In light of rapid developments in many geographical areas in the world, one issue of strategic importance is the determination of new facilities' locations. This can no longer be viewed in a static manner where the behavior of the weights, effecting this decision, remains constant through out the time. The facility location problem(FLP) discussed in this paper not only assumes the weights are time dependent, but also, if economically justified, the new facility can be relocated one or more times at predetermined time junctures within a finite planning horizon. Relocation times are the solution to a binary integer programming (BIP) model while optimal locations are found through employing procedures relevant to constant weights FLP. A computer program in PASCAL helps the analyst to solve the location problems and convert the input data to the appropriate coefficients of the BIP model. Using LINGO, subsequently, the optimal relocation times are found.