planners are targeting the trade-off between completion time & project cost for . The overall procedure for scheduling project crashing time with the minimum total Including all of these relationships the objective function of the proposed. Crashing is reducing project time by expending additional resources crashing alternative method approach to obtain optimum cost and time and also . The project total time-cost relationship can be determined by adding up the direct cost . A compression technique such as crashing allows the project manager to offers re-planning advice based on the functional relationship between time and cost.
Network analysis - cost/time tradeoff
In such cases the activity with the lowest incremental cost may not be the best choice. For example if there are two critical paths A-E-F and B-E-F in a network and activity A has the lowest incremental cost then crashing activity A will have no effect on the critical path B-E-F, and hence no effect on the overall project completion time.
We would still need to crash one activity on B-E-F before we could reduce the completion time for the entire project. In fact in this situation we would need to consider three options: Clearly once there is more than one critical path the situation becomes more complicated.
Indeed we stressed the word perfectly above. More technically, choosing to crash the critical activity with the lowest incremental cost is guaranteed to be an optimal approach i. However once we encounter two or more critical paths we cannot guarantee that we can still crash the project in an optimal way.
Returning for the moment to our network above the solution associated with 23 weeks has one critical path, namelyas before. Of these activities only 1, 5, 8 and 9 are capable of being crashed if we were to crash activity 1 by one week we would incur an additional cost of 70 if we were to crash activity 5 by one week we would incur an additional cost of 40 if we were to crash activity 8 by one week we would incur an additional cost of 20 if we were to crash activity 9 by one week we would incur an additional cost of 40 Clearly the best choice is to crash the activity with the lowest incremental additional cost - so in this case we would choose to crash activity 8 by one week at an additional cost of Hence we could continue as above, and eventually we would have crashed the network down to its lowest possible completion time of 16 weeks.
Package crashing Whilst you might expect that the package would crash the project in the same manner as considered above look at incremental costs in fact it uses a totally different approach. The package calculates the optimal minimum cost way to crash the project using linear programming. As discussed previously we can formulate a network problem using linear programming.
This formulation can be easily modified to deal with the problem of crashing as will be seen later below.
The advantage of using linear programming to crash a project is that we can automatically guarantee that, for any particular project completion time, we have achieved that time by crashing in a minimum cost fashion. Crashing using incremental costs may, because of the difficulty of dealing with multiple critical paths, not lead us to a minimum cost solution for each possible project completion time.
The package output giving the cost associated with crashing the project from its normal completion time of 24 weeks to 19 weeks for example is given below. It can be seen that the minimum cost way to achieve an overall project completion time of 19 weeks is by crashing activity 5 by one week, activity 8 by three weeks and activity 9 by one week. The output below shows the minimum cost way of achieving the lowest possible overall project completion time of 16 weeks.
It can be seen that this can be done for a cost of This contrasts with the cost of associated with using all activities at their crash times. The difference arises because it is not necessary to crash all activities to their maximum extent to achieve an overall project completion time of 16 in this case activity 2 does not need to be crashed. By varying the number of weeks by which we crash the project we can construct the graph shown below.
In that graph we have plotted, for each possible project completion time, the minimum cost associated with achieving that completion time. Note here that this graph contains three distinct straight line segments 16 to 18, 18 to 21, 21 to This arises because of the linear relationship that was assumed to hold between cost and completion time for each activity.
Note there that the package merely provides information, in this case the cost of the project for all possible completion times between 16 and 24 weeks. It does not tell you which completion time you should choose as you can have any completion time between 16 and 24 weeks provided you are prepared to pay for it!
What the package does is enable you, as the project manager, to make an informed choice about the completion time to have. Activity splitting For the network considered above we have seen that the minimum possible completion time associated with the maximum cost is 16 weeks.
But what if we really wanted a completion time of 15 weeks - is there any possible way of achieving that? The simple answer is NO, but with a caveat, not with the project as currently represented by the network. It may be that we can change our project network, opening up the possibility of potentially reducing the overall project completion time below 16 weeks.
