## A Framework for Estimating Task Durations

In this post we shall construct a framework to host the duration estimate and it to the painting task discussed in the previous post.  However here we will take a more general approach, identifying the building blocks that will provide the platform for all estimates.  The chief characteristic of our framework is that it explicitly recognises and identifies the major factors that will influence the duration.  These are:
a)      The size of the task.
b)      The availability and productivity of resources, both human and equipment or materials.
c)       Interruptions and delays from both within the task and without.
Let’s examine these in the context of the paint job, but this time slow down the calculations a little, making some refining modifications as we go.
The task size was given as 450 square meters to paint (3 coats for a 150 square meter space – assuming that each coat requires the same effort.   There we had
Let’s assume that this calculation was made on the basis of using a short-handle brush for the entire job and suppose further that longer-handle rollers can increase productivity by 10%.  We can incorporate this into our model by introducing a materials resource factor (MRF) which here would be 1.1 giving us
where we have rounded the result up to the nearest whole number.
Let us further suppose there is now a full time and a half-time painter are available up to do the work, giving us a crew size of 1.5 full time equivalents (FTEs).   To convert effort to duration we needed to consider the number of painters available per unit of duration, which we will call ‘attendance rate’.   The relationship between duration and effort is given by the general expression;
Where was this step in our initial presentation of the problem?  In that case there was only one painter and then, as is clear from the above equation, effort and duration are numerically equal although they have different units of dimension (work-hours vs hours).  This part of the duration may be thought to represent ‘effort driven’ effects.  Now we have
which has been rounded up as always.
It is important to remember that by adding to the team size (attendance), we could have some (possibly negative) effect on the productivity. This is the ‘law of diminishing returns’ effect.  On the one hand, perhaps there is some synergy between the two individuals which would raise this value and therefore reduce the effort while on the other hand they could provide obstructions to each other, thereby lowering the value and increasing the effort required.  Also, there could be a difference in their relative skills, requiring us to use an average value to reflect this.  In our example we will use the original productivity.
Remember that we added half a day (say 4 hours) for various small but important sub-tasks, which we will call ‘time-driven’ effects since they are expressed in the form of additional duration.  This gives us a new value of 28 hours and with a half-day allowed for contingencies giving us a final result of 32 hours.  At seven hours per day, this is approximately 5 days.   In general then we have
Formally by combining the general formulae above we obtain
From now on, we shall combine all of the time effects, including contingency, call them ‘External Factors’ and simply write
This provides not just a formula for calculation but a framework to guide our thinking.  All duration estimates can benefit by this kind of systematic thinking.
As we hinted in the previous post, the major challenge is bound up in defining the size of the task.  We are almost ready to tackle this hurdle in the posts that follow.