identifying the Work to Be Done. Gantt Chart. A Gantt Chart. Given: Activity Sequencing Network Diagrams

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1 Project Planning Identifying the Work to Be Done Activity Sequencing Network Diagrams Given: Statement of work 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 Gantt Chart Popular tool for project scheduling Graph with bar representing time for each task Provides visual display of project schedule Also shows slack for activities (amount of time activity can be delayed without delaying project) Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work Month A Gantt Chart

2 Critical Path Method (CPM) - DuPont & Remington-Rand (956) CPM/PERT - deterministic task times - activity-on-node network construction (AON) Project Evaluation & Review Technique (PERT) - U.S. Navy, Booz, Allen & Hamilton - multiple task time estimates - activity-on-arrow network construction (AOA) Simplified Project Network Construct forms Pour concrete The Project Network Network consists of branches & nodes Branch Node Network Construction In AON, nodes represent activities & arrows show precedence relationships In AOA, arrows represent activities & nodes are events for points in time An event is the completion or beginning of an activity A dummy shows precedence for two activities with same start & end nodes

3 Project Network For A House Critical Path Lay foundation Dummy Build Finish house work 6 7 Design house Order and and obtain receive Select Select financing materials paint carpet 5 A path is a sequence of connected activities running from the start to the end node in a network The critical path is the path with the longest duration in the network A project cannot be completed in less than the time of the critical path All Possible Paths Concurrent Activities A: = 9 months; the critical path B: = 8 months C: = 8 months D: = 7 months Lay foundation Order material Incorrect precedence relationship Lay foundation Dummy Order material Correct precedence relationship

4 Early Times (Housebuilding example) ES - earliest time activity can start Forward pass starts at beginning of network to determine ES times EF = ES + activity time ES ij = maximum (EF i ) EF ij = ES ij + t ij ES = EF = ES + t = + = months Computing Early Times ES = max (EF ) = months ES 6 = max (EF ) = max (5,) = 5 months EF 6 = ES 6 + t 6 = 5 + = 8 months EF 67 =9 months, the project duration Late Times LS - latest time activity can start & not delay project Backward pass starts at end of network to determine LS times LF - latest time activity can be completed & not delay project LS ij = LF ij - t ij LF ij = minimum (LS j ) LF 67 = 9 months Computing Late Times LS 67 = LF 67 - t 67 = 9 - = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = 8 - = 7 months LF = minimum (LS ) = min(5, 6) = 5 months LS = LF - t = 5 - = months

5 Early And Late Times Activity Slack ES=, EF=5 ES=5, EF=5 LS=5, LF=5 LS=, LF=5 ES=5, EF=8 ES=8, EF=9 LS=5, LF=8 LS=8, LF=9 6 7 ES=, EF= ES=, EF= LS=, LF= LS=, LF=5 ES=6, EF=7 ES=5, EF=6 LS=6, LF=7 5 LS=7, LF=8 Activities on critical path have ES = LS & EF = LF Activities not on critical path have slack S ij = LS ij - ES ij S ij = LF ij - EF ij S = LS - ES = - = month Activity Slack Data Activity LS ES LF EF Slack (S) -* * * * * Critical path Probabilistic Time Estimates Reflect uncertainty of activity times Beta distribution is used in PERT Mean (expected time): t = a + m + b 6 Variance: σ = b - a 6 where, a = optimistic estimate m = most likely time estimate b = pessimistic time estimate

6 Example Beta Distributions PERT Example Equipment testing and modification 6 P (time) P (time) Equipment installation Dummy Final debugging P (time) a m t b a t m b Position recruiting System development System Training 5 7 Manual System 9 Testing changeover System Testing Job Dummy training a m = t b Orientation 8 Activity Information Time estimates (wks) Mean Time Variance Activity a b c t σ Early And Late Times Activity t σ ES EF LS LF S

