You can have those two in separate tables, but there has to be a way to tie a Provider to a Solicitation.
It seems like you may be describing dependent drop-down lists. Where what you select in box 1 determines what is selectable in box 2.
Such a relationship would look like this:
Solicitation >> has many >> Providers ( if that is the correct direction )
Solicitation >> has many >> Details
Providers >> has many >> Details.
In the Details table you will have Solicitation as as drop down list, and Providers as a drop down list. If my above relation is correct, you'd select a Solicitation, then the Provider list would customize its selections according to the selected Solicitation.
Do you know how to set up dependent drop-down lists?
