Facility Location Problem

Nloc=20;

loc=RandomInteger[100,{Nloc,2}]

ListPlot[loc]

soln=NMinimize[Sum[Norm[{x,y}-loc[[k,;;]],2],{k,1,Nloc}]/Nloc,{x,y}]

Show[ListPlot[loc,PlotStyle->{Blue,PointSize[Medium]}],ListPlot[{{x,y}/.soln[[2]]},PlotStyle->{Red,PointSize[Large]}]]