Before revision:  In these problems, we are often given a metric space , and asked to open a set of at most k facilities and provide a certain assignment of these facilities to a set of clients, in order to minimize the ordered weighted sum of the induced service costs from all facility-client assignments c is minimized.
After revision:  In these problems, we are often given a metric space , and asked to open a set of at most k facilities and provide a certain assignment of these facilities to a set of clients, in order to minimize the ordered weighted sum of the induced service costs from all facility-client assignments :=\{d(j,S):j\in X\} is the service cost vector of connection distances, the objective w^Tc is minimized.