As the expert gear of the emergency rescue system, drones are frequently utilized to distribute supplies following a calamity. The cost and effectiveness of rescue efforts as well as equitable distribution should be taken into account when allocating emergency supplies to disaster-affected areas. This work explores the emergency material allocation problem for truck-drone joint transportation with dynamic energy restrictions based on taking the fairness of emergency material allocation into consideration. In order to guarantee the equitable distribution of materials, the psychological stress experienced by the victims at each catastrophe site is measured using the relative deprivation cost. An adaptive large-scale neighborhood search method serves as the foundation for the creation of a two-stage heuristic algorithm, which reduces the overall cost of the system. The integer programming model MIP is built for this purpose. The research findings can serve as a useful guide for developing a just and effective emergency drone rescue system, and the testing results demonstrate the viability and effectiveness of the two-stage heuristic algorithm.