To ensure optimal economic operation of multi-bus DC microgrids (MGs), the optimal power flow (OPF) problem can be formulated to minimize the generation cost. However, due to the weak inertia property of DC MGs, an inappropriate droop gain may lead to instability issues. To address this problem, this paper proposes an OPF with stability constraints for the trade-off design of droop gains among multiple dispatchable units. The method can simultaneously ensure the economic and stable operation of DC MG. The proposed OPF can be efficiently solved by a warm-start optimization algorithm, which ensures that the OPF algorithm can be reliably operated online. The accuracy of the proposed method is verified through a case study of a three-bus DC MG.