# 6-5-3 Solution to Crashing problem

1. The first step is to calculate the crash cost per unit duration. You will use the formula attached here. formula-for-calculating-the-crash-cost-per-unit-time . Do this yourself before checking your answer in the attached table shown here  crashing-example1

2.  The second step is to complete the network diagram.  The network diagram is also shown here. Keep in mind that the network diagram is based on the normal duration for each task.

3. From the network diagram, you will identify all the paths in the network and their durations and thus identify the critical path(s).

4. Using the crash cost per unit time and the potential tasks on the critical path, you identify the first task to be crashed and calculate the result extra cost and the new duration for each path.  The complete solution to the problem is shown below.

 Paths Initial Duration 1ST step and duration 2nd step & duration 3rd step & duration 4th step & duration ACEFH 48 47 46 45 44 ACEGH 45 44 43 42 41 ADEFH 45 45 44 43 43 ADEGH 42 42 42 41 41 BDEFH 47 47 46 45 44 BDEGH 44 44 43 42 41

The initial critical path is ACEFH, normal project duration is 48 weeks and total normal cost is \$2300.

• 1. 1st step: crash C by 1 week, extra cost is \$50 and the project duration is 47 weeks with 2 critical paths. New project total cost is \$2350. This also means that if we had to reduce the duration by only 1 week, this will be the best option and we will stop here.
• 2. 2nd step, we have to crash a task on each of the two critical paths. It is cheaper to crash F on both paths for a cost of \$75 than say to crash C on path ACEFH and task B on path BDEFH for total extra cost\$50+ \$45= \$95. With crashing of F, the project duration is now 46 weeks and the critical paths remain unchanged. New project total cost is \$2425. The goal of 44 weeks is not reached yet so we continue the process.
• 3. 3rd step, we can crash F by 1 more week (it can be crashed from 7 weeks to 5 weeks; see previous table). The column shows the outcome. New total cost is \$2500
• 4. Crash E by 1 week,  extra extra cost = \$85 and new project cost is \$2585 with an expected duration of 44 weeks. Thus, by spending an extra \$285 we are able to reduce the completion time by 4 weeks.

You can see a  set of short videos on the above steps by clicking on the following links.

It’s now your turn to practice how to crash projects. Here is a practice problem. Practice-Problem-on-Crashing

The solution to the problem is attached here. Crashing-problem-solution