Annex A - TIME-COST TRADEOFF
A-1 GENERAL
Time-cost tradeoff (also known as schedule crashing or schedule compression) is a process to reduce the project duration with a minimum increase in the project direct cost, by buying time along the critical path(s) where it can be obtained at the least cost. It is a procedure by which the project duration is reduced to threshold value normally assigned by the project owner. It is an important part of the time management process as project managers are often asked to meet an externally dictated shortened project schedule.
A-2 METHODS
A number of heuristics/algorithms are available in the literature for time-cost tradeoff. One of the commonly adopted/adapted time-cost tradeoff algorithms is called the Siemen’s approximation method (SAM)1) of time cost tradeoff. The central principle on which SAM and in fact other similar algorithms are based is the time-cost slope of project activities. This is shown in Fig. 8. While estimating the duration of a construction activity the scheduler provides the estimate under a most likely scenario. This translates to the normal point on the time cost curve shown in Fig. 8. The direct cost associated with this point is called normal cost (CN) and the duration estimate associated with this point is called normal time (TN).
In an effort to reduce the duration of the project activity a project manager will normally deploy more resources for the activity, for example, add more equipment, deploy additional labour, add labour work shifts, etc. All this translates to additional direct costs.
So in general it is clear that as direct cost is increased the activity duration reduces. To simplify the calculations a linear time-cost relationship is assumed as shown in the figure below. Realistically there is a limit to the deployment of additional resources for a given activity beyond which additional deployment of resources may not result in any reduction in
duration in fact activity duration may start increasing due to site congestion. This limiting point is shown as the crash point on the time-cost curve. The cost associated with this point is called crash cost (CC) and the duration associated with this point is called crash time (TC).
Figure 8 is then used to calculate the cost slope of the activity, which is the amount of money needed to reduce the duration of the activity under consideration by one day. For the cost slope calculations an estimate of the crash cost (CC), normal cost (CN), normal time (TN) and crash time (TC) are needed. These may be obtained from the historical databases or from experts. The equation used to calculate cost slope of an activity is provided below:
Cost slope = CC - CN / TN - TC
The cost slope equation given above is essential to perform the time cost tradeoff exercise on a given project network. The assumption used for the calculation is that there exists a linear relationship between time and cost of an activity. This is an
approximation. Numerous enhancements such as piecewise linear approximation, non-linear relationship, etc are available in literature.
Steps used in the SAM algorithm are broadly as listed below:
a) Perform CPM calculations for the project network under consideration. Calculate the project normal duration (PN).
b) Identify in consultation with the project stakeholders the required reduction in the project duration to establish the reduced project duration (PR), where PN > PR.
c) From the project network identify all project paths. For each identified project path calculate its length by adding normal time of all activities on the path.
d) Compare each paths expected length with PR.
Select all the paths from the original list whose expected lengths are greater than the reduced project duration PR. These are paths that require shortening.
e) Identify all activities present in at least one of the selected paths requiring shortening noting for each activity its cost slope and time reduction available.
f) Determine the effective cost slope of each identified activity where effective cost slope is defined as the cost slope of the given activity divided by the number of inadequately shortened paths which contain that activity.
g) For the path(s) with the highest time reduction required, select the activity with the lowest effective cost slope. Break ties by:
1) giving preference to the activity which lies on the greatest number of inadequately shortened paths.
2) giving preference to the activity which permits the greatest amount of shortening.
3) choose an activity at random.
h) Shorten the selected activity as much as possible, which will be equal to the minimum of the following:
1) the unallocated time remaining for the selected activity or
2) the smallest demand of those inadequately shortened paths containing the activity
i) Continue the process till all the path needing shortening are below the desired threshold, that is, PR. Once
this condition is met the shortening process can be stopped. A strategy for project duration reduction is now
available along with the increased cost.
Some scheduling software implement the time-cost tradeoff procedure using proprietary algorithms.
