Slide 1GoalCommon Inputs to Project SchedulingWork Breakdown StructureProducing a Documentary DVDCommon Formats for Project SchedulesCommon Formats for Project SchedulesFinding Project Duration using the Network DiagramFinding Project Duration using the Network DiagramThe Project Schedule is…The Project Schedule is… (according to MS Project)Sensitivity AnalysisEstimating task durationsProgram Evaluation and Review Technique (PERT)Let’s revisit our DVD projectThe Project Schedule is for ETCan now answer additional questionsFind1BA 341 – Lean OperationsDr. Bogdan BichescuIntroduction to Project SchedulingGoal Want to identify and use effective tools for planning, scheduling and monitoring project progressWhat should we focus on in projects?Common Inputs to Project SchedulingList of project tasks, subtasks, work packages and activitiesLogical sequence of activities in the projectActivity durationsResources involved and their availabilityUsually presented as Work breakdown structure (WBS)Precedence tablesWork Breakdown StructureProjectMajor TasksSubtasksActivities (Work Packages)Producing a Documentary DVDPrecedence TableActivity Description Predecessor DurationABCDEFGScript writingSchedule shootsScript approvalRevise scriptShootingEditingCover Design ----AABCD, E107571135Common Formats for Project SchedulesGantt chartsHow do we find the project duration?Common Formats for Project SchedulesProject Network DiagramsStart, 0A,10B, 7C, 5D, 7E, 11End, 0F, 3G, 5Activity Name & DurationFinding Project Duration using the Network DiagramOne alternative is to identify all possible paths through the projectProject duration is given by longest path (critical path)No. Path Duration1Start  A  C  F  End182Start  A  D  G  End223Start  B  E  G  End23Critical Path: Start  B  E  G  End23Finding Project Duration using the Network DiagramUsing the Critical Path Method (CPM) Start, 00000A, 10111100B, 77070C, 520151510D, 718111710E, 11187187End, 023232323F, 323201815G, 523182318Earliest Start Time (ES)Earliest Finish Time (EF)Latest Start Time (LS)Latest Finish Time (LF)Activity Name & DurationSlack=LS-ES=LF-EFThe Project Schedule is… Using the Critical Path Method (CPM)The Project Schedule is… (according to MS Project)11Sensitivity AnalysisAssuming that all activities start at their earliest times, find the impact on project scheduling if: Activity C takes 7 days?Activity G is delayed to 9 days?Activity D now takes 8 days?Estimating task durationsCPM assumes durations are deterministicIs this realistic?How is it done in practice?Do your normal cautious estimating Add a generous safety marginThen…double it!!TimeProbabilityMost likelyMedianPessimisticOptimistic50% of probabilityProgram Evaluation and Review Technique (PERT)Similar to CPM but able to incorporate duration uncertaintyLet, for each project taska = optimistic time estimateb = pessimistic time estimatem = most likely time estimateThen, compute for each project taskET (Expected Time) = (a + 4m + b)/6σ2 (Variance) = ((b-a)/6)2Let’s revisit our DVD projectActivityOptimistic (a)Most Likely (m) Pessimistic (b)ET(a+4m+b)/6Variance σ2 =((b-a)/6)2ABCDEFG 274292210757113512712121948976712352.780.001.782.782.780.111.00The Project Schedule is for ETUsing PERT Start, 00000A, 912390B, 77070C, 62115159D, 71912169E, 12197197End, 024242424F, 324211815G, 524192419Earliest Start Time (ES)Earliest Finish Time (EF)Latest Start Time (LS)Latest Finish Time (LF)Activity Name & DurationSlack=LS-ES=LF-EF; Critical Path = Longest Path or Path with Least Slack!Can now answer additional questionsThe probability of finishing the project in 26 days?First, compute , where D = the desired project completion timeTE = expected completion time, i.e., the length of the critical path (sum of ETs for critical activities) σCP2 = variance of the critical path (sum of variances of critical activities)In our example, D= 26, TE = 24 and σCP2 = 0+ 2.78 +1 = 3.78. Then, Z= (26-24)/sqrt(3.78)=1.0287This corresponds to 84.8% (using a normal distribution table)2/)(CPETDZFindThe project duration corresponding to 95% confidence Start from same equation but now solve for D  According to a normal distribution table, a Z of 1.65 corresponds to 95% probabilityThus, D= 24 + 1.65*sqrt(3.78)= 27.21