As discussed above, most projects and tasks will have a trade off relationship between the time taken to complete a task and the cost of said task. In general, this relationship will be driven by an proportional relationship: taking too long will increase the cost as wages and other costs will increase; and an inversely proportional relationship: reducing the time requirement sharply is likely to increase costs as more direct materials, overtime and other resources must be directed towards the task. As such, there generally exists an optimal time for any task, at which overall costs are minimised. This can be understood by looking at the types of costs associated with projects: both direct costs and indirect costs.
Direct costs, often referred to as variable costs, are directly associated with the activity level of a task or project. For example, they can include hourly wages, travel costs and materials. When the speed of a task is increased, direct costs generally increase also, due to the law of diminishing returns. Whilst five employees may be able to complete a task in ten days, it may take 15 people to complete the same task in five days, hence the direct cost would be 75 days wages rather than 50. In contrast, indirect costs, similar to fixed costs, are generally overhead costs. These costs often depend on the overall duration of the project. For example, if a task duration was reduced from ten days to five days, the project would only incur five days of rent and electricity costs, and would only need to pay the project manager and administrative staff’s wages for five days. As the project cost is comprised of the sum of both the direct and indirect costs, there is a trade off between these two costs.
If a project is at risk of delays, the schedule can often be compressed, or crashed, through the investment of more resources and an increase in direct costs. As the duration of a project is dependent on the length of the critical path, these resources must be focused on the critical path. As such, in order to determine the optimal project time and cost, a project manager needs to understand the minimum time in which a task can be completed and how much this will cost; the normal time in which a task will be completed with minimum cost; and how the costs will vary with the time taken.
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Once this has been done for all activities on the critical path, the activities which can be crashed for the greatest time benefit but with the lowest additional cost should be focused on. This allows a project manager to go through the critical path and find all the areas where it is cost effective to crash the project. The project manager can then determine how much it would cost to complete the project earlier than planned, and the costs associated with a variety of project durations.
When attempting this, project managers need to ensure that the critical path is still the critical path after any crashing has occurred. If another critical path emerges, then the project manager will need to consider both these paths, and crash them both to ensure that neither of them holds the project up. Eventually, there may be three and even four critical paths requiring simultaneous crashing, at which point the costs of further reductions in the project duration are likely to be severe. However, to minimise the overall cost of crashing, it is possible to extend the duration of activities which aren’t critical, thus saving some money here. Ideally, this would result in a project where all paths were roughly equal in duration, so no one path would hold up the project and there would be minimum slack time. However, when attempting this it is important to note the increasing impact of indirect costs if some paths are slowed down.
In addition to the trade off between direct and indirect costs, it is important to consider the environment that the project exists in, and other considerations outside the project cost. For example, the project may incur penalties if it overruns, or may receive an incentive for early completion. These costs and benefits should be compared with the cost required to crash the project to meet the respective deadline. In addition, if other aspects of a firm’s business will depend on the project, there may be corporate benefits from accelerating the project to boost the overall performance of the firm.