2PERT (Program evaluation and review technique) and CPM (Critical Path Method) makes a managerial technique to help planning and displaying the coordination of all the activities.
3Activity Description Immediate Predecessors Estimated Time Activity BCDEFGHIJKLMNExcavateLay the foundationPut up the rough wallPut up the roofInstall the exterior plumbingInstall the interior plumbingPut up the exterior sidingDo the exterior paintingDo the electrical workPut up the wallboardInstall the flooringDo the interior paintingInstall the exterior fixturesInstall the interior fixtures-ABCEDE,GF,IJHK,L2 weeks4 weeks10 weeks6 weeks5 weeks7 weeks9 weeks8 weeks
4Immediate predecessors: For any given activity, its immediate predecessors are the activities that must be completed by no later than the starting time of the given activity.
5AOA (Activity-on-Arc): Each activity is represented by an arc.The arcs are used to show the precedence relationships between the activities.
7Path and Length START A B C D G H M FINISH = 40 weeksSTART A B C E F J K N FINISH= 43 weeksSTART A B C E F J L N FINISH= 44 weeksCritical Path
8Critical Path:A project time equals the length of the longest path through a project network. The longest path is called “critical path”.Activities on a critical path are the critical bottleneck activities where any delay in their completion must be avoided to prevent delaying project completion.
9ES :Earliest Start time for a particular activityEF :Earliest Finish time for a particular activity
11Earliest Start Time Rule: If an activity has only a single immediate predecessor, then ES = EF for the immediate predecessor.Earliest Start Time Rule:The earliest start time of an activity is equal to the largest of the earliest finish times of its immediate predecessors.ES = largest EF of the immediate predecessors.
13Latest Finish Time Rule: LS:Latest Start time for a particular activityLF:Latest Finish time for a particular activityLatest Finish Time Rule:The latest finish time of an activity is equal to the smallest of the latest finish times of its immediate successors.LF = the smallest LS of immediate successors.
17Slack:A difference between the latest finish time and the earliest finish time.Slack = LF - EFEach activity with zero slack is on a critical path.Any delay along this path delays a whole project completion.
18Three-Estimates Most likely Estimate (m) = an estimate of the most likely value of time.Optimistic Estimate (o)= an estimate of time under the most favorableconditions.Pessimistic Estimate (p)= an estimate of time under the mostunfavorable conditions.
20Mean critical path:A path through the project network becomes the critical path if each activity time equals its mean.ActivityOEMPEMeanVariance1232ABC28416918104OE: Optimistic EstimateM : Most Likely EstimatePE: Pessimistic Estimate
21Activities on Mean Critical Path VarianceABCEFJLN241058614Project Time
22Approximating Probability of Meeting Deadline Assumption:A probability distribution of project time is a normal distribution.T = a project time has a normal distributionwith mean and ,d = a deadline for the project = 47 weeks.
23Using a table for a standard normal distribution, the probability of meeting the deadline isP ( T d ) = P ( standard normal )= 1 - P( standard normal )=0.84.
24Time - Cost Trade - Offs Activity cost Crash Crash cost Normal Crashing an activity refers to taking special costly measures to reduce the time of an activity below its normal value.ActivitycostCrashCrash costNormalNormal costCrashtimeNormaltimeActivitytime
25Activity J: Normal point: time = 8 weeks, cost = $430,000. Crash point: time = 6 weeks, cost = $490,000.Maximum reduction in time = = 2 weeks.Crash cost per week saved == $30,000.
26MaximumReductionin Time(week)Time(week)Cost($1,000)Crash Costper WeekSavedActivityNCNCABJ248126$180$320$430$280$420$49012$100$ 50$ 30N: Normal C: Crash
27Using LP to Make Crashing Decisions Let Z be the total cost of crashing activities.A problem is to minimize Z, subject to the constraint that its project duration must be less than or equal to the time desired by a project manager.
28= the reduction in the time of activity j by crashing it= the project time for the FINISH node
29= the start time of activity j Duration of activity j = its normal timeImmediate predecessor of activity F:Activity E, which has duration =Relationship between these activities:
30Immediate predecessor of activity J: Activity F, which has time =Activity I, which has time =Relationship between these activities: