In　this　article,　we　investigate　the　dynamic　(multi-period)　facility　location　problem　with　potentially　unserved　clients　or　outliers.　We　propose　a　3-approximation　primal-dual　algorithm　based　on　an　integer　linear　program　formulation　of　the　problem.　We　further　improve　the　approximation　ratio　to　2　by　combining　the　cost　scaling　and　greedy　improvement　techniques.