In humanitarian aid, emergency relief routing optimization needs to consider equity and priority issues. Different from the general path selection optimization, this paper builds two models differentiated by considerations on the identical and diverse injured degrees, where the relative deprivation cost is proposed as one of the decision-making objectives to emphasize equity, and the in-transit tolerable suffering duration is employed as a type of time window constraint to highlight rescue priority. After proving the NP-hardness of our models, we design a meta-heuristic algorithm based on the ant colony optimization to accelerate the convergence speed, which is more efficient than the commonly-used genetic algorithm. Taking 2017 Houston Flood as a case, we find results by performing the experimental comparison and sensitivity analysis. First, our models have advantages in the fairness of human sufferings mitigation. Second, the role of the in-transit tolerable suffering time window cannot be ignored in humanitarian relief solutions. Various measures are encouraged to extend this type of time window for achieving better emergency relief. Finally, our proposed hybrid transportation strategy aiming at diverse injured degrees stably outperforms the separated strategy, both in operational cost control and psychological sufferings alleviation, especially when relief supplies are limited.