Please don’t ask me to tell you what I will be doing next week. I am not quite sure what I am doing right now. However, I can tell you, to the day and hour when our three year, \$100-million project will be complete.

One of the advantages that CPM (Critical Path Method planning and scheduling) provides the project manager is the ability to calculate (and recalculate as Change so often occurs) a schedule of when tasks are to performed some time in the future, leading to a definitive expectation of a completion date. At least that is what we were taught in the software tutorial. But the real truth is somewhat more complex.

Network logic calculations involve a field of mathematics called merge bias wherever two or more paths of the logic network meet. As a result, normal rules of statistics and averaging are not applied in standard CPM analysis. This was well known (and written about) by the original developers of CPM and its cousin, PERT (Project Evaluation Review Technique, developed by U.S. Navy for its Polaris Missile program shortly after the development of CPM). The developers of CPM and PERT both understood that individual activity durations are estimates and have a known degree of error. Both understood that (subject to systemic errors in estimating) these errors tend to cancel each other out to a large degree. Both also understood the same is not true when solving CPM calculations. But these mathematicians also knew the computers of the 1950s could not solve these types of problems.

Therefore, the developers of CPM used a “fudge factor” – they suggested that the completion date of the CPM was overly optimistic and required a contingency. To quote James J. O’Brien, in his original edition of his classic text, CPM in Construction Management (1965, McGraw-Hill):

There is a definite tendency for the actual completion date to exceed the first CPM end date. It is, then, reasonable to allow for some contingency between the CPM end and the actual desired completion dates. There is no definite answer on how much contingency to allow for, because it will vary with the specific circumstances of the project. However, if you need a 12-month period for completion of the project, set your CPM goal at about 11 months, and so forth. Some people have been reluctant to set a flat contingency at the end of the schedule. Contingency can be buried in the activity estimates, but if it is, you will not be able to separate true estimates from contingency.

The developers of PERT used a “pseudo-fudge factor,” a statistical averaging approach to the tolerances for each activity (or time period between events) using the famous formula of (Optimistic + 4 x Most Likely + Pessimistic)/6. This formula approximates a normal distribution and provides a statistically adjusted solution. While their method is valid when working with a list of numbers, such as a cost estimate, it fails to account for merge bias. Having claimed the mantle of a statistical approach, many practitioners forgot or ignored that the PERT solution still requires the same contingency as CPM. Witness the many government R&D projects that overrun their schedule.

The average for a cost estimate with a symmetrical variance is the same as the original total. If each item in the estimate may be high or low by 20%, the total may range from 32 to 48, but the average total will still be 40. For scheduling, this rule does not apply because of merge bias. If each duration may be high or low by 20%, the total may range from 24 to 36, but the average is not 30 (as expected,) instead being 32 (rounded to integer days). Why? 32 is the ‘correct’ answer because if B is high and C is low, the CPM calculation goes through B; but when B is low and C is high, the calculation goes through C.  The calculation goes high 75% of the time and low only 25% of the time. If there are more than two activity paths merging, the merge bias gets larger.

With this in mind, it is understandable that the average project has only a 22% probability of on-time completion. To have a 50% chance of timely completion, a one-year project needs about a month contingency, and so forth, as noted above by Mr. O’Brien. To have a 90% probability of completion, that project needs five to six weeks of contingency.

This is not rocket science. It is more difficult than rocket science. After all, rocket science is merely calculus. (Algebra is the basis of ballistics – firing a canon with an initial velocity and calculating where it will land. Rocket science is calculus – a constant thrust adds increasing velocity to a steadily decreasing mass as fuel is burned and expelled). But, the project manager who understands the need for this level of calculation nowadays may obtain the most likely, rather than only the possible project duration, from the computer at the touch of a button.

So why does the standard CPM specification call for providing a CPM to meet the project completion date only? Does the specification require submission of a bracing shop drawing that will only provide the theoretical strength needed without a factor of safety? Why shouldn’t the CPM specification call for provision of a CPM with an 80% or 90% probability of timely completion?

Perhaps until recently, computer hardware and software could not provide that more complex calculation in an economical format. But software products released in recent years do provide this capability. Examples include Oracle Risk Analysis (previously named Primavera Pertmaster), Deltek Open Plan, and a number of add-on programs such as Risk+, Monte Carlo, and others. The primary reason a contractor should prepare a CPM schedule is better to manage the project for a timely completion. The primary reason an owner should ask for a CPM submittal is to provide further assurances of timely completion. Perhaps it is time for owners to ask for what they want and contractors to provide more accurate schedules calculated from their plans.