One can solve the Bateman equation with hypotheses (one group cross sections that were convoluted with the neutron spectrum, main decays, no self shielding and neutron spectrum change during evolution...). Then you can end with a simple differential equation you can calculate by hand.
You may obtain an idea of your composition under irradiation under some assumptions.
As for how to solve Bateman equation, the following document describes its procedure, with required inputs such as cross-sections. (I provided this system to IAEA)