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# How to Calculate PERT & CPM Analysis

Updated April 17, 2017

The program evaluation review technique (PERT) and critical path method (CPM) are two program management techniques used to plan, schedule and manage projects. Project managers use PERT to calculate an estimate of project completion time based on optimistic, pessimistic and likely estimates, as well as a probability of completing the task on time based on these estimates. Project managers use CPM to calculate one completion date based on crashing or reducing project timelines by adding resources.

Define the critical project steps. Place the steps in logical order. Do not include concurrent steps or steps not crucial to project completion. Record completion time estimates including most optimistic (t^o), most pessimistic (t^p) and most likely (t^l). These are project estimates based on actual past measurements and negotiated with the project owner.

Calculate the expected time (t^e). Add together the t^o x 1, the t^l x 4 and the t^p x 1 and divide by 6 to get the expected time. Calculate the desired completion time (d) by adding together the optimistic completion time from each task.

Calculate the standard deviation (s^1) for each task. Project management defines the standard deviation as the (t^p -- T^o)/6. Add together the standard deviations for each task to calculate the total standard deviation(s^t).

Calculate a z-score, which is a standard score from which a probability can be calculated. Project management uses the formula: z = (d - t^e) / s^t. If d = 15, t^e = 15.5 and s^t = 1.58 then z = (15-15.5)/1.58 or (-0.32). Use a z distribution table located in the back of most statistics books to look up z. Z is an absolute value meaning you disregard the negative sign in front of the number. Find the intersection between the 0.3 part of the number on the left with the 0.02 part on the top to get a z of 0.6255. Subtract this number from one and multiply by 100 to get the probability, in this case 37.5 per cent. Using PERT you calculated a 37.5 per cent chance this project will be completed on time.

Obtain the normal time, crashed time, normal cost and crashed costs to complete each critical project step. Obtain these figures in discussion with the project owner and based on your knowledge of similar projects. For example:

Step one: crashed time = 5 weeks, normal time = 10 weeks, crashed cost = £1,950, normal costs = £650.

Step two: crashed time = 1 week, normal time = 2 weeks, crashed cost = £650, normal costs = £325.

Calculate time saved per task by subtracting crashed time from normal time. In this example, for task one the time saved is five weeks. In task two, the time saved is one week.

Calculate cost to crash the project at each project step by subtracting normal costs from crashed costs. In this example at step one the costs of crashing are £1,300 and in step two the costs of crashing are £325. Calculate cost per week of crashing the project by dividing the costs of crashing by the time saved. In step one the cost per week is £1,300/5 or £260 per week and in Step 2 the cost is £325/1 or £325 per week.

Use CPM to report the total number of days you would save based on the total additional cost incurred. In this example, you would save six days at an additional cost of £1,625.

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