Question

Cost and schedule data for a small project are given below. Assume an indirect Cost of $ 500/day. Determine the minimum contract duration and project cost. ActivityPreceded by Cost (S) Duration (days) Crash Normal Crash Normal 3900 6500 7200 4900 2200 1700 1200 7200 10000 9450 4700 3600 5500 6350 4700 2050 19 7200 10 4500

Answer 1

Find the table below that we will use for our calculation.We calculated the ES, EF, LS, LF and the slack in order to determine the critical path. We have also drawn the network diagram.

There are three paths.

ABCFGI = 41

ABDI = 38

ABEHI = 40

Now if we crash A, B and I then all the other paths gets reduced as well. However, that is not the case with other activities. Among these the critical path is ABCGHI with 41 days.

We first crash the least expensive activity. The lease expensive activity is I and we can maximum crash it by 1 day. This will incur an additional cost of 200. However this will reduce the duration for all the paths. So ABCFGI still remains the critical path. Next cheapest option on the critical path is activity F and crashing it will cause an overall cost of 200 +250 = 450. The value of the paths now become

ABCFGI = 39

ABDI = 37

ABEHI = 39

Now the best option is to crash A so that all the paths will get impacted. This will cause a total cost of 750 and the duration of all the paths will be reduced by 1 day. The next best option is to crash E and F by 1 day each. It will cost total of 400 and the overall crash cost will become 1150. The value of the paths will become

ABCFGI = 37

ABDI = 36

ABEHI = 37

Along the two longest routes the only options to crash are B, C, and H. Instead of crashing C and H individually, let’s crash B. This will cost 500 and the overall cost will become 1650 for crashing. This will also reduce all the paths. This means the critical path will not change. Next we can crash B again for another 500 and that will make the total cost as 2150. The paths will become

ABCFGI = 35

ABDI = 34

ABEHI = 35

Now we need to crash C and H combined. It will cost us 975 for 1 day. The total crashing cost will become 3125. The paths will become

ABCFGI = 34

ABDI = 34

ABEHI = 34

Now even though we can crash other activities such as C and D, there is no point in doing that because we cannot reduce the duration of ABEHI. This is the critical path now.

As a result the minimum duration for the project is 34 days.

The total cost will be

Total normal cost + total crashing cost + total indirect cost

= 44550 + 3125 + 500*34

= 64675