After reading this article you will learn about the procedure for crashing the network.
The time-cost relationships can be visualized graphically in the form of a time verses cost curve which is for a limited portion at least, sloping downward, as depicted in the following fig.
Here it is assumed that for each activity, there is an activity duration for which the direct cost is minimum. If the activity takes more time then cost increases due to inefficient use of resources. Also, if the activity has to be completed in less time, then more funds have to be spent, which implies more costs.
For any given activity a point will reach beyond which no further reduction in time will be possible irrespective of the resources spent on this activity. The time for the activity at which minimum cost is called normal time and the minimum time for the activity is called crash time. The cost associated with these times are called normal cost and crash cost respectively.
The total direct cost of the project can be determined by adding the direct costs of each individual activities. Initially, for all activities, normal time estimates are assumed and the total project duration is computed using the computational procedure.
If the project duration has to be reduced, then time of one or more activities has to be reduced. The activities selected should be such that the total project duration is reduced at the least cost. This process can be repeated till no further reduction in the project duration can be achieved.
The reduction in the project duration can be achieved by reducing the time requirement of few selected activities from their normal time, the maximum reduction in time possible for any activity being upto its crash time. This process of reducing the total project duration by reducing activity timing is known as crashing project network.
Crashing of a network can be done in following steps:
1. Critical path:
Find the normal critical path and identify the critical activity.
2. Cost slope:
Calculate the cost slope for the different activities by using the formula.
Cost slope = Crash cost-Normal cost/Crash time-Normal time
The cost slope indicates the extra cost required to expedite an activity per unit time.
Rank the activities in the ascending order of cost slope . The activity having the minimum cost slope have to be crashed first, crash the selected activity to its minimum duration.
Crash the activities in the critical path as per the ranking i.e., activity having lower cost slope would be crashed first to the maximum extent possible. Calculate the new direct cost by cumulative adding the cost or crashing to the normal cost.
5. Parallel crashing:
As the critical path duration is reduced by the crashing in step 3, other paths also become critical, i.e., we get parallel critical path. This means that project duration can be reduced duly by simultaneous crashing or activity on the parallel critical path.
6. Total cost:
Crashing as per steps 3 and 4, one reaches a point when further crashing is either not possible or does not result in the reduction or crashing or project duration. For the different project durations total cost is found up to total cost is got by adding corresponding fixed cost to the direct cost, and the direct cost is got by adding the expediting crashing cost commutative to the normal cost.