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P E R T

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  • 1. PERTPERT
  • 2. PERTPERT In 1957 the Critical Path Method (CPM) wasIn 1957 the Critical Path Method (CPM) was developed as a network model for projectdeveloped as a network model for project management.management. It is a deterministic method that uses a fixedIt is a deterministic method that uses a fixed time estimate for each activity.time estimate for each activity. While CPM is easy to understand and use, butWhile CPM is easy to understand and use, but does not consider uncertainty in activity timedoes not consider uncertainty in activity time estimation.estimation. Uncertainty such as weather, equipment failure,Uncertainty such as weather, equipment failure, absenteeism can have a great impact on theabsenteeism can have a great impact on the completion time of a complex project.completion time of a complex project.
  • 3. PERTPERT TheThe Program Evaluation and ReviewProgram Evaluation and Review TechniqueTechnique (PERT) is a network model that(PERT) is a network model that allows for randomness in activityallows for randomness in activity completion times.completion times. Generally used when there is a risk of timeGenerally used when there is a risk of time associated with project.associated with project. – R & D projects where correct timeR & D projects where correct time determinations cannot be made.determinations cannot be made. – Example : project launching the spacecraft.Example : project launching the spacecraft.
  • 4. PERTPERT PERT was developed in the late 1950's forPERT was developed in the late 1950's for the U.S. Navy's Polaris ballistic missilethe U.S. Navy's Polaris ballistic missile system project having thousands ofsystem project having thousands of contractors.contractors. This project was notable in that it finished 18 months ahead of schedule and within budget. It has the potential to reduce both the timeIt has the potential to reduce both the time and cost required to complete a project.and cost required to complete a project.
  • 5. PERTPERT This method uses statistical tools forThis method uses statistical tools for Implication of uncertainties on project timeImplication of uncertainties on project time OrOr Stochastic Modeling of NetworkStochastic Modeling of Network A distinguishing feature of PERT is itsA distinguishing feature of PERT is its ability to deal with uncertainty in activityability to deal with uncertainty in activity completion times. For each activity, thecompletion times. For each activity, the model usually includes three timemodel usually includes three time estimates:estimates:
  • 6. Three Time EstimatesThree Time Estimates 1 2 3 4 5 2-5-12 4-7-16 1-6-23 3-7-20 2-5-10
  • 7. TimesTimes Optimistic timeOptimistic time – Shortest possible time in which an– Shortest possible time in which an activity can be completed under ideal conditions.activity can be completed under ideal conditions. This is denoted by tThis is denoted by too Pessimistic timePessimistic time - the longest time that an activity- the longest time that an activity might require. If everything went wrong andmight require. If everything went wrong and abnormal situation prevails.however, it doesn't”tabnormal situation prevails.however, it doesn't”t include highly unusual catastrophies such asinclude highly unusual catastrophies such as earthquake, floods, fires. It is denoted by tearthquake, floods, fires. It is denoted by tpp Most likely timeMost likely time (Most Frequent-Mode)- the(Most Frequent-Mode)- the completion time having the highest probability.completion time having the highest probability. Normal condition prevails. It is denoted by tNormal condition prevails. It is denoted by tLL
  • 8. 1 2 3 4 5 2-5-12 4-7-16 1-6-23 3-7-20 2-5-10 t0 tptm
  • 9. Problem: 54 trenches of same dimensions by different partiesProblem: 54 trenches of same dimensions by different parties Find :Optimistic, Pessimistic & Most Likely TimesFind :Optimistic, Pessimistic & Most Likely Times
  • 10. TimesTimes
  • 11. Most Likely TimeMost Likely Time Tallest peak of the curve- Most Likely time or Mode
  • 12. Expected Time & StandardExpected Time & Standard Deviation: Beta DistributionDeviation: Beta Distribution Expected time = ( Optimistic + 4 xExpected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6Most likely + Pessimistic ) / 6 Expected time : Time corresponding 50Expected time : Time corresponding 50 % probability of performance% probability of performance SD: How tightly a set of values is clustered around the mean. Standard Deviation: Sigma: measure of uncertainty = (b-a)/6
  • 13. Calculate Expected Time &Calculate Expected Time & Standard Deviation:Standard Deviation: Write down their significanceWrite down their significance
  • 14. Expected Time & StandardExpected Time & Standard DeviationDeviation ActivityActivity ttoo ttmm ttpp 11 44 77 1616 22 11 66 2323 Comment on Standard Deviation: Second case measure of dispersion is higher
