**Just What ***Is* Total Float?

*Is*Total Float?

It may seem like an odd question to ask. After all, Total Float is the same age as the Critical Path Method (CPM), of which it is the Key Value — over fifty years now. Is it possible that we still don’t agree on just what Total Float is? That is what I am submitting with this blog.

Let’s start with the classic technical explanation, one which most every authority agrees with: *Total Float is the difference between Earliest Dates and Latest Dates*. That much, at least, we seem all to agree on. And for those less familiar with CPM fundamentals, Earliest Dates are derived through a simple arithmetic process (called a Forward Pass) in which, by aggregating activity durations through addition, the *earliest* *possible* start and finish time is calculated for each activity in a CPM schedule. Conversely, through the Backward Pass process and by using simple subtraction, the *latest possible* start and finish time for each activity is computed. And, as I said, virtually everyone agrees that Total Float is the difference between these Earliest Dates and the Latest Dates.

But that is where the harmony fades away. Once we get into the details, all hell breaks loose. Voices get louder and tempers rise. Fingers start pointing and books are snapped off the shelves … as if, by seeing a mistake in print, it suddenly becomes “right.”

**Most Total Float Formulas are Simply … ***Wrong*

*Wrong*

Here are four cited formulas for Total Float. Hint: Only one is right.

- Formula 1: Total Float = Latest Start minus Earliest Start
- Formula 2: Total Float = Latest Finish minus Earliest Finish
- Formula 3: Total Float = Latest Finish minus Earliest Start minus Duration
- Formula 4: Total Float = the lesser result of Formulas 1 and 2

The correct answer is … Formula 4. Below I will get into the details, but as a summary opinion:

- Formula 1 yields what is known as Start Total Float, but it completely ignores Finish Total Float.
- Formula 2 yields what is known as Finish Total Float, but it completely ignores Start Total Float.
- Formula 3 is misleading because it yields the
*greater*of Start Total Float and Finish Total Float. - Formula 4 is right because it yields the
*lower*of Start Total Float and Finish Total Float.

**Why Do We Want the Lower Total Float Value?**

To answer this question, let’s apply a little common sense. Imagine yourself being an orange grower in Central Florida and one of your employees mentions that he heard about a Canadian front approaching and that it might bring freezing temps. So you call home and ask your wife to take a quick listen to the Weather Channel and find out what the temperature will be over the next few days. She calls you back an hour later and reports that the temperatures will be in the low 40s. You are relieved by this news, and accordingly make no plans to distribute and operate heaters across the groves. That night, as you calmly sleep, a deep freeze descends and ruins your entire crop. What went wrong?

Because you did not specify to your wife *why* you were asking, she merely reported the expected *High* Temperature for each of the next few days. The High Temps were 43, 44, and 42. Of course, the Low Temps were 23, 28, and 26. Had you asked for the *Low* Temps specifically, you would have received a far different report from your wife, and your crops might still be good.

My point is that when it comes to Total Float, every activity has two Total Float values: Start Total Float and Finish Total Float. And, for all of the ways that we use Total Float in the management of projects, we always want to know the *lowest* Total Float?

Total Float tells us how much time we can squander before some downstream deadline is no longer achievable. Let’s use an example. Think about the delivery of structural steel for a multi-story structure. The steel will be arriving in five truckloads across two weeks. Now the first of these deliveries is most critical because until at least *one* truckload arrives, the steelworkers have nothing to work with, or to do! But once that first truckload arrives, the other truckloads merely supply what becomes a backlog of material, which is rightly stacked in a nearby staging (lay down) area.

In the schedule, the entire shipment of structural steel is captured in a single activity, titled *Deliver Structural Steel*, and it has a duration of ten work days (two weeks). Since the delivery includes transport time, the first truckload will not arrive until the third day. Hence there is a Start-to-Start relationship of three days between the *Deliver Structural Steel* activity and its successor, *Erect Structural Steel, 2 ^{nd} Floor*, which awaits so impatiently for the truck to arrive.

Even without seeing drawn logic I hope you can recognize that the first three days of *Deliver Structural Steel* is critical to downstream activities, whereas the remaining seven days of *Deliver Structural Steel* have a certain amount of positive Total Float. For the purposes of the following discussion, let us assume that the Start Total Float is zero, and the Finish Total Float is 18 days.

Now, if you are the Project Manager on the phone with the steel supplier, and you want to emphasize the urgency of their timeliness in delivering the steel, which of the following statements would you make?

*“The structural steel is critical to our schedule, and is on the critical path. Your activity has zero Total Float. We cannot afford for you to be even one day later than what we agreed to!”*Or,*“Based on when the last of it is needed on site, the Structural Steel enjoys more than three weeks of positive Total Float. So if you can get it here in the next week or so, that would be great.”*

Obviously, if we are only allowed to cite *one* of the two possible Total Float values, we would always want to use the lesser of the two. Now, take another look at those first three Formulas. The problem with the first two is that they don’t even acknowledge that there are two possible values; only the one they mention. If we adopted Formula 2, then the Total Float for *Deliver Structural Steel* would be 18 days of positive Total Float!

Likewise, there can be many situations where the completion of an activity is far more critical than the start of the activity. For instance, a Landscaping Subcontractor might be able to do a fair amount of its work as soon as spring rolls around, but the final work (right up against the building) must wait on completion of all building enclosure activities of others. Once these others are “out of the way,” the Landscaper can wrap up his final work. That “final work” will likely be far more critical (meaning, lower Total Float) than its earlier work. If we use Formula 1, however, this entire activity would be classified as having a boatload of extra Float.

The third Formula is misleading, if not also just plain wrong. It does consider both Start Total Float and Finish Total Float, but … it computes the *larger* of the two values! You see, when you subtract the Earliest Start from the Latest Finish and then further subtract the Activity Duration, you are left with the *greater* of the Start Total Float or the Finish Total Float. Of what practical value is knowing the larger of the two values?

And because I might get flak from some of my colleagues, let me offer the technical explanation. Go back to the structural steel example. Suppose that the set of *Erect Structural Steel* activities is expected to take ten weeks, or 50 workdays. Now we already said that the entire *Deliver Structural Steel* activity will take two weeks, or 10 workdays. Assuming that all involved activities perform at a steady rate, then every one of those five truckloads will provide materials for ten days of work. This means that the last truckload needs to arrive no later than Day 43.

Here are the facts and figures that you need to know.

*Deliver Structural Steel*** (Duration 10)**

- Earliest Start = Day 0; Earliest Finish = Day 10
- Latest Start = Day 0; Latest Finish = Day 40
- Start Total Float = 0
- Finish Total Float = 30

**Set of Erect Structural Steel Activities (Duration 50)**

- Earliest Start = Day 3; Earliest Finish Day = 53
- Latest Start = Day 3; Latest Finish = Day 53
- Start Total Float = 0
- Finish Total Float = 0

Now, let’s apply Formula 3.

- Latest Finish minus Earliest Start minus Duration
- Day 40 minus Day 0 minus 10 = 30

Is this really what we want to know? Does *Deliver Structural Steel* really have six weeks of extra time? Well, yeah … part of it does. But part of it does not. And don’t we want to highlight that critical portion of the delivery activity? And yet, this is the formula advanced by some of the world’s leading “authorities” on Project Management.

**Free Float Has Nothing to Do with Total Float**

Every once in a while I encounter a Project Management “expert” who insists that Free Float is a subset of Total Float, as if the two are somehow related. Let me go on record to say, emphatically, that they only happen to share some of the same derivative values.

Free Float compares Earliest Dates to Earliest Dates; they have nothing to do with Latest Dates. And because Total Float is derived by subtracting Latest Dates from Earliest Dates, all that they have in common are those Earliest Dates. Logically, if the Earliest Dates change, they will affect both Free Float *and* Total Float. But if Latest Dates change, Free Float is not at all affected.

**How Do We Stop the Flow of Misleading Information?**

What bugs me is how these “authorities” continue to spread bad information. Today, the fastest, easiest, and cheapest education is found on the Internet. Those with a need to know, rather than taking a competent course from a truly qualified instructor, instead start with a Google search. This then leads them to Wikipedia or LinkedIn comments. I can point to scores of examples, at both sources, of where the information being given is flat-out wrong!

I guess, at the end of the day, it comes down to *Buyer Be ‘Ware*. If you really want to know about the Critical Path Method, then consult an authority that knows what he or she is talking about. The problem with that advice is that, if you are asking a basic question, you are probably not qualified to know whether an authority is trustworthy or not. This is where one would hope to rely on professional institutions to “get it right.” Unfortunately, they are some of the biggest culprits.

I don’t think there is any easy answer.

That is a tough question, “How Do We Stop the Flow of Misleading Information?” Realistically speaking, I don’t think it’s possible to stop it completely, but I think you are on the right track by opening as many eyes as you can reach out to with this symposium. As well as inviting academic participants, then they can listen to what you offer and hopefully understand your logic and incorporate into their curriculum. Just as the dominant authorities spread their messages, (lectures, books, word of mouth, training, etc) CPM mechanics will have an impact as well. This was a really interesting and informative read, as well as the chapter in the book. I know I will have to reread it all to better and fully comprehend all the information that is packed in one chapter. It’s a tough battle, to be sure, but I believe that all that participate will also aid in the process.

Thank you for your concise definition of total float. As schedules are a compromise between granularity and workability logic ties don’t always tell the whole story and hide assumptions. In the bridges I am building I had the exact scenario with steel deliveries and steel erection. If I had entered every single tub girder, or I-beam and every single bearing the schedule would be too granular to do anything but sap my time updating it., As can be inferred from some of your other articles on float and in my own limited experience, a high density of logic ties can inadvertenly sequester float. This is and emergent property of granular schedules. Just as Christmas lights take up more room when you repack them then the did out of the box, working and reworking a schedule through re-sequencing often atrificially inflates the schedule.

In my case, as construction went on the out of sequence work piled up. Some of the bridges went from east to west, some east to west, and one stage actually went from the middle to the ends. Fortunately, fabrication started three years out when steel prices were down and thus the steel was mostly ready way ahead of the structures it was going to land on, this meant we only had to worry about the two week travel time for delivery. If we were looking at the start of fabrication during a period of high steel prices we might have procured it in a “just in time” method and maybe a more granular schedule would be in order to make sure that the right pieces were ready when we needed them.

Weather, differing site conditions and sub-contractor performance drove the work down avenues of least resistance that could never have been projected at bid time.

The schedule activities were granular enough to be able to calculate delay impacts to the schedule and we were able to bracket the delivery needs from; early in the project when we were predicting at the beginning of the job as “Fall 2012” — to “Late August” and finally as the trucks were staging to deliver the steel — “August 23rd.”

When we are talking about the cost of steel workers and crane rentals, it is not just the early start you are worried about, but the early finish and late finish. Scheduling isn’t an academic exercise that is performed in a vacuum. We needed to know what was the latest we could bring the cranes in so it’s idle time wouldn’t eat up all of our profit. Simply submitting the early dates and float was not enough, we had to look at all four dates of all the activities. Luckily our schedule performed well in this case and it was flexible enough to be used as a tool to find the most efficient logistics for this project.