Before revision:  The goal is to find a transportation map, a non-negative assignment \tau : P \times P \to R_{ \geq \ge 0} to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., r \in P \tau(q, r) - p \in P \tau(p, q) = \mu(q) for all points q \in P.
After revision:  The goal is to find a transportation map, a non-negative assignment \tau : P \times P \to R_{ \ge 0} to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., r \in P \tau(q, r) - p \in P \tau(p, q) = \mu(q) for all points q \in P.