Uncapacitated Metric Facility Location Problem (umfl)

• Let L be a set of locations. • Let F ⊂ L be a set of potential facility locations. • Let C ⊂ L be a set of clients (cities). • Let c : L × L → R ∀i, j ∈ L be a distance function. Alternatively think of the function as describing the cost of assigning city j to facility i. • Let f : F → R ∀i ∈ F be a cost function describing the cost of opening a facility at i. • Let φ : C → F ∀j ∈ C be an assignment function. I.e. φ(j) = i if city j is assigned to facility i.