One of the most important measures needed to be done in crisis condition is to optimize the allocation and distribution of resource among individuals. Time is an effective critical factor to increase the number of people rescued by the relief activities. We present a relief vehicle routing model in affected areas which use covering tour approach in order to reduce total response time. Also it is too difficult to determine the real amount of demands for essential commodities e.g. first aids, drinking water, etc. Therefore the consider a fuzzy chance constrained programming model based on the fuzzy credibility theory. In order to validate the model several numerical examples are solved. Response time reduction plays an important role in reducing deaths and disabilities caused by this disaster. So the aim of this model is to minimize the latest arrived time of vehicles crossing points. Also as the determining of exact demands for basic commodities during disasters is very difficult and in many cases it is impossible, demand parameter in this model is considered as a fuzzy number. To provide Metaheuristic the result of the exact solution the harmony search algorithm and variable neighborhood search algorithm evaluated and compared with each other. The result shown that the harmony search algorithm is more effective than variable neighborhood algorithm. Finally, by using the earthquake data of Azerbaijan, the harmony search algorithm has been implemented and the results are evaluated and analyzed.