This paper proposes a novel bi-objective mixed-integer linear programming (MILP) model for allocating and scheduling disaster rescue units considering the learning effect. When a natural phenomenon (e.g., earthquake or flood) occurs, the presented decision support model is expected to help decision-makers of emergency relief centers to provide efficient planning for rescue units to minimize the total weighted completion time of rescue operations, as well as the total delay in rescue operations. The problem has some features in common with unrelated parallel machine scheduling (UPMS) problem and traveling salesman problem (TSP). To deal with the inherent uncertainty and bi-objective nature of the problem, an uncertainty-set based robust optimization technique and multi-choice goal programming (MCGP) with utility functions are applied. To demonstrate the applicability of the proposed model, a real case study in Mazandaran province in Iran is presented. The computational results confirm the high complexity of the problem and the significant impacts of the uncertainty on the solution. Moreover, the analytical results provide useful insights to decision-makers for disastrous situations.