Suppose you are a project manager. You can estimate an effort in days for specific task for specific developer. After performing estimation you obtain some min and max values.

After this you delegate a task to developer. Actually you also set up deadline.
Which estimation is better to use when set up deadline: min or max?

As I see min estimation can result in stress for developer, max estimation can result in using all the time which is allocated to developer even if task can be complete faster (so called Student syndrome). Which other pros and cons of two approaches?

Small clarification: I speak about setting up deadlines for subordinates when delegating the task, NOT for reporting to my boss.