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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 …