Program Evaluation and Review Technique

Program Evaluation Review Technique (PERT) Report by: Raymund N. Sanchez

Content of the Presentation Definition Differences between PERT & CPM Purpose Historical Perspective Terminologies Creating a PERT/CPM diagram Schedule Duration Crash Probabilistic Time Estimates uncertainty of activities and paths path probabilities Problem Exercises

Definition A method to analyze the tasks involved in completing a given project. Focus is paid to the time needed to complete each task, and identifying the minimum time needed to complete the total project.

Purpose To simplify the planning and scheduling of large and complex projects. To incorporate uncertainty in the sense that it was possible to schedule a project not knowing precisely the details and duration's of all the activities. Event-oriented technique rather than start- and completion-oriented. Used more in R&D-type projects where Cost is not a major factor but Time is.

PERT & CPM Similarities Both follow the same steps and use network diagrams Both are used to plan the scheduling of individual activities that make up a project They can be used to determine the earliest/latest start and finish times for each activity

PERT & CPM Differences PERT is probabilistic whereas CPM is deterministic In CPM, estimates of activity duration are based on historical data In PERT, estimates are uncertain and we talk of ranges of duration and the probability that an activity duration will fall into that range CPM concentrates on Time/Cost trade off.

Historical Background PERT was invented by Booz Allen Hamilton, Inc. under contract to the United States Department of Defense's US Navy Special Projects Office in 1958 A part of the Polaris mobile submarine-launched ballistic missile project. This project was a direct response to the Sputnik crisis CPM was developed by the dupont company & Remington-Rand-Univac Used for large construction projects Each were unaware of the others existence until the 1960’s

Terminologies PERT event : is a point that marks the start or completion of one (or more) tasks. It consumes no time , and uses no resources . It marks the completion of one (or more) tasks. It is not “reached” until all of the activities leading to that event have been completed. P redecessor event : an event (or events) that immediately precedes some other event without any other events intervening. It may be the consequence of more than one activity. Successor event : an event (or events) that immediately follows some other event without any other events intervening. It may be the consequence of more than one activity.

Terminologies PERT activity : is the actual performance of a task. It consumes time , it requires resources (such as labor, materials, space, machinery), and it can be understood as representing the time, effort, and resources required to move from one event to another. A PERT activity cannot be completed until the event preceding it has occurred. Optimistic time (O): the minimum possible time required to accomplish a task, assuming everything proceeds better than is normally expected Pessimistic time (P): the maximum possible time required to accomplish a task, assuming everything goes wrong (but excluding major catastrophes).

Terminologies Most likely time (M): the best estimate of the time required to accomplish a task, assuming everything proceeds as normal. Expected time (T E ): the best estimate of the time required to accomplish a task, assuming everything proceeds as normal (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time). Critical Path : the longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.

Terminologies Lead time : the time by which a predecessor event must be completed in order to allow sufficient time for the activities that must elapse before a specific PERT event is reached to be completed. Lag time : the earliest time by which a successor event can follow a specific PERT event. Slack : the slack of an event is a measure of the excess time and resources available in achieving this event. Positive slack would indicate ahead of schedule ; negative slack would indicate behind schedule ; and zero slack would indicate on schedule .

Terminologies Early Start (ES): maximum EF of all predecessor activities, unless the activity in question is the the first activity, wherein ES is 0 Early Finish (EF): ES plus task duration Late Start (LS): LF minus task duration Late Finish (LF): minimum LS on all successor activities, unless the activity is the last activity, wherein LF equals EF Activity on Arrow (AOA): a type of PERT diagram wherein the activities are written on the arrows Activity on Node (AON): a type of PERT diagram wherein the activities are written on the nodes

Creating a PERT Diagram STEPS 1: Determine the tasks that the project requires and the order in which they must be completed Determine the optimistic, most likely, and pessimistic time of each task Compute for the Expected time using the formula Te=(O+4M+P)/6 Determine whether to use AOA or AON diagrams

Creating a PERT Diagram STEPS 2: Determine the ES & EF of each activity by: Start at the beginning moving towards the end ES & EF for the start activity is always 0 since they are milestones Use the EF of the predecessor activity as the ES of the current activity EF of an activity is computed by adding its ES with its duration For activities with 2 or more predecessor activities, use the predecessor with the higher EF as the ES of the current activity

Start ES:0 EF:0 F D:4.5 ES:10.33 EF:14.83 C D:5.17 ES:4 EF:9.17 G D:5.17 ES:14.34 EF:19.51 E D:5.17 ES:9.17 EF:14.34 D D:6.33 ES:4 EF:10.33 B D:5.33 ES:0 EF:5.33 A D:4 ES:0 EF:4 Finish D:0 ES:19.51 EF:19.51

Creating a PERT Diagram STEPS 3: Determine the LS & LF of each activity by: Start at the end and work towards the beginning The LF for the finish activity is equal to EF since it is the last activity in the project. Since duration is 0, LS is equal to LF Use the LS of the successor activity as the LF of the current activity LS of an activity is computed by subtracting its LF with its duration For activities with 2 or more successor activities, use the successor with the lower LS as the LF of the current activity

Start D:0 ES:0 EF:0 LS:0 LF:0 F D:4.5 ES:10.33 EF:14.83 LS:15.01 LF:19.51 C D:5.17 ES:4 EF:9.17 LS:4 LF:9.17 G D:5.17 ES:14.34 EF:19.51 LS:14.34 LF:19.51 E D:5.17 ES:9.17 EF:14.34 LS:9.17 LF:14.34 D D:6.33 ES:4 EF:10.33 LS:8.68 LF:15.01 B D:5.33 ES:0 EF:5.33 LS:3.84 LF:9.17 A D:4 ES:0 EF:4 LS:0 LF:4 Finish D:0 ES:19.51 EF:19.51 LS:19.51 LF:19.51

Creating a PERT Diagram STEPS 4: Compute for the critical path by adding the duration's of various paths for all activities Determine if any activities have slack by subtracting the activity’s LF & EF

Critical Path Critical Path: A-C-E-G Path A-D-F = 14.83 work days Path A-C-E-G = 19.51 work days Path B-E-G = 15.67 work days

Schedule Duration Crash Crash : an effort to reduce the overall time duration of a project by employing one or all of the following techniques Adding resources (human or otherwise) Increasing work hours (overtime or weekends) Lessening quality A trade-off between shorter task duration and higher task costs If the cost savings on a delay penalty are higher than the incremental cost of reducing the project duration, then the crashing is justified.

Activity Uncertainty Standard Deviation of an activity is estimated as one sixth of the difference between the pessimistic and optimistic time estimates Variance is determined by squaring the standard deviation The size of the variance reflects the degree of uncertainty associated with the activity’s time. The larger the variance, the greater the uncertainty. Standard Deviation = t p - t o 6

Path Uncertainty Standard Deviation of a path can also be computed to know the uncertainty of a particular path. SD of Path=  variances of activities on a path

Path Probability The probability that a given path will be completed in a specified length of time can be determined using the following formula: Z = Specified Time - Path Mean Path Standard Deviation If the value of Z is 2.50 more, treat the path probability as 100%. If the value of Z is less than 2.50, use the table of values under the standardized normal curve.

Program Evaluation and Review Technique

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Program Evaluation and Review Technique