China is one of the countries that suffer the most natural disasters in the world. The situation of emergency response and rescue is extremely tough. Establishing the emergency warehouse is one of the important ways to cope with rapid-onset disasters. In this paper, a mixed integer programming (MIP) model based on time cost under uncertainty is proposed, which help solve the emergency warehouse location and distribution problem. Comprehensive consideration of factors such as time cost, penalty cost for lack of resources, alternative origins of resources from both suppliers and emergency warehouses, different means of transportation and multiple resources types are involved in our study. We also introduce uncertain scenarios to describe the severity of the disaster. Particle swarm optimization (PSO) and variable neighborhood search (VNS) are designed to solve the MIP model of different scales of instances. Numerous examples have been tested to compare two heuristics with commercial solver (CPLEX). Both of two algorithms can obtain the exact solution same as CPLEX in small-scale instances while show great performance on larger instances with 10 candidate warehouses, 25 disasters and 50 scenarios.