We assume that m facility units (hospital, bank, post office, fire department, police station, bus station, etc.) are requested to be established for n cities which are on the same line. We have to choose m cities where the facility units will be established such that total distance from all cities to nearest facility units is minimum. Here, it is supposed that the person who is in the city which does not have a facility unit will prefer a city which is the nearest among all the other cities having a facility unit. In this problem, we assume that any two cities cannot have the same location. The only selection criterion is the distance between these locations. In this paper, a new mathematical model was proposed and based on this model, a new dynamic programming method was developed and its program was written in DELPHI. program is available at http://sci.ege.edu.tr/~math/projects/flpsol/. © IDOSI Publications, 2011.