7 ES=, EF=8 ( LS=, LF=9 ) ES=, EF=6 LS=, LF=6 6 8 ES=, EF= LS=, LF=5 ES=8, EF= LS=6 LF= ES=8, EF=8 ( LS=9, LF=9 ) Network With Times LS=9, LF= ES=6, EF=9 7 ES=, EF=5 LS=6, LF=9 5 ( LS=, LF=6) ES=, EF=7 LS=5, LF=9 ES=, EF=5 LS=, LF=6 6 ES=9, EF= ES=9, EF= 8 ES=, EF=5 ( LS=6 LF=5 ) LS=6 LF=5 ES=, EF= LS=6 LF=6 Project Variance Project variance is the sum of the variances along the critical path σ = σ + σ 5 + σ 57 + σ 79 = = 6.89 weeks Probabilistic Network Analysis Determine the probability that a project is completed within a specified period of time where Z = x - µ σ µ = t p = project mean time σ = project standard deviation x = proposed project time Z = number of standard deviations x is from mean Normal Distribution Of Project Time Zσ Probability µ = t p x Time

8 Probabilistic Analysis Example What is the probability that the project is completed within weeks? σ = 6.89 weeks σ = 6.89 =.6 weeks Z = x - µ = - 5 =.9 σ.6 P(Z <.9) =.979 Determining Probability From Z Value Z P( x < weeks) = =.9767 µ = 5 x = Time (weeks) What is the probability that the project will be completed within weeks? Benefits of PERT/CPM Z = = = P(Z< -.) =.7 P( x< weeks) =.7 x = µ = 5 Time (weeks) Useful at many stages of project management Mathematically simple Uses graphical displays Gives critical path & slack time Provides project documentation Useful in monitoring costs

9 Advantages of PERT/CPM Networks generated provide valuable project documentation and graphically point out who is responsible for various project activities Applicable to a wide variety of projects and industries Useful in monitoring not only schedules, but costs as well Limitations of PERT/CPM Assumes clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over-emphasis on critical path PERT and GERT: A Comparison Project Crashing GERT each activity has a probability of occurrence the nodes indicate the nature of the branch probabilistic deterministic PERT all activities must take place the nodes (events) are circles and the activities are arrows Crashing reduces project time by expending additional resources Crash time is the amount of time an activity is reduced Crash cost is the cost of reducing an activity s time The goal of crashing is to reduce a project s duration at minimum cost

10 Activity times in weeks Housebuilding Network Normal Activity And Crash Data Total Normal Crash Allowable Crash Time Time Normal Crash Crash Time Cost per Activity (wks) (wks) Cost Cost (wks) Week - 7 $, $5, 5 $ - 8 5,,5 5 -, 7,, , , 7, 7, 5-6 5, 6-7 5,, 7, $75, $,7 Network With Crashing Costs Normal And Crash Relationships Activity - can be crashed a total of 5 weeks for $ Crash cost per week = Total crash cost / Total crash time = $, / 5 = $ per week $5 8 $7, $7, 6 $ $, 7 $ $ 5 $ 7, 6, 5,,,,, Crash cost Crashed activity Slope = crash cost per week Normal cost Normal activity Crash time Normal time 6 8 Weeks

11 Crashing Solution Normal Crash Total Crash Total Activity Time Time Time cost per Crashing Crashed week Cost $ $, ,5 -, ,, , 7, $,5 Crashed Project Original time Crashed time Time-Cost Relationship Time-Cost Tradeoff Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Cost ($) Minimum cost = optimal project time Total cost Indirect cost Project length should be reduced as long as crashing costs are less than indirect costs Crashing Project Duration Direct cost Time

CISC 322 Software Architecture

CISC 322 Software Architecture CISC 22 Software Architecture Project Scheduling (PERT/CPM) Ahmed E. Hassan (Edited For Course Presentation, 206) Project A project is a temporary endeavour undertaken to create a "unique" product or service