The continuously low efficiencies of flood relief service in responding to flooding disasters in Taiwan highlight a need for research. This service efficiency is negatively influenced by flood relief facility locations and their operational management structure. The Fazih River floodplain has been previously identified as a high-flood-risk area using an analytic hierarchy process. The purpose of this study is to use the location set covering problem and the maximal covering location problem to determine the number of relief facilities required and the maximum covering area of each facility for the case study area of the Fazih River floodplain. The findings showed that covering distances range from 3.0 to 6.6 km and the number of facilities required for improved service efficiency is between 1 and 4.