PERT (Program Evaluation & Review Technique) PERT was evolved by navy engineers James E. Casie &Margan E. Walter, in charge of special projects of United States Navy. It wasformally applied to planning & control of missile program, in October 1958. PERT deals with the problem of uncertain activities times by theapplication of statistical analysis to determination of estimated time for eachactivity concerning the project. In order to arrive at most reliable estimate of time,“Three Time Estimates”. 1. The Optimistic Time – It is the shortest time possible if everything goes perfectly with no complications, the chance of this optimum actually occurring might be in 1 in 100. 2. The Pessimistic Time – It is the longest time considerable, it includes time for unusual delay and thus the change of its happening might be in 1 in 100. 3. The Most Likely Time – It would be the best estimate of what normally would occur.METHODOLOGY / STEPS OF PERT The steps involved in PERT are:- A. Preparing the network: - First of all a list of activities that constitute the project is prepared. The predecessor and successor activities are determined. A network diagram is prepared on the basis of dependence between different activities and events. This is project planning phase of PERT. Events are numbered in ascending order from left to right. B. Network Analysis: - Estimates of time required to perform each activities are made.
C. Scheduling: - Expected time for each activity is computed from the three time estimates. Earliest and latest start time and finished time for each activity are determined. Then the critical path through the network is determined. The slack times associated with the non critical activities are also computed. D. Time-Cost-Trade off: - If management wants to reduce the project completion time, crashing or compressing the project is done. The cost of reducing project completion time is computed. E. Resources Allocation: - The feasibility of each schedule is checked with respect to manpower and equipment requirements. F. Project Control: - The project is controlled by checking programs against the schedule, assigning and scheduling manpower and equipment and analysing the effects of delay. Whenever major changes are made in the schedule, the network is revised accordingly, and a new schedule is prepared. Thus, monitoring of program may require periodic updating of project and rescheduling to ensure completion of the project in time. Latest Finished Time (LFT) It is calculated by moving backward i.e. from last event to firstevent of the network diagram. Latest Start Time (LST) It is the latest possible time by which an activity can start. LST = LFT – Duration of that activity
Earliest Start Time (EST) It is the earliest possible time by which an activity can start. Earliest Finished Time (EFT) It is the earliest time of an activity. FLOAT / SLACK It means spare time, a margin of extra time over and above its durationwhich a non-critical activity can consume without delaying the project. Float is the difference between the time available for completing anactivity and the time necessary to complete the same. Total Float = LST – EST OR Total Float = LFT - EFT Free Float If all the non critical activities start as early as possible thesurplus time is the free flow. If an activity is delayed by the free flow period, thesucceeding activity will not be delayed.
Free Float = EST of tail event – EST of head event – Activity durationIndependent Float The use of independent float of an activity does not changethe float in other activities. Independent Float = EST of tail event - LFT of head event - Activity duration (*Note: - Independent float, if it turns out to be negative, it is taken as zero.)
NUMERICALActivity Optimistic Time Most Expected Time Pessimistic Time Expected Variance (to) (tm) (tp) Time1-2 4 8 12 8 1.782-3 1 4 7 4 1.002-4 8 12 16 12 1.783-5 3 5 7 5 0.444-5 0 0 0 0 0.004-6 3 6 9 6 1.005-7 3 6 9 6 1.005-8 4 6 8 6 0.447-9 4 8 12 8 1.788-9 2 5 8 5 1.009-10 4 10 16 10 4.006-10 4 6 8 6 0.44Expected Time=[(to+4tm+tp)/6]2Varience=[(tp-to)%6]2Q.Present the activity in the form of a PERT network and determine-a.Critical pathb.Earliest and latest expected timec.Probability of computing the project within schedule completion of 48 days.
Critical Path=(1-2-4-5-7-9-10)B. The earliest expected time [E(U1)]=0E (U2)=0+8=8E (U3)=8+4=12E (U4)=12+8=20E (U5)=(12+5,20+0)=20E (U6)=20+6=26E (U7)=26E (U8)=20+6=26E (U9)=34E (U10)=34Latest expected time are-E(L10)=44E(L9)=34E(L8)=29E(L7)=20E(L6)=38E(L5)=20E(L4)=20E(L3)=15E(L2)=8
E(L1)=0C. Expected Project Completion time8+12+0+6+8=44 daysProject variance=(∂T)2 =1.78+1.78+0+1+1.78+4=10.34Varience=∂T=3.216If due date of completion of the project is 48 days then=(48-44)/3.216=1.24From the Standard normal table, probability of meeting the due date is 0.3925