When I am updating the schedule on the current date then some activity showing "Start no earlier than" constraints.
I want to know why these constraints are coming. If constraints came means my schedule is wrong or what?
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In most project scheduling software, the start date of a task is determined by either the task's driving predecessor(s) or a driving constraint date.
If you want to move a task's start date to a date that would be later than the date it would be driven to from it's predecessor(s), your options are to either put a constraint date on the task or put a lag time on the predecessor(s). It seems your scheduling tool is automatically applying a Start-No-Earlier-Than constraint for you when you edit the start date and it meets this condition.
There isn't anything wrong with having some soft constraints on your schedule, however, having too many of them is a clear sign of poorly planned schedule logic (predecessor and successor relationships between tasks), and usually a metric schedule auditors will look at when evaluating a schedule.
The Planning and Scheduling Excellence Guide (PASEG) has a good section on the best practices regarding the use of constraints.
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Here is the highly simplified version of how you use the tool:
At the time of preparing the project plan
Based on this input, the tool calculates the start date and end date for each task.
Updating the project status day-to-day
The tool will show today's line and whether your progress is ahead or behind schedule with respect to that, based on the percentage completion you entered.
It is not a good practice to change the start date (or end date) directly for status update purposes. If you do, the tool assumes that you are setting a task start date constraint. The default constraint for a start date is "Start no earlier than".
Here is the link: Set a task start or finish date (constraint) for a task
Project management tip: Let Project do what it does best — schedule your project. Set task durations yourself and create links between tasks, and then Project will calculate the task start and finish dates.