How can I make the solver produce the same solution (i.e., "By Changing
Cells") run after run assuming no change to the underlying data?

Maybe by solver's nature this is impossible.

The model is fairly simple. At one point I thought if the initial values in
the "By Changing Cells" remained the same, the final solution (i.e., in "By
Changing Cells) would be unchanged assuming no changes to the underlying
data. This however does not seem to be true.

Thanks for your comments.

Mark