Can someone give me an example of total negative slack and why it is not recommended in critical path calculations.
Negative slack/float can indicate several things and while generally it is inadvisable to have it, there are some occasions where it is useful. You probably know how to produce negative float, but if not, go to a task on your current critical path and assign it a deadline date earlier than its planned finish date. This will show total negative float by the additional days you added to your task.
It’s generally not good to have total negative float because this indicates your plan as defined will not work. It means you needed to start earlier or finish earlier on one or more of the tasks that show the total negative float. It also is mis-leading. Tasks that now have zero slack are not really on the critical path. Those with the largest negative float are. For this and other reasons it is typically not good to have total negative float. If you do have it, you may have assigned a deadline date (or a must finish by date) to a task that is now planned to exceed that date. Look for these and correct them. If indeed these dates must be met, you have to find tasks on the path with the total negative float and find ways to cut their duration, or work in parallel/semi-parallel, etc. You can find these tasks by using the Task Driver feature.
All that being said, I have used total negative float recently with a Customer to show them the impact to our end date from a delay they caused. I assigned the original end date as the deadline” of that original end task. Then I placed into the schedule a task detailing how the Customer delayed the project and tied it to the former critical path in its proper place in the schedule. Now I have total negative float of a number of days (in my case 78 working days) that shows clearly to the Customer the working days impact from their delay. We received a change order for the delay and the related costs of the delay. There were other ways to show the impact, but this was a highly visible one that worked for us. Once the change order was approved, I removed the deadline date and now the critical path is those tasks with zero total float.