The study seeks to find the optimal sites to locate a refuse dump at Ejisu, small town and the capital of Ejisu-Juaben Municipal, a district in the Ashanti Region of Ghana, using the Maxisum location model. We seek to locate facilities so that the average distance covered by the inhabitants of Ejisu will be minimized. Various location models and methods were studied and we proposed the appropriate model for the location problem. Greedy Add heuristic was used to estimate the demand-weighted distance. Data on distances between various suburbs and population were collected and the Floyd’s algorithm was used to find the shortest distance matrix between suburbs. The results show that the first facility has to be located at Krapa No. 2 and the second facility, at Serwaa Akura. Overall solution is 23465km (Total demand weighted distance) and in this case the average maximum of distance (4.13km) is covered by the inhabitants. The researcher recommended that corporate bodies including Zoomlion Ghana, Ejisu Municipal Assembly and individuals, who want to develop a refuse dump at Ejisu Township must be sited at the two stated towns accordingly.