This paper explores an approach to softening of constraints in a class of model predictive control (MPC) algorithms that employ off-line-computed feasible sets for simplified online operations. The proposed approach relies on the use of an exact penalty function in order to ensure that the solution to the problem coincides with the actual optimal solution if the original MPC problem is feasible and that the there are minimum possible constraint violations if the original problem is infeasible. The approach is considered for a class of linear systems with multiplicative and additive disturbances, and its performance is analyzed for specific cases of non-stochastic and stochastic disturbances. The implementation of the approach with a dynamic-policy-based algorithm is also discussed.