A common approach to do this is activity splitting. In activity splitting we typically examine each critical activity since critical activities are the determining factor in overall project completion and see if they can be split into two or more separate activities.
For example, for the network considered before we might decide that activity 1, requiring 6 weeks can be split as below: Here we have split this activity into 4 sub-activities 1a,1b,1c,1d and their precedence relationships.
It can be seen that by so doing we have actually increased the time required to complete activity 1 to 7 weeks, from the original 6 weeks. However, it may be that this subdivision of activity 1, when considered from the cost crashing point of view, gives us more flexibility. For example before subdivision we could only crash activity 1 down from 6 weeks to 4 weeks. If we could now crash activity 1b by 2 weeks and activity 1c by 3 weeks then we could crash activity 1 down from 7 weeks to 3 weeks - hence potentially reducing the overall project duration below the 16 week barrier we previously encountered.
Obviously the practicality of subdividing, and then crashing, critical activities depends upon the context but the above example does illustrate that sometimes close examination of critical activities with a view to subdivision can pay benefits.
Exploring the package Because cost crashing can be modelled and solved via linear programming we have a number of alternative options available, as the package illustrates. For example we might be interested in finding the minimum time in which we can complete the project subject to a constraint limitation upon the total cost. This is illustrated below using the package for a total cost of It can be seen above that the minimum completion time subject to a cost constraint of is The package also allows us to balance rewards in meeting a target desired project completion time as against penalties for missing this completion time.
The example below illustrates this where the desired project completion time is 20 weeks, each week we are late complete after week 20 costs us 50 and each week we are early complete before week 20 earns us a reward of The linear relationships between crash cost and crash time and between normal cost and normal time are illustrated in Figure The objective of project crashing is to reduce project duration while minimizing the cost of crashing.
Since the project completion time can be shortened only by crashing activities on the critical path, it may turn out that not all activities have to be crashed. However, as activities are crashed, the critical path may change, requiring crashing of previously noncritical activities to reduce the project completion time even further.
Suppose the home builder needed the house in 30 weeks and wanted to know how much extra cost would be incurred to complete the house by this time. The normal times and costs, the crash times and costs, the total allowable crash times, and the crash cost per week for each activity in the network in Figure We start by looking at the critical path and seeing which activity has the minimum crash cost per week. Activity will be reduced as much as possible.
The table shows that the maximum allowable reduction for activity is 5 weeks, but we can reduce activity only to the point where another path becomes critical. When two paths simultaneously become critical, activities on both must be reduced by the same amount. If we reduce the activity time beyond the point where another path becomes critical, we may be incurring an unnecessary cost. This last stipulation means that we must keep up with all the network paths as we reduce individual activities, a condition that makes manual crashing very cumbersome.
For that reason we will rely on the computer for project crashing; however, for the moment we pursue this example in order to demonstrate the logic of project crashing. It turns out that activity can be crashed by the total amount of 5 weeks without another path becoming critical, since activity is included in all four paths in the network. The revised network is shown in the following figure. Since we have not reached our crashing goal of 30 weeks, we must continue and the process is repeated.
Activity can be crashed a total of 3 weeks, but since the contractor desires to crash the network only to 30 weeks, we need to crash activity by only 1 week.Crashing in PERT and CPM -- Crashing of Project Part 1 in hindi with solution by JOLLY Coaching
Crashing activity by 1 week does not result in any other path becoming critical, so we can safely make this reduction. Crashing activity to 7 weeks i. Suppose we wanted to continue to crash this network, reducing the project duration down to the minimum time possible; that is, crashing the network the maximum amount possible.
We can determine how much the network can be crashed by crashing each activity the maximum amount possible and then determining the critical path of this completely crashed network.
Chapter 17, Head 5
For example, activity is 7 weeks, activity is 5 weeks, is 3 weeks, and so on. The critical path of this totally crashed network is with a project duration of 24 weeks. This is the least amount of time the project can be completed in. It is basically a trial-and-error approach useful for demonstrating the logic of crashing. It quickly becomes unmanageable for larger networks.
This approach would have become difficult if we had pursued even the house building example to a crash time greater than 30 weeks, with more than one path becoming critical.