Big data analytics has started to use data collected from the sensors in smartphones. This data may be used by disaster response teams for locating problems. But the regular communication infrastructure can be destroyed after disasters. Movable base stations (MBS), as studied by the company NTT, offer an easily deployable solution to construct an emergency communication network (ECN), but are not suitable for transmitting big data from sensing devices to the cloud for data processing in the cloud. To address this issue, MBSs have been equipped with processing capabilities of their own, which creates an MBS-based Fog-computing Network. We proposed a novel algorithm to minimize the overall cost of the system while maintaining 0 data overflow. This will allow the resources to be used at the most efficient level. Our genetic algorithm solution had a reduced system cost over various network sizes when compared to some conventional solutions. During the simulation, it was clear that the best conventional method for preventing data overflow was the fog-based solution, but its cost was quite high. The cloud-based solution had the lowest cost but would lead to a large amount of data overflow, which would need to be cached. The GA-based solution maintained the ideal solution throughout the variation of all bandwidth parameters: the processing rate, the data compression ratio, and the cost coefficient ratio. Because none of the conventional solutions were able to match the capabilities of the GA for the current constraints, we believe that this should be investigated further with a faster algorithm.