The Kohn-Sham SCE formulation is a natural way for using the strictly correlated electron (SCE) functional via an optimal transport formulation, especially when the Coulomb interaction dominates over the kinetic part. In this talk I will discuss some numerical issues associated with solving Kohn-Sham SCE using primal and dual formulations, as well as modeling issues for molecular systems regardless of how the optimal transport problem is solved. In the end I will discuss some on-going work for applying the Kohn-Sham SCE formulation to model problems with effective convex relaxation strategies. (Joint work with Yuehaw Khoo, Michael Lindsey and Lexing Ying.)