In: Operations Management
You are the manager of a project to improve the healthcare insurance claims auditing process. For each day that the claims auditing process takes, there is an associated cost of $1,700 so this cost is saved for each day reduction in the project completion time. Following is the information for the healthcare claims auditing process. The normal time and crash time are the times it will take to complete each activity under each of those scenarios (normal and crash). The Total Normal Cost and the Total Crash Cost are the total costs for completing that activity in that time.
Activity |
Normal Time (days) |
Crash Time (days) |
Total Normal Cost |
Total Crash Cost |
Immediate Predecessor(s) |
A |
6 |
4 |
$4,000 |
$6,000 |
-- |
B |
4 |
2 |
$4,000 |
$7,000 |
-- |
C |
6 |
3 |
$3,000 |
$6,000 |
B |
D |
6 |
5 |
$4,500 |
$5,000 |
A |
E |
3 |
3 |
$10,000 |
$10,000 |
C |
slope of an activity = crash cost - normal cost / normal time - crash time
activity | slope |
A | 1000 |
B | 1500 |
C | 1000 |
D | 500 |
E | Na |
BCE is the critical path with duration 13.
crashing schedule
(a) The cheapest activity to crash on the critical path is C which can be crashed by 1 day at a cost of 1000.
Now there are 2 critical paths BCE and AD with duration 12 each.
(b) Now, the two cheapest activites to crash on CP are D and C,
which can be crashed for one day each at a cost of 1500. Duration
is now 11.
(c) Now, the two cheapest activites to crash on CP are A and C, which can be crashed for one day each at a cost of 2000. Duration is now 10.
(d) Now, the two cheapest activites to crash on CP are A and B, which can be crashed for one day each at a cost of 2500. Duration is now 9.
No more crashing is possible now.
cost with different durations
Duration | Direct cost | Crash cost | saving | net cost |
13 | 25500 | 0 | 0 | 25500 |
12 | 25500 | 1000 | 1700 | 24800 |
11 | 25500 | 2500 | 3400 | 24600 |
10 | 25500 | 4500 | 5100 | 24900 |
9 | 25500 | 7000 | 6800 | 25700 |
least cost duration is 11.