  • 15. A systematic and scientific method of finding critical path lies in the calculation of event time which is described by i) The Earliest Expected Occurance Time (TE) ii) The Latest Allowable Occurance Time (TL) The Earliest Expected Time (TE) is the time when an event can be expected to occur earliest. The calculation of TE of an event is same as calculation of EOT of CPM network If more than one activity are directed to the event, maximum of the sum of TE's along various path will give the expected mean time of the event. Expected mean time of the initial event is taken as zero and process is repeated for each succeeding event and ultimately to the final event. The method is usually called the forward pass. (TE)j = Max [(TE)i + tij] The Latest Allowable Occurence Time (TL) : The latest time by which an event must occur to keep the project on schedule is called the latest allowable occurence time (TL). The calculation of TL of an event is same as that LOT of CPM network by the method known as Backward Pass. ; (TL)i = min ((TL)j – tij)
  • 16. Scheduled Completion Time (Ts) Whenever a PERT network is taken in hand decision is made regarding the completion time of the project and the accepted figure is called the Scheduled Completion Time (Ts). Naturally. Ts refers to the latest allowable occurence time (TL) of the last event of the project, i.e. (Ts= TL)· SLACK . Time box having two compartments is made at each event. the value in the left compartment indicating the value of TE and that of in the right compartment indicating TL of that event. And the slack of the event is given by, Slack (S) = (TL – TE ) Thus the slack is difference between event times denoting the range within which an event time can vary. Thus, slack gives the idea of "time to spare". Slack means more time to work and less to worry about. It also spots which are potential trouble areas. Slack may be positive, zero or negative depending upon the value of TE and TL of that event.
  • 17. POSITIVE SLACK When TL is more than TE. positive slack is obtained. It indicates the project is ahead of schedule meaning thereby the excess resources. ZERO SLACK When TL is equal to TE zero slack' is obtained. It indicates that the project is going on schedule meaning thereby adequate resources. NEGATIVE SLACK When the scheduled completion time Ts (and hence TL ) is less than TE negative slack is obtained. It indicates the project is behind schedule meaning thereby the lack of resources. CRITICAL EVENT The event having the least slack value is known as a critical event CRITICAL PATH The path joining the critical events is called a critical path of the PERT network. The critical path may be one or more than one. Time wise. the critical path is the longest path connecting the initial event to the final event. A critical path is distinctly marked in the network. usually by a
  • 18. Determine the Expected time forDetermine the Expected time for Each Path & Find the critical PathEach Path & Find the critical Path
  • 19. Critical PathCritical Path
  • 20. Probability of Meeting TheProbability of Meeting The Schedule DateSchedule Date
  • 21. Normal Distribution FunctionNormal Distribution Function Sum of all expected time of all activities alongSum of all expected time of all activities along critical path is equal to the expected time of lastcritical path is equal to the expected time of last event= 50 % time of completion of projectevent= 50 % time of completion of project Though individual activities assumeThough individual activities assume random( beta distribution) but Trandom( beta distribution) but TEE of the project asof the project as a whole assume normal distributiona whole assume normal distribution
  • 22. Normal Distribution FunctionNormal Distribution Function
  • 23. Normal Distribution FunctionNormal Distribution Function
  • 24. Normal DeviateNormal Deviate (x): Distance from(x): Distance from the meanthe mean expressed inexpressed in terms of sigmaterms of sigma 1. Normal Deviate = 0, it is the expected time, probability of completion = 50 % 2. Normal Deviate = 1, probability of completion = 84 %. 3. Normal Deviate = -1, probability of completion = 16 %
  • 25. Normal DeviateNormal Deviate If Ts is the schedules time of completionIf Ts is the schedules time of completion & Te is the expected time of completion& Te is the expected time of completion Z = Ts-Te/sigmaZ = Ts-Te/sigma Sigma = (Sum of variances along critical path)Sigma = (Sum of variances along critical path)0.50.5 Variance = (tp-to/6)Variance = (tp-to/6)22
  • 26. Exp. For the given PERT network, determine a) Expected time, Standard deviation and variance of the PROJECT and show the critical path also. b) Probability of completion of project in 35 days. c) Time duration that will provide 90% probability of its completion in time. The three time estimates of each activity. are mentioned on the network.
  • 27. Expected mean time of activity te = (ta + 4tm + tb )/6 Standard deviation of activity δt = (tb - ta)/6 Variance of activity vt = (standard deviation)2 . Earliest Expected Mean Time (TE ) and Latest allowable occurrence time (TL ) are marked in time box at each event. Slack (S) = (TL - TE ) is also mentioned on the network. Since scheduled completion time of project is not mentioned, for the last event (8), TL = TE has been taken.
  • 28. Least slack value = 0 :: All the events having zero slack are critical. CRITICAL PATH-I = 1- 2- 3 - 6-7 - 8 CRITICAL PATH-II = 1- 2-4 - 6-7 – 8 Expected Mean Time of Project (µT) = 31 days. Variance of project along critical path I (VT I) = 1 + 7.1 + 5.44 +1.78 + 0.44 = 15.76 Variance along critical path II (VrII ) = 1 + 4 + 1 + 1.78 + 0.44 = 2.86 :. Variance of the project (VT) = 15.76 Standard Deviation of the project (δT ) = sqrt(15.76) = 3.97 b) Probability factor (z) corresponding to x = 35 days z = (x- µT )/ δt = (35-31)/3.97 = 1.007 = 1.0 probability % corresponding to z = 1.0 (from table) pr= 84.13% c) for 90% probability, the value of z = 1.32 (from table ) 1.32 = (x- 31 )/3.97 So x = 36.24 days.
  • 29. Four activities to be undertaken in series for the completion of II project are as follows, Estimate the time required at (i)95% probability, and (ii)5% probability to complete the work. (iii)Also which of the above four activities has the most reliable time estimates?
  • 30. Problem:Problem: Expected Project Length is 50 weeksExpected Project Length is 50 weeks Variance 16Variance 16 How many weeks required to complete theHow many weeks required to complete the project to complete withproject to complete with – 95 % Probability95 % Probability – 75 % probability75 % probability – 40 % Probability40 % Probability 57 weeks 53 weeks 49 weeks
  • 31. Find The probability of completionFind The probability of completion within 35 dayswithin 35 days 10 9 9 7 11 5 8 Critical path 1-2-4-5, Te= 30 Variance 1-2= (18-6/6)2 =4, + 9 + 9 = 22 SD= 4.69
  • 32. Benefits of PERTBenefits of PERT PERT is useful because it provides the followingPERT is useful because it provides the following information:information: – Expected project completion time.Expected project completion time. – Probability of completion before a specified date.Probability of completion before a specified date. – The critical path activities that directly impact theThe critical path activities that directly impact the completion time.completion time. – The activities that have slack time and that can lendThe activities that have slack time and that can lend resources to critical path activities.resources to critical path activities. – Activity start and end dates.Activity start and end dates.
  • 33. LimitationsLimitations The activity time estimates are somewhat subjective andThe activity time estimates are somewhat subjective and depend on judgement. In cases where there is littledepend on judgement. In cases where there is little experience in performing an activity, the numbers mayexperience in performing an activity, the numbers may be only a guess.be only a guess. Even if the activity times are well-estimated, PERTEven if the activity times are well-estimated, PERT assumes a beta distribution for these time estimates, butassumes a beta distribution for these time estimates, but the actual distribution may be different.the actual distribution may be different. Even if the beta distribution assumption holds, PERTEven if the beta distribution assumption holds, PERT assumes that the probability distribution of the projectassumes that the probability distribution of the project completion time is the same as the that of the criticalcompletion time is the same as the that of the critical path. Because other paths can become the critical path ifpath. Because other paths can become the critical path if their associated activities are delayed, PERT consistentlytheir associated activities are delayed, PERT consistently underestimates the expected project completion time.underestimates the expected project completion time.

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