Especially with scheduling models, solutions tend to differ widely from one run to the next. Often this is the case without a significant impact on the objective. See also: http://yetanothermathprogrammingconsultant.blogspot.com/2009/11/persistency-in-math-programming-models.html.
Currently I am involved in developing a MIP based scheduling tool for TV advertisements. It is interesting to see that the original home-brew scheduling software (I am supposed to “beat” this existing system) actually has facilities to achieve persistency (without using this term). The conclusion is: this is a problem real users observe and we better make sure this is also handled by our implementation.