Operations > Time-Cost

There is a relationship between a project's time to completion and its cost. For some types of costs, the relationship is in direct proportion; for other types, there is a direct trade-off. Because of these two types of costs, there is an optimal project pace for minimal cost. By understanding the time-cost relationship, one is better able to predict the impact of a schedule change on project cost.

#### Types of Costs

The costs associated with a project can be classified as direct costs or indirect costs.

• Direct costs are those directly associated with project activities, such as salaries, travel, and direct project materials and equipment. If the pace of activities is increased in order to decrease project completion time, the direct costs generally increase since more resources must be allocated to accelerate the pace.

• Indirect costs are those overhead costs that are not directly associated with specific project activities such as office space, administrative staff, and taxes. Such costs tend to be relatively steady per unit of time over the life of the project. As such, the total indirect costs decrease as the project duration decreases.

The project cost is the sum of the direct and indirect costs.

#### Compressing the Project Schedule

Compressing or crashing the project schedule refers to the acceleration of the project activities in order to complete the project sooner. The time required to complete a project is determined by the critical path, so to compress a project schedule one must focus on critical path activities.

A procedure for determining the optimal project time is to determine the normal completion time for each critical path activity and a crash time. The crash time is the shortest time in which an activity can be completed. The direct costs then are calculated for the normal and crash times of each activity. The slope of each cost versus time trade-off can be determined for each activity as follows:

Slope  =  (Crash cost - Normal cost) / (Normal time - Crash time)

The activities having the lowest cost per unit of time reduction should be shortened first. In this way, one can step through the critical path activities and create a graph of the total project cost versus the project time. The indirect, direct, and total project costs then can be calculated for different project durations. The optimal point is the duration resulting in the minimum project cost, as show in the following graph:

#### Project Cost Versus Duration Attention should be given to the critical path to make sure that it remains the critical path after the activity time is reduced. If a new critical path emerges, it must considered in subsequent time reductions.

To minimize the cost, those activities that are not on the critical path can be extended to minimize their costs without increasing the project completion time.

#### Time-Cost Model Assumptions

The time-cost model described above relies on the following assumptions:

• The normal cost for an activity is lower than the crash cost.
• There is a linear relationship between activity time and cost.
• The resources are available to shorten the activity.

The model would need to be adapted to cases in which the assumptions do not hold. For example, the schedule might need to take into account the need to level the load on a limited resource such as a specialized piece of equipment.

There are other considerations besides project cost. For example, when the project is part of the development of a new product, time-to-market may be extremely important and it may be beneficial to accelerate the project to a point where its cost is much greater than the minimum cost.

In contract work, there may be incentive payments associated with early completion or penalties associated with late completion. A time-cost model can be adapted to take such incentives and penalties into account by modeling them as indirect costs.

Because of the importance of the critical path in compressing a project schedule, a project planning technique such as the Critical Path Method or PERT should be used to identify the critical path before attempting to compress the schedule